THE AMERICAN UNIVERSITY IN CAIRO
MENG 4606-82 UT: Heat Transfer Lab Report #4: Forced convection Submitted by: Cherif Youssef Chokeir SID: 900140712 Date of Submission: 21/7/2017 Dr. Amr Serag Eldin Ta: Eng. Mohamed Fayed
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Abstract The purpose of this study is to study the heat transfer by forced convection and to determine experimentally and empirically the heat transfer coefficient by forced convection. Temperature measurements helped to obtain heat transfer by convection and to conclude form it the experimental value of the forced convection heat transfer coefficient. The heat transfer coefficient could then be obtained empirically through empirical equation based on Reynolds number and the effect of varying the fluid velocity could be seen by varying the pressure inside the tube. The obtained result showed an increase of heat transfer coefficient with an increase in velocity.
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Contents Abstract............................................................................................................................................... 2 List of figures ...................................................................................................................................... 4 List of Tables ...................................................................................................................................... 5 Introduction ......................................................................................................................................... 6 Theory: ............................................................................................................................................... 8 Apparatus ......................................................................................................................................... 10 Results and Discussion: .................................................................................................................... 11 Conclusion and Recommendations ................................................................................................... 12 References: ...................................................................................................................................... 13
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List of figures Figure 1 Forced Convection apparatus ............................................................................................. 10
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List of Tables Table 1 Empirical Constants for determination of heat transfer coefficient .......................................... 9 Table 2 Experimental Readings ........................................................................................................ 11
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Introduction “Heat transfer is the transition of thermal energy from a heated item to a cooler item. When an object or fluid is at a different temperature than its surroundings or another object, transfer of thermal energy, also known as heat transfer, or heat exchange, occurs in such a way that the body and the surroundings reach thermal equilibrium. Heat transfer always occurs from a hot body to a cold one, a result of the second law of thermodynamics. Where there is a temperature difference between objects in proximity, heat transfer between them can never be stopped; it can only be slowed down. Classical transfer of thermal energy occurs only through conduction, convection, radiation or any combination of these. Heat transfer associated with carriage of the heat of phase change by a substance (such as steam which carries the heat of boiling) can be fundamentally treated as a variation of convection heat transfer. In each case, the driving force for heat transfer is a difference of temperature.” [4]
“Convection is a type of heat transfer via moving fluids that can be utilized in process equipment. Depending on how the flow begins, the convection can be natural or forced. Natural convection is any fluid movement by natural means such as warmer fluid moving upward and cooler fluid moving downward. A type of driving force would also be a difference in density between two locations, resulting in the heat of one fluid being absorbed by another fluid. Natural convection can be found throughout nature, such as in earth’s oceans and atmosphere, which are heated by this force.
Forced convection occurs when a fluid flows over a surface by induced external forces, like a pump, fan, or mixer. The motion of the fluid increases heat transfer; there is a direct relationship between velocity and heat transfer- higher velocity equals more heat transfer. A practical example of this type of heat transfer would be home heating systems which heat the air by force. Air in this equipment is
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heated by a type of furnace and blown by fans into a room. The fan acts as the driving force for the fluid to move into the room and transfer the heat gained by the furnace into the room
The heat transfer by convection depends mainly on the heat transfer coefficient between the fluid and the surface and the surface area and the temperature difference between the fluid stream and the surface that is exposed to the fluid. In forced convection, the heat transfer coefficient depends mainly on the ratio between inertia forces and viscous forces which is the Reynolds number and the ratio between momentum diffusivity and thermal diffusivity called the Prandtl number. The Reynolds number increases with an increase in velocity which could be checked experimentally by varying the pressure inside a pipe. The dimensionless form of the heat transfer coefficient called Nusselt number and defined by 𝑁𝑢 =
ℎ∗𝑑 𝑘
for a pipe is highly dependent on Reynolds number. Physically this means that the higher
the fluid velocity the more rapid is the heat lost by convection.
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Theory: In this experiment, the mode of heat transfer to be studied is forced convection through a tube pipe. The rate of heat transfer obtained from the electric heater could be obtained using the relationship
̇ =𝑉∗𝐼 𝑄𝑡𝑜𝑡
(1)
This heat input rate is equal to the heat lost by convection on the inside walls of the tube
𝑄̇ 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛 = ℎ𝑒𝑥𝑝 ∗ 𝐴 ∗ (𝑇𝐻 − 𝑇∞ )
(2)
The area of surface exposed to convection is given by A = π *d*L
(3)
with d = 12.7 mm, L=142 mm The pressure difference as read from the manometer could be related to the velocity by the relationship 𝑉𝑒𝑙 = 1.291 ∗ √∆𝑃
(4)
where ΔP is the pressure difference in Pa In order to obtain the value of the heat transfer coefficient empirically, it is important to calculate Reynolds number 𝑅𝑒 =
𝜌∞ ∗𝑉∗𝑑 𝜇𝑓
(5)
where 𝜌∞ is the air density at free stream conditions, v is the air velocity, d is the pipe diameter, and 𝜇𝑓 is the viscosity of the air calculated at the film temperature given by 𝑇 +𝑇
𝑇𝑓 = ∞ 2 𝑤 (6) Where 𝑇∞ is air temperature at free stream conditions, 𝑇𝑤 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑖𝑟 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑤𝑎𝑙𝑙 To obtain the empirical value of the heat transfer coefficient, we use the relationship ℎ𝑒𝑚𝑝 ∗𝑑 = 𝑁𝑢 = 𝐵 ∗ 𝑅𝑒 𝑛 (7) 𝑘 where B and n are emperical constants determined from table 1
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Re 0.4-4 4-40 40-4000 4000-40000 40000-400000
B 0.891 0.821 0.615 0.174 0.0239
n 0.33 0.385 0.466 0.618 0.805
Table 1 Empirical Constants for determination of heat transfer coefficient
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Apparatus The apparatus used in this experiment is presented in figure 1. It has multiple measuring devices for temperature, voltage and current. It has a pressure controller section to be able to vary pressure levels and therefore velocity of the flowing air
Figure 1 Forced Convection apparatus
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Results and Discussion: At first, the experimental reading values are tabulated in table 1 presenting values of the pressure readings, fluid and duct temperatures as well as corresponding values for voltage and current measurements. The equations for calculating heat transfer rates and the heat transfer coefficients were presented in the theory section.
Δp (kPa)
T∞ (°C) 0.01 0.65 1.35
TH Tf V I vel Re B N hemp q hexp % error (°C) (°C) (volts) (A) (m/s) W/m2.K W W/m2.K 23 131 77 19.76 2.5 4.0825 2979.53 0.615 0.466 60.47551 49.4 80.73489 33.50014 23 63 43 19.66 2.506 32.914 25968.9 0.174 0.618 201.1242 49.26796 217.4016 8.093185 23 58 40.5 19.62 2.503 47.434 37649.5 0.174 0.618 251.2716 49.10886 247.6566 1.438706
Table 2 Experimental Readings
The first observation from table 2 is that the increase in pressure difference across the manometer which reflected the increase in the flow velocity resulted in an increase in the Reynolds number which was accompanied by an increase in the value of the heat transfer coefficient for both empirical calculation and experimental determination.
The variation of the heat transfer coefficient in the case of forced convection is thus mainly dependent on the velocity of the flowing fluid, as presented by the Reynolds number. It also depends on other parameters, like the material of the duct (k) and its size (characteristic dimension or diameter) and properties of the fluid (like density ρ and viscosity μ)
Furthermore, it appears that the error decreases with increase in velocity reflecting that the accuracy of the prediction of the heat transfer coefficient experimentally is higher at higher Reynolds number, the error decreased from 33.5% to 1.43%. This shows that the experiments match the empirical relationship rather in the case of turbulent flow than in the case of laminar flow.
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Conclusion and Recommendations To sum up, the main objective of this study was to examine the effect of the variation in fluid velocity on the value of the heat transfer coefficient in forced convection At first, the experimental readings taken through measurements of the temperatures of the fluid and the tube wall temperatures helped to obtain Reynolds number from which it had been possible to determine through empirical relation the value of the heat transfer coefficient. This value was then compared with the experimental value obtained by measuring current and voltage values. Further measurements at different pressures were obtained which helped to study the effect of variation in the velocity on the heat transfer coefficient. Results showed that the increase in velocity as presented by the increase in the Reynolds number was reflected by and increase in the Nusselt number and therefore also in the heat transfer coefficient for both experimental relations and empirical ones. This showed that the more rapid is the flow, the higher convection rate. Furthermore, the error between empirical and experimental values decreased showing that experiments are close to empirical relationship more for turbulent flow as the fluid surpass the transition region between regimes.
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References: [1] Csongradi et al.“ Convective and Radiant Heat Transfer CHE 0201” Retrieved 9 July 2017 from http://www.pitt.edu/~ges39/webpage/ConvectiveandRadiantHeatTransfer.pdf
[2] “ Thermal Conductivity: Stainless Steel” Retrieved 21 June 2017 from http://www-ferp.ucsd.edu/LIB/PROPS/PANOS/ss.html [3] “Natural Convection Theory” Retreived 9 July 2017 from http://www.eetimes.com/document.asp?doc_id=1274163
[4] “Thermal conductivity of metals ” Retrieved 22 June 2017 from http://www.fizica.unibuc.ro/Fizica/Studenti/Cursuri/doc/VFilip/IntThPh/Lucrari_practice/Thermal_co nductivity_of_metals.pdf [5] Holman, J.P. Heat Transfer, 2010
[6] Gabra, Samuel. G, “MENG 466 Lab Report # 3” (2014)
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