HMT Lab Report ndergraduate Course (7th Semester) U ndergraduate
ASSIGNMENT NAME:- MUHAMMAD JUNAID TABASSUM DEGREE :- MECHANICAL ENGINEERING SUBMITTED To:- SIR UMAR SAB Reg No # 2014-ME-537
Table of Contents HMT Lab Report ............................................................................................................................................ ............................................................................................................................................ 0 Experiment No. 1 ......................................................................................................................................... 1 ......................................................................................................................................... 3 Theory: ......................................................................................................................................................... Theory: ......................................................................................................................................................... 3 Fourier’s Law: ......................................................................................................................................
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Assumptions of Fourier equation:........................................................... equation: ........................................................... ................................. 4 Features of Fourier equation: ..................................................................................................... equation: ..................................................................................................... 4 Experimental Setup:........................................................ Setup: ........................................................ ................................................................. 4 Observations and Calculations:....................................................................................................... Calculations:....................................................................................................... 5 Graphs: ......................................................................................................................................................... Graphs: ......................................................................................................................................................... 5 Comments:........................................................... Comments:........................................................... ................................................................. ...................... 7 Experiment No. 02 ...................................................................................................................................... 02 ...................................................................................................................................... 8 Theory: ......................................................................................................................................................... Theory: ......................................................................................................................................................... 8 Theoretical Value of U (U TH): ....................................................................................................... ): ....................................................................................................... 9 Observations and Calculation: Calculation: ...................................................................................................... . 10 10 Calculations: ........................................................................................ Calculations: ........................................................................................ .................................................... 10 Comments:........................................................... Comments:........................................................... ................................................................. .................... 11 Experiment No. 03 .................................... 03 .................................... ................................................................. ............................... 12 Theory: .................................................................................................. Theory: .................................................................................................. ..................................................... 12 12 Fourier law of heat conduction: ........................................................................... conduction: ........................................................................... .................... 12 12 Heat flow in thermal conductor: conductor: ..................................................................................... ......... 13 Observations:..................................................... Observations:..................................................... ................................................................. .................... 14 Comments:........................................................... Comments:........................................................... ................................................................. .................... 15 Experiment No. 04 .................................... 04 .................................... ................................................................. ............................... 16 Apparatus ............................................................ Apparatus ............................................................ ................................................................. .................... 16 Theory: .................................................................................................. Theory: .................................................................................................. ..................................................... 16 16 After taking the readings draw the graph of temp vs positions to determine the temperature temperature profile. ..................................................................................... ....................... .............................................................. .......................................... 17 17 Observations and Calculations:........................................................... Calculations:........................................................... .......................................... 17 17 Graphs: ............................................................................. Graphs: ............................................................................. ................................................................. ......... 17 Comments:........................................................... Comments:........................................................... ................................................................. .................... 17 Experiment No. 05 .................................... 05 .................................... ................................................................. ............................... 18 Apparatus ............................................................ Apparatus ............................................................ ................................................................. .................... 18 Theory ................................................................... Theory ................................................................... ................................................................. .................... 18 Graph: .................................................................... Graph: .................................................................... ................................................................. .................... 20 1
Table of Contents HMT Lab Report ............................................................................................................................................ ............................................................................................................................................ 0 Experiment No. 1 ......................................................................................................................................... 1 ......................................................................................................................................... 3 Theory: ......................................................................................................................................................... Theory: ......................................................................................................................................................... 3 Fourier’s Law: ......................................................................................................................................
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Assumptions of Fourier equation:........................................................... equation: ........................................................... ................................. 4 Features of Fourier equation: ..................................................................................................... equation: ..................................................................................................... 4 Experimental Setup:........................................................ Setup: ........................................................ ................................................................. 4 Observations and Calculations:....................................................................................................... Calculations:....................................................................................................... 5 Graphs: ......................................................................................................................................................... Graphs: ......................................................................................................................................................... 5 Comments:........................................................... Comments:........................................................... ................................................................. ...................... 7 Experiment No. 02 ...................................................................................................................................... 02 ...................................................................................................................................... 8 Theory: ......................................................................................................................................................... Theory: ......................................................................................................................................................... 8 Theoretical Value of U (U TH): ....................................................................................................... ): ....................................................................................................... 9 Observations and Calculation: Calculation: ...................................................................................................... . 10 10 Calculations: ........................................................................................ Calculations: ........................................................................................ .................................................... 10 Comments:........................................................... Comments:........................................................... ................................................................. .................... 11 Experiment No. 03 .................................... 03 .................................... ................................................................. ............................... 12 Theory: .................................................................................................. Theory: .................................................................................................. ..................................................... 12 12 Fourier law of heat conduction: ........................................................................... conduction: ........................................................................... .................... 12 12 Heat flow in thermal conductor: conductor: ..................................................................................... ......... 13 Observations:..................................................... Observations:..................................................... ................................................................. .................... 14 Comments:........................................................... Comments:........................................................... ................................................................. .................... 15 Experiment No. 04 .................................... 04 .................................... ................................................................. ............................... 16 Apparatus ............................................................ Apparatus ............................................................ ................................................................. .................... 16 Theory: .................................................................................................. Theory: .................................................................................................. ..................................................... 16 16 After taking the readings draw the graph of temp vs positions to determine the temperature temperature profile. ..................................................................................... ....................... .............................................................. .......................................... 17 17 Observations and Calculations:........................................................... Calculations:........................................................... .......................................... 17 17 Graphs: ............................................................................. Graphs: ............................................................................. ................................................................. ......... 17 Comments:........................................................... Comments:........................................................... ................................................................. .................... 17 Experiment No. 05 .................................... 05 .................................... ................................................................. ............................... 18 Apparatus ............................................................ Apparatus ............................................................ ................................................................. .................... 18 Theory ................................................................... Theory ................................................................... ................................................................. .................... 18 Graph: .................................................................... Graph: .................................................................... ................................................................. .................... 20 1
Comments:........................................................... Comments:........................................................... ................................................................. .................... 20 Experiment No. 06 .................................... 06 .................................... ................................................................. ............................... 21 Apparatus: ............................................................................................ Apparatus: ............................................................................................ .................................................... 21 Theory: .................................................................................................. Theory: .................................................................................................. ..................................................... 21 21 Procedure: ................................................................................................................. Procedure: ................................................................................................................. ............................... 22 22 Observations and Calculations:........................................................... Calculations:........................................................... .......................................... 22 22 Comments:........................................................... Comments:........................................................... ................................................................. .................... 22 Experiment No. 07 .................................... 07 .................................... ................................................................. ............................... 23 Apparatus ............................................................ Apparatus ............................................................ ................................................................. .................... 23 Theory ................................................................... Theory ................................................................... ................................................................. .................... 24 Experiment No. 08 .................................... 08 .................................... ................................................................. ............................... 26 Theory: .................................................................................................. Theory: .................................................................................................. ..................................................... 26 26 Procedure:..................................................... Procedure:..................................................... ................................................................. ............................... 30 32 = −ℎℎℎ= ........................................................ ............................................................... 32 Observations and Calculations: .......................................... Calculations: .......................................... .............................................................. . 33 Procedure :............................................................... :............................................................... ................................................................. .................... 35 Theory:............................................................... Theory: ............................................................... .............................................................. ............................... 36 36 36 = −ℎℎℎ= ........................................................ ............................................................... 36 Comments: .................................................... Comments: .................................................... ................................................................. ............................... 39
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Experiment No. 1 “Investigation of the Fourier’s law for linear conduction in one dimension along a simple bar”
Theory: Fourier’s Law:
The law of heat conduction is also known as Fourier’s law. Fourier’s law states that: “The time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area.” Mathematically it is written as
= Where,
Q is the heat flow rate by conduction (W)
k is the thermal conductivity of o f body material (W·m−1·K−1)
A is the cross-sectional area normal to direction of heat flow (m 2)
dT/dx is the temperature gradient (K·m −1).
Negative sign in Fourier’s equation indicates that the heat flow is in the direction of negative gradient temperature temperature and that serves to make heat flow positive. Thermal conductivity ‘k’ is one of the transport properties. Thermal conductivity ‘k’ provides an indication of the rate at which heat energy is transferred through a medium by conduction process. The above equation can be rearranged in the following way:
= As both k and A are constants therefore
= This is another interpretation of Fourier’s law which we use in this experiment.
Fourier's Law of Heat Conduction: Fourier's Law of Heat Conduction is most simply demonstrated with the linear conduction module. This comprises a heat input section fabricated from brass fitted with an electrical heater. Three temperature sensors are installed at 10mm intervals along the working section, which has a diameter of 25mm. A separate heat sink section also of brass is cooled at one end by running water while its working section is also fitted with thermistor temperature sensors at 10mm intervals.
3
The heat input section and the heat sink section may be clamped directly together to form a continuous brass bar with temperature sensor at 10mm intervals, alternatively any one of three intermediate sections can be fitted between these two.
Assumptions of Fourier equation: The Fourier’s law is valid under the following assu mptions:
Steady state heat conduction.
One directional heat flow.
Bounding surfaces are isothermal in character that is constant and uniform temperatures are maintained at the two faces.
Isotropic and homogeneous material and thermal conductivity ‘k’ is constant.
Constant temperature gradient and linear temperature profile.
No internal heat generation.
Features of Fourier equation:
Fourier equation is valid for all matter solid, liquid or gas. The vector expression indicating that heat flow rate is normal to an isotherm and is in the direction of decreasing temperature.
It cannot be derived from first principle.
It helps to define the transport property ‘k’.
Linear Conduction Heat Transfer: It is often necessary to evaluate the heat flow through a solid when the flow is not steady e.g. through the wall of a furnace that is being heated or cooled. To calculate the heat flow under these conditions it is necessary to find the temperature distribution through the solid and how the distribution varies with. Using the equipment set-up already described, it is a simple matter to monitor the temperature profile variation during either a heating or cooling cycle thus facilitating the study of unsteady state conduction. From continuity the heat flow rate (Q) is the same for each section of the conductor. Also the thermal conductivity (k) is constant (assuming no change with average temperature of the material).
Experimental Setup: The bar on which experiment is to be performed consists of three parts. The two ends are made of brass and the conducting material in between them is made of steel. One end is exposed to electric heating source and the other end is cooled with water at room temperature. Each part is of 30 mm length which makes the total length of the bar to be 90 mm. Temperature at various points on the bar can be measured with the help of temperature sensors that are placed at every 10mm distance on the bar. The apparatus used is shown in figure below:
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Figure 1
Figure 2
PROCEDURE:
Start the electric supply. Adjust the temperature in the temperature indicator by means of rotating the knob for compensation of temperature equal to room temperature. (Normally this is per adjusted) Give input to the heater by slowly rotating the dimmerstat . Go on checking the temperature at some specified time interval say 5 minute and continue this till a satisfactory steady state condition is reached. Note the temperature reading.
Observations and Calculations: Sr. no
1 2 3
He at
̇
10 15 20
Temp eratu re T1 54 68.6 80
Temp eratur e T2 53.3 68.1 76
Temp eratur e T3 51 64.5 70
Temp eratur e T4 49.7 62.3 68
Temp eratur e T5 47 55.3 65
Temp eratur e T6 44 46.2 42
Temp eratur e T7 34.7 37.2 40
Graphs: Temperature Distribution 90
e d 80 o n 70 h c 60 a e 50 t a 40 e r 30 u t a r 20 e p 10 m e 0 T
0
5
10
15
20
25
30
Distance between 5 two nodes
35
40
45
Temp eratur e T8 34 35.4 35
Tem perat ure T9 33.6 34.6 34
Calculations: (i)
44.931.9 ( ) = 9010 ( )=0.1625 As,
̇ == Thus,
3.1 =19.07 = 0.1625 − (ii)
48.232.1 ( ) = 9010 ( )=0.2012 As,
̇ == Thus,
7 =34.78 = 0.2012 −
6
Comments: Temperature profile obtained is a linear profile which is in accordance with the mathematical equation. Slope of the profile at two different temperature should be constant but a slight variation is seen in the experiment. This variation is due to the fact that when the heat supplied is changed to the bar, time is required for complete establishment of thermal equilibrium. If readings are taken before this state reaches, some variation from the theoretical values is seen.
There is sudden temperature drop in the graph this is due to the contact resistance between the two surfaces. There is gas entrapped between the junction due to which resistance increases and temperature drop on junction. Ensure that the temperature measurement points are aligned along the longitudinal axis of the unit. It’s necessary to give some time to the apparatus to develop steady state otherwise temperature values varies improperly and we get some abnormal behavior of the temperature profile. Be sure to amply coat both surfaces of the sample where contact will be made to reduce thermal contact resistance Be careful not to touch any surfaces (metallic or plastic) on the heating end as they might cause a burn. If not indicated on the apparatus, all temperature sensors are number from left to right.
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Experiment No. 02 “To study the conduction of heat along a composite bar and calculate overall heat transfer co-efficient. ”
Apparatus
Heat conduction apparatus
Stainless steel sample with thermistors
Theory:
Figure 2
Let's assume that we have a combination of different materials put together to form a composite structure as shown in figure. Let's also assume that the cross-sectional area normal to the flow of heat transfer is constant and that heat flows in a one-dimensional direction. Taking only one of the slabs for now and we know that the heat transfer is governed by Fourier's Law, given by
. = = We already have an idea of the concept of thermal resistance for conduction. Resistance in general is defined as the ratio of driving potential over the transfer rate. As transfer rate goes to zero, the resistance becomes infinite and, similarly, as the driving potential goes to zero, resistance fails to exist. By using Fourier's Law and the definition of resistance, we can derive the thermal resistance for co nduction mode of heat transfer
. = = where R is the sum of resistances for each portion.
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If we sum up all the individual heat transfers, the intermediate temperatures cancel and we get:
= ∑ = + + = ……… + + =∆= 1⁄∆ ……… From (i) and (ii)
1⁄ = + + and the overall heat transfer coefficient is:
= 1 + + Theoretical Value of U (UTH): Theoretical value of U can be found by using theoretical values of K b and Ks which are 43 and 110 respectively [1], Experimental value of U (U EXP): First of all, the experimental values of Kb and Ks are found and then plugged into equation to find the experimental value of U by using following formulae:
= . ⁄ = . ⁄
9
Observations and Calculation: Diameter of the bar= 25 mm Area of cross section of tube = 0.00049m2 L1= L2 =L3=0.03m Sr. no
1 2 3
He at
Temp eratu re T1 44.6 51 65
̇
5 20 25
Temp eratur e T2 44.5 50 62.8
Temp eratur e T3 43.2 48.2 61.7
Temp eratur e T4 33.1 40 44.7
Temp eratur e T5 32.7 35 39.2
Temp eratur e T6 30.7 33 35
Temp eratur e T7 30.1 30 30
Temp eratur e T8 29 29.8 20.4
Graph: Temperature Distribution 50 e 45 d o 40 n h 35 c a e 30 t a 25 e r u t 20 a r 15 e p m10 e t 5
0 0
5
10
15
20
25
30
Distance between two nodes
Calculations:
. = 1 + + 1 . = 0.03 0.03 0.03 + + 110 48 110 . =804.42 = . ⁄ 10
35
40
45
Tem perat ure T9 29.9 29.7 30.1
= 25.98.280.5 0.03⁄0.00049 =86.47 = . ⁄ = 25.80.531.5 0.03⁄0.00049 =31.26 . = 1 + + 1 . = 0.03 0.03 0.03 + + 86.47 31.26 86.47 . =604.491 Comments: There is a quite large difference between theoretical and experimental value of U. One of the reasons is that the theoretical values of conduction coefficients that we are using are valid only under certain standard conditions as k is a weak function of temperature.
During assembling the sample between the heater and the cooler take care to match the shallow shoulders in the housings. There is sudden temperature drop in the graph this is due to the contact resistance between the two surfaces. There is gas entrapped between the junction due to which resistance increases and temperature drop on junction. Ensure that the temperature measurement points are aligned along the longitudinal axis of the unit. It’s necessary to give some time to the apparatus to develop steady state otherwise temperature values varies improperly and we get some abnormal behavior of the temperature profile. If not indicated on the apparatus, all temperature sensors are number from left to right. Be careful not to touch any surfaces (metallic or plastic) on the heating end as they might cause a burn. The surfaces of the composite bars must match while assembly in the housing, otherwise the heat transfer co-efficient might vary from expected value.
11
Experiment No. 03 “To investigate the effect of change in the cross-sectional area on the temperature profile along a thermal conductor. ”
Apparatus: Heat conduction apparatus, Brass rods of different dia are used.
25mm
Brass
Brass
(Heater)
Brass (Cooler)
Theory: Fourier’s Law states that the rate of heat transfer is proportional to the cross sectional area normal to the direction of heat flow. Since the outer surface is insulated, the heat flow rate qx is the same for each section of the bar and since it is the same material, the thermal conductivity k is assumed to be constant. Where the subscripts h, s, and c denote the hot, sample, and cold segments of the bar, respectively. In other words, the temperature gradient is inversely proportional to the cross-sectional area. In this experiment, the hot and cold segments will have the same cross-sectional area, which will differ from that of the sample inserted in between the two segments. Consider a bar of a certain length comprising of a hot region and a cold region made up of brass. A steel cylinder is attached in between these regions having a different cross-section then the whole bar.
Fourier law of heat conduction: “Heat transfer per unit area is proportional to the normal temperature gradient.”
∝ = Where,
= ℎ = ℎ = ℎ = . Negative sign is an indication that second law of thermodynamics is satisfied. Area is perpendicular to the surface of heat transfer.
12
Heat flow in thermal conductor: Let's assume that we have a combination of hot region, sample and cold region. These are put together to form a composite structure as shown in figure 1. The sample is made
Figure 3
up of brass material and the material is same throughout the composite structure. Both sample bar and (hot and cold) regions are made up of brass material, therefore, they will have same thermal conductivity due to the same material. Heat flow will also be the same in each section of the conductor, so we can mathematically write: [2]
= = From Fourier law of heat conduction,
) = ( Where, the temperature gradients and the areas will be different for the sample bar and the hot region, so
= On re-arrangement of the equation
= =
……… ………
Where,
= = ℎ On comparing equation (i) and (ii), we get:
=
……… 13
Observations:
= = 25 = = 13
Sr no
He at
̇
1 2
10 15
Temp eratu re T1 72.7 38.8
Temp eratur e T2 72.5 36.2
Temp eratur e T3 68.9 36
Temp eratur e T4 -
Temp eratur e T5 -
Temp eratur e T6 -
Temp eratur e T7 30.7 34.2
Temp eratur e T8 30 29.8
Graph: Temperature Distribution 90 e 80 d o 70 n h c 60 a e t 50 a e r 40 u t a r 30 e p 20 m e T 10
0 0
5
10
15
20
25
30
Distance between two nodes
Calculations: (i)
Theoretical:
( ) =3.69 . (ii)
Experimental:
= ( ) = 32.467.6 7030 = 0.88 .− And,
14
35
40
45
Tem perat ure T9 29.5 29
= ( ) = 67.676.8 3010 = 0.46 .− Hence,
( ) = 0.88 . 0.46 ( ) =1.91 . Comments: It is seen from the mathematical derivation that temperature gradient across a bar is inversely proportional to its cross-section area and this fact is proved by experimental results as has come out to be greater than .
Our experimental and theoretical is not alike there may be some inaccuracies in performing experiments ,steady state conditions may not be established or reading may be incorrect. In our experiment one sensor is not working so we take estimated value of that temperature. From the graph take the correct temperature gradient (slope). When the specimen is placed between two ends (heated and cold) perfect conduction may not be present at the ends due to surface finish and roughness of both the specimen ends and the holder ends. This experiment shows that the temperature profile is steeper in small cross sectional area than in large cross sectional area. If not indicated on the apparatus, all temperature sensors are number from left to right. Be careful not to touch any surfaces (metallic or plastic) on the heating end as they might cause a burn.
15
Experiment No. 04 “To investigate the temperature profile and determination of rate of heat transfer resulting from radial disc (steady state 1 dimensional)”
Apparatus
A cylindrical bar with inner radius = 4mm and outer radius = 54 mm is used in this experiment. Sensors are placed at every 10mm radius to measure the temperature.
Theory: Consider transfer of heat only along the radial direction in a cylindrical bar. The heat transfer rate is given by:
= Here
A=2πrL The above equation can be written as:
2πrL ∫ = ∫ 2πL ∫ = 1 ∫ = 2πL ln So, the heat transfer depends on the factors that are bold in the above equation and the temperature profile can be observed by plotting a curve between the bold factor in numerator and the one in denominator. [3]
Procedure:
Switch on the apparatus Start from the cooling side that is open the coolant valve to avoid the overheating of the equipment. Allow the system to reach stability and take readings corresponding to the specified locations by adjusting the Nob to that position. Record the temperatures and also note the power of the heat source which is actually the heat transfer rate.
16
After taking the readings draw the graph of temp vs positions to determine the temperature profile.
Observations and Calculations: Sr no
1 2
He at
̇
10 15
Temp eratu re T1 35.8 38.8
Temp eratur e T2 34.8 36.2
Temp eratur e T3 33.2 34.5
Temp eratur e T7 31.9 32.1
Temp eratur e T8 31.2 29.8
Temp eratur e T9 30.6 29.8
Graphs: Temperature Distribution 37 e d 36 o n h 35 c a e t 34 a e r 33 u t a r e 32 p m e 31 T
30 0
5
10
15
20
25
30
35
40
45
Distance between two nodes
Comments: Temperature profile obtained in the graph shows an overall logarithmic trend which is in accordance with the theoretical formula for this case. A slight abnormality is observed in the graph which can be due to a faulty sensor.
This approach can be used to determine the critical thickness. The thermostat was out of order so technically we have values of temperature to plot graph. There may have variation in specimen i-e it may have not been a perfect cylinder. Although the temperature for higher q should be higher but lower values of T for high q shows enough time was not given to sample to achieve steady state. The experiment shows that the heat transfer in the radial direction decreases exponentially as the distance from the centre increases. The results are quite obvious from the graphical figure. The heat transfer is governed by the Fourier’s law and is dependent on the conductivity of the material and the temperature gradient with respect to the radius.
17
Experiment No. 05 ‘To measure the temperature distribution along a linear homogeneous bar for the steady state conduction ’’
Apparatus Heat transfer unit, linear bar
Theory Thermal conduction is the mode of heat transfer, which occurs in a material by virtue of a temperature gradient. A solid is chosen for the demonstration of pure conduction since both liquids and gases exhibit excessive convective heat transfer. In a practical situation, heat conduction occurs in three dimensions, a complexity which often requires extensive computation to analyse. In the laboratory, a single dimensional approach is required to demonstrate the basic law that relates rate of heat flow to temperature gradient and area. The apparatus comprises two heat-conducting specimens, a sectioned bar for the examination of linear conduction and a disc for radial conduction. A console provides electrical power to heaters in the specimens and digital readout of the temperature at selected points along the heat-conducting paths. A stream of cold water provides a heat sink at the end of the conducting path in each specimen.
EQUIPMENT: The equipment comprises two heat-conducting specimens, a multi-section bar for the examination of linear conduction and a metal disc for radial conduction. A control panel provides electrical and power digital for display heaters in the specimens as well as the selector switch for data acquisition system. A small flow of cooling water provides a heat sink at the end of the conducting path in each specimen.
Control Panel
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Heater Power Indicator
Heater Power Regulator
Heater Power
Temperature Indicator
Temperature Selector
Main Power Switch
Temperature Sensors
Radial Module
Linear Module
Procedure: 1. Make sure that the main switch is initially off. Then Insert a brass conductor (25mm diameter) section intermediate section into the linear module and clamp together 2. Turn on the water supply and ensure that water is flowing from the free end of the water pipe to drain. This should be checked at intervals 3. Turn the heater power control knob control panel to the fully anticlockwise position and connect the sensors leads 4. Switch on the power supply and main switch, the digital readouts will be illuminated 5. Turn the heater power and allow sufficient time for a steady state condition to be achieved before recording the temperature at all nine sensor points and the input power reading on the wattmeter (Q). After each change, sufficient time must be allowed to achieve steady state conditions.
Observation and Calculation: Sr. no
1 2 3
He at
̇
10 15 20
Temp eratu re T1 54 68.6 80
Temp eratur e T2 53.3 68.1 76
Temp eratur e T3 51 64.5 70
Temp eratur e T4 49.7 62.3 68
19
Temp eratur e T5 47 55.3 65
Temp eratur e T6 44 46.2 42
Temp eratur e T7 34.7 37.2 40
Temp eratur e T8 34 35.4 35
Tem perat ure T9 33.6 34.6 34
Graph: Temperature Distribution 90 e 80 d o n 70 h c 60 a e t 50 a e r 40 u t a r 30 e p 20 m e T 10
0 0
5
10
15
20
25
30
35
40
45
Distance between two nodes
Comments: The thermal conductivity value obtained from experiment t is very low which shows that paper is insulating material
After turning on the apparatus wait for some time so that it becomes stable otherwise it will alter our results.
The power supply was fluctuating about
0.1 W which may be the cause of fluctuation
in readings.
Slope gets decreased when the temperature decreases and the heat flow also decreases, so it is clear that at the start heat flow from the hot body is large and with the passage of time it decreases.
Before starting experiment firstly develop steady state otherwise temperature values varies improperly and there will be abnormal behavior of the temperature profile.
There may be fault in the apparatus as the apparatus is too old.
20
Experiment No. 06 ‘To demonstrate the relationship between power input and surface temperature in free convection’’
Apparatus: Heat conduction apparatus
Theory: A heated surface dissipates heat primarily through a process called convection. Heat is also dissipated by conduction and radiation, however these effects are not considered in this experiment. Air in contact with the hot surface is heated by the surface and rises due to a reduction in density. The heated air is replaced by cooler air which is in turn heated by the surface and rises. This process is called free convection. The hotter the temperature of the surface, the greater the convective currents and the more heat (power) will be dissipated. If more power is supplied to a surface, the temperature of the surface must rise to dissipate this power. When analyzing convection heat transfer coefficients, three dimension-less values must be acquired. To determine what numerous constants are the initial conditions must be known so tables can be utilized.
Methodology & Experimental System The equipment used for this experiment is basically one piece equipment which includes different components. An electric boiler is the driving force of the experiment. The boiler is set to a constant output (1100 watts) and as a result it heats the water and 21
turns it into steam. This steam is fed into a condensing tower. This tower is comprised of a closed jacket and a central single aluminum tube. Cooling water passes upward though the inside of this condenser tube, causing the steam to condense on the outside surface. Steam also condenses on the inside surface of the jacket as heat escapes out into the room. A boiler supply tank is used to provide and maintain a constant level in the boiler this insures that the mass within the system remains constant during the experiment (glass tube). Cooling water is provided by reservoir that allows the experiment to be performed with either free or forced convection. All the copper-constantan (type T) thermocouples are monitored using a high impedance mili-voltmeter. Tube wall and shell wall condensates are collected separately from drain tubes provided, and cooling water flow through the condenser tube is collected in the weigh tank mounted on the scale.
Procedure: 1. 2. 3. 4. 5.
Turn on the apparatus and Allow cold water to flow through the test unit. Set the power of the heater. Wait for 10 minutes until the temperature achieved at every measuring point is stable. Record the respective final temperature values at every point. Record temperatures for power input between 0 to 20 watts.
Observations and Calculations: Diameter of the rod = 25 mm Thickness of the paper = 125 micron
Comments: The thermal conductivity value obtained from experiment t is very low which shows that paper is insulating material.
Conclusions
It was noted that by increasing the power input the temperature of heated plate was increased. By increasing the power input, with increment in temperature of plate, however, the energy of molecules was also increased. When the molecular energy was studied on microscopic level, it was noticed that molecules enhanced their motion. 22
Experiment No. 07 ‘’ To demonstrate the relationship between power input and surface
temperature in forced convection’’
Apparatus Heat transfer by simultaneous conduction and convection, whether free or forced, forms the basis of most industrial heat exchangers and related equipment. The measurement and prediction of heat transfer coefficients for such circumstances is achieved in the Free & Forced Convection Heat Exchanger by studying the temperature profiles and heat flux in an air duct with associated flat and extended transfer surfaces. The vertical duct is so constructed that the air temperature and velocity can be readily measured, and a variety of “plug -in” modules of heated solid surfaces of known dimensions can be presented to the air stream for detailed study. A fan situated at the top of the duct provides the air stream for forced convection experiments. A Control Panel contains temperature measurement, power control, and fan speed control circuits with appropriate instrumentation. Temperature measurement, to a resolution of 0.1oC is effected using RTD sensors with direct digital read-out in 0C. Air velocity is measured with portable anemometer mounted on the duct. The power control circuit provides a continuously variable, electrical output of 0-100 watts with a direct read-out in watts.
Fan/Blowe
Temperature Selector Power
Heater Switch
Heated Surface
Fan Anemomet Main
Figure 3: Unit Assembly
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Theory In free convection the heat transfer rate from the surface is limited by the small movements of air generated by this heat. More heat is transferred if the air velocity is increased over the heated surface. This process of assisting the movement of air over the heated surface is called Forced Convection. Therefore a heated surface experiencing forced convection will have a lower surface temperature than that of the same surface in free convection, for the same power input.
Heat transfer from an object can be improved by increasing the surface area in contact with the coolant i.e air by adding fins or pins normal to the surface. From the Newton’s Law of Cooling, the convection heat transfer rate is:
̇ = ℎ ∞ The illustration of experimental equipment. Where;
̇ = Power input h = convection heat transfer coefficient As = area of plate Ts = heater temperature T∞ = air temperature For this experiment, we use finned plate and pinned plate to compare the effect of heat transfer by each plates under the same conditions of power and flow. To calculate the area for finned plate and pinned plate used, we use the equation shown below: 24
=9 ×+ =17 × 2 +
Conclusion: The objective of this experiment is to determine the use of fin (extended surface) in order to improve the heat transfer in forced convection. In conclusion, the heat transfer in force convection can be improved by using a finned surface compared to pinned surface. This is due to the larger cross sectional area that is exposed to air. There are several factors that we need to take in order to improve the heat transfer in force convection which are first, the temperature difference between the two fluids. Second, the heat transfer coefficient between each of the fluids and the tube wall and lastly, the surface area to which each fluid is exposed. Therefore, we can say that the objectives are achieved and this experiment is conducted successfully.
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Experiment No. 08 ‘’ To demonstrate the use of extended surfaces to improve heat transfer from the surface’’
Theory: Extended surfaces have fins attached to the primary surface on one side of a two-fluid or a multifluid heat exchanger. Fins can be of a variety of geometry —plain, wavy or interrupted—and can be attached to the inside, outside or to both sides of circular, flat or oval tubes, or parting sheets. Pins are primarily used to increase the surface area (when the heat transfer coefficient on that fluid side is relatively low) and consequently to increase the total rate of heat transfer. In addition, enhanced fin geometries also increase the heat transfer coefficient compared to that for a plain fin. Fins may also be used on the high heat transfer coefficient fluid side in a heat exchanger primarily for structural strength (for example, for high pressure water flow through a flat tube) or to provide a thorough mixing of a highly-viscous liquid (such as for laminar oil flow in a flat or a round tube). Fins are attached to the primary surface by brazing, soldering, welding, adhesive bonding or mechanical expansion, or extruded or integrally connected to tubes. Major categories of extended surface heat exchangers are TubefinTube-fin (Figure 1), and Tube-fin (Figure 2, individually finned tubes – Figure 2a and flat fins on an array of tubes – Figure 2b) exchangers. Note that shell-and-tube exchangers sometimes employ individually finned tubes —low finned tubing (similar to Figure 2a but with low height fins) [Shah (1985)].
Figure 1.
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Figure 2.
Fin (extended surface): In the study of heat transfer, fins are surfaces that extend from an object to increase the rate of heat transfer to or from the environment by increasing convection. The amount of conduction, convection, or radiation of an object determines the amount of heat it transfers. Increasing the temperature gradient between the object and the environment, increasing the convection heat transfer coefficient, or increasing the surface area of the object increases the heat transfer. Sometimes it is not feasible or economical to change the first two options. Thus, adding a fin to an object, increases the surface area and can sometimes be an economical solution to heat transfer problems.
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Fin efficiency and extended surface efficiency: The concept of fin efficiency accounts for the reduction in temperature potential between the fin and the ambient fluid due to conduction along the fin and convection from or to the fin surface,depending on fin cooling or heating situation. The fin temperature effectiveness or fin efficiency is defined as the ratio of the actual heat transfer rate through the fin base divided by the maximum possible heat transfer rate through the fin base, which can be obtained if the entire fin is at base temperature (i.e., its material thermal conductivity is infinite).
Heat transfer and flow friction characteristics: Accurate and reliable surface heat transfer and flow friction characteristics are key input for exchanger heat transfer and pressure drop analyses, or the rating and sizing problems.
Analytical solutions: Analytical solutions for developed and developing velocity/temperature profiles in constant cross-section noncircular flow passages are important for extended surface (plate-fin) heat exchangers. Fully developed laminar flow solutions are applicable to highly compact plate-fin exchangers with plain uninterrupted fins, developing laminar flow solutions to interrupted-fin geometries, and turbulent flow solutions to not-socompact extended surfaces.
Experimental correlations: Analytical results presented in the preceding section are useful for well-defined constant cross-sectional extended surfaces with essentially unidirectional flows. Flows encountered in enhanced extended surfaces are generally very complex, having flow separation, reattachment, recirculation and vortices. Such flows significantly affect Nu and f for specific exchanger surfaces. Since no analytical or accurate numerical solutions are available, the information is derived experimentally. Kays and London (1984) and Webb (1994) have compiled most of the experimental results reported in open literature. Empirical correlations for some important extended surfaces are summarized.
Offset Strip Fins: This is one of the most widely used, enhanced fin geometries in aircraft, cryogenics and many other industries that do not require mass production. This surface has one of the highest heat transfer performance relative to the. friction factor.
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Louver Fins: Louver or multilouver fins are extensively used in the auto industry due to their mass production manufacturability and hence, lower cost. It has generally higher j and f factors than those of the offset strip-fin geometry; also, the increase in the friction factors is usually higher than the increase in the j factors. However, the exchanger can be designed for higher heat transfer and the same pressure drop compared with offset strip-fins by a proper selection of exchanger frontal area, depth and fin density. Published literature on and correlations for louver fins have been summarized by Webb (1994) and Cowell (1995) while flow and heat transfer phenomena have been discussed by Cowell (1995). Because of the lack of systematic studies on modern louver fin geometries in the open literature, no correlation can be recommended for design purposes.
Tube-fin extended surfaces: Two major types of tube-fin extended surfaces are: a) individually-finned tubes, and b) flat fins (also sometimes referred to as plate fins) with or without enhancements/ interruptions on an array of tubes.
Individually-Finned Tubes: This fin geometry, helically-wrapped (or extruded) circular fins on a circular tube is commonly used in process and waste heat recovery industries.
Conclusions: The subject of extended surface heat transfer is very extensive and is difficult to condense in a few pages. This attempt to summarize some important typical results, both analytical and experimental, is but an introduction to the subject. Key references are provided below for further exploration of the subject.
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Experiment# 09 ‘’To Determine the Working Principal of Concentric Tube Heat Exchanger Operating under the Condition of Parallel Flow ‘’
Apparatus: Concentric tube heat exchanger apparatsus
Procedure:
First of all switch on the apparatus. After that set the temperature of reservoir at 60 C. Now set the flow rate of hot water at 2 liter per minute. Set the temperature of cold water at one liter per minute. Wait for some time so that temperature of reservoir reaches to 60 C. After that note the temperature reading of hot and cold water at entering and leaving the heat exchanger. Find the log mean temperature difference and heat flow. Draw the graph of temperature with respect to length of heat exchanger.
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Theory: Heat Exchanger: A heat exchanger is a device which transfers heat from one medium to another, a Hydraulic Oil Cooler or example will remove heat from hot oil by using cold water or air. Alternatively a Swimming Pool Heat Exchanger uses hot water from a boiler or solar heated water circuit to heat the pool water. Heat is transferred by conduction through the exchanger materials which separate the mediums being used. A shell and tube heat exchanger passes fluids through and over tubes, where as an air cooled heat exchanger passes cool air through a core of fins to cool a liquid.
Types of Heat Exchangers: 1. 2. 3. 4.
Plate and frame heat exchanger. Spiral heat exchanger. Shell and tube heat exchanger. Plate fin heat exchanger.
Selection Criteria of Heat Exchangers: To select an appropriate heat exchanger, the system designers (or equipment vendors) would firstly consider the design limitations for each heat exchanger type.
High/low pressure limits Thermal performance Temperature ranges Product mix (liquid/liquid, particulates or high-solids liquid) Pressure drops across the exchanger Fluid flow capacity Clean ability, maintenance and repair Materials required for construction Ability and ease of future expansion Material selection, such as copper, aluminum, carbon steel, stainless steel, nickel alloys, ceramic
Fouling Factor: Fouling occurs when impurities deposit on the heat exchange surface. Deposition of these impurities can decrease heat transfer effectiveness significantly over time and are caused by:
Low wall shear stress Low fluid velocities High fluid velocities Reaction product solid precipitation Precipitation of dissolved impurities due to elevated wall temperatures
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Applications in industry: Heat exchangers are widely used in industry both for cooling and heating large scale industrial processes. The type and size of heat exchanger used can be tailored to suit a process depending on the type of fluid, its phase, temperature, density, viscosity, pressures, chemical composition and various other thermodynamic properties. Heat exchangers are used in many industries, including:
Waste water treatment Refrigeration Wine and beer making Petroleum refining nuclear power
In waste water treatment, heat exchangers play a vital role in maintaining optimal temperatures within anaerobic digesters to promote the growth of microbes that remove pollutants. Common types of heat exchangers used in this application are the double pipe heat exchanger as well as the plate and frame heat exchanger
As we know,
= ∆ For the parallel flow heat exchanger shown the heat transfer is given by,
= −ℎℎℎ= The heat transfer is also given as,
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Putting the value of dqfrom previous equation,
Putting these values in the above equation,
Comparing this equation with the general equation of heat transfer that is written above,
Observations and Calculations: Area =A= .067 m 2 Set temperature
=T s= 60 C
Hot water flow rate =Qh= 2 litr/min Cold water flow rate =Qc= 1litr/min Table of Experiment 9 Vc L/min 2.2 2.5 2.9
Vh L/min 2.4 3.3 3.4
Tc1 °C 28 28 28
Tc(mean) °C 30 30 31
Tc2 °C 34 34 36
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Th1 °C 47 50 53
Th(mean) °C 42 43 48
Th2 °C 43 45 50
Graph:
1.0
Comments:
The experiment shows that as the water flows from inlet towards the outlet, the cold water gains heat from hot water, if enough time or length is supplied to the water to flow both the lines of hot and cold water should meet at a point but this doesn’t happens because the exchanger cannot be 100 percent efficient. Thermal stresses are less in parallel heat exchangers. Because average temperature remains constant. From the graph it is clear that hot water losing its heat and slope is decreasing, and cold water getting heat and slope is increasing. Wait for some time so that supply water temperature reaches to set temperature.
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Experiment#10 ‘’To Determine the Working Principal of Concentric Tube Heat Exchanger Operating under the Condition of Counter Flow’’
Apparatus: Concentric tube heat exchanger
Procedure :
First of all switch on the apparatus. After that set the temperature of reservoir at 60 C. Now set the flow rate of hot water at 2 liter per minute. Set the temperature of cold water at one liter per minute. Wait for some time so that temperature of reservoir reaches to 60 C. After that note the temperature reading of hot and cold water at entering and leaving the heat exchanger. Find the log mean temperature difference and heat flow. Draw the graph of temperature with respect to length of heat exchanger.
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Theory: Heat exchanger is a device that is used to transfer heat between two fluids. The heat exchanger has main application in thermal power plant, engines and many industries. A shell and tube heat exchanger has two concentric tubes the inner tube may contains the hot fluid whereas the outer tube may contain the cold fluid flowing in it. The heat exchange takes place from hot fluid to cold fluid and this heat exchange is governed mainly by conduction. A shell and tube heat exchanger can be operated in approximately counter flow by having both fluids enter at opposite end and exit at the opposite end. With counter flow the temperature difference between the two fluids remains almost same. The overall measure of heat transfers driving force, the log mean temperature difference is greater for counter flow, so the heat exchanger surface area requirement for parallel will be larger than for a counter flow heat exchanger with the same inlet and outlet temperatures for the hot and the cold fluid.
Figure
8 : Double Tube Counter
Heat Exchanger
As we know,
= ∆ For the parallel flow heat exchanger shown the heat transfer is given by,
= −ℎℎℎ= The heat transfer is also given as,
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Putting the value of dqfrom previous equation,
Putting these values in the above equation,
Comparing this equation with the general equation of heat transfer that is written above,
Preference of counter over parallel heat exchangers:
Maximum cold fluid temperature o
Fast heat transfer o
If we want to ensure that the temperature of the cold fluid never exceeds a particular temperature, then concurrent exchanger designs are advantageous due to their inbuilt restriction to this effect.
The temperature difference between the hot and cold streams at this location is very large in the concurrent design. In fact, it's the largest possible temperature difference achievable! Since the heat transfer rate is directly proportional to the temperature difference, the heat transfer rate will also be maximum here. Therefore, to achieve fast heat transfer away from thermal equilibrium conditions, parallel flow configurations will perform better.
Isothermal heat transfer –
Suppose one of the two interacting fluids is undergoing a phase change due to the heat transfer (e.g. condensation of saturated steam), then both designs are identical. In this case, there is no change in temperature for one of the two streams and hence, no difference in the performance between configurations. 37
Structural factors Sometimes, the equipment structure is such that it's impossible to prevent parallel flow. For instance, in the 1-2 shell-and-tube heat exchanger design shown below, parallel flow arises unavoidably. Hence, even if a countercurrent heat exchanger is more efficient, concurrent flow situations often arise and require consideration.
Observation and Calculations: =A= .067 m 2 =T s= 60 C
Area Set temperature Hot water flow rate =Qh= 2 litr/min Cold water flow rate =Qc= 1litr/min
Table of Experiment 10 Tc1
Th1
Tc2
Th2
Tc3
Th3
0c
0c
0c
0c
0c
0c
43
59
36
55
32
53
Graph:
70 60 50 40 30 20 10 0 0
0.2
0.4
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0.6
0.8
1
1.2
1.4
1.6
Comments:
The experiment shows that as the water flows from inlet towards the outlet, the cold water gains heat from hot water, if enough time or length is supplied to the water to flow both the lines of hot and cold water should have same temperature but this doesn’t happens because the exchanger cannot be 100 percent efficient. Thermal stresses is more in counter flow because average temperature varies with time. Wait for some time so that supply water temperature reaches to set temperature. From the graph it is clear that hot water losing its heat and slope is decreasing, and cold water getting heat and slope is increasing but co ld water enters from right to left . Take the reading of temperature carefully.
If the direction of flow is not conform then touch the pipe to conform that
either hot water is flowing or cold water.
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