CH1 What are the physical mechanisms associated with heat transfer by conduction, convection, and radiation? Conduction- no bulk or macroscopic motion Convection- random molecular motion, diffusion, bulk, or macroscopic motion Radiation- emitted of energy What is the driving potential of heat transfer? Temperature difference (high to low) low ) What is the difference between a heat flux and a heat rate? Heat flux- !, "#m$%, heat divided by an area Heat rate- , ", &roduct of heat flux and area What is a temperature gradient, dt#dx, '#m, property What is thermal conductivity? K , "#m', it is a transport property What is !ourier"s #aw? !)-k(dt#dx* What is the difference between natural convection and forced convection? +atural- the flow is induced by buoyancy forces, which are due to density differences caused by temperature variations in the fluid orced- flow is caused by external, like a fan What conditions are necessary for the development of a hydrodynamic boundary layer? Hydrodynamic- the velocity velocity varies varies from from .ero .ero at at the surface to a finite value ambient associated associated with the flow, flow, velocity varies to .ero in a hydrodynamic layer What conditions are necessary for the development of a thermal boundary layer? Thermal- Ts / y)0 to T ambient in the outer flow, velocity varies varies !)h(Ts-T ambient) ambient) What is $ewton"s #aw of cooling 1 !)h(Ts-T What role is played by the convection heat transfer coefficient in $ewton"s $ewton"s law of cooling? %t depends on conditions in the thermal boundary layer, which are influenced by the surface geometry, the nature of the fluid motion, and an assortment of fluid thermodynamics and transport properties h2"#m$%'3 What effect does convection heat transfer from or to a surface have on the solid bounded by the surface? none What is predicted by &tefan'(oltmann law, and what unit of temperature must be used with this law? *he upper limit to the emissive power, the unit unit of of temper temperatu ature re is absolu absolute te k, 4b) 4b)Ts$5 What is the emissivity, emissivity, and what role does it play does it play in characteriing radiation transfer at a surface? +missivity' a radiation property of the surface6 this property provides a measure of how efficiently a surface emits energy relative to a blackbody or ideal radiator radiator What is %rradiation? 7rradiation- the rate at which all such radiation is incident on a unit area of the surface 8nits are "#m$% "#m$% What conditions are associated with use of the radiation heat transfer coefficient? Hr, depends strongly on temperature temperature $et radiation !rad)#9)4b(Ts*-:)(Ts$5- Tsurr$5* What is the inherent difference between application of conservation of energy over a time interval and at an instant of time? Time interval- all energy terms are measured in ;oules 7nstant of time- all energy terms are balanced and measured in ;oules#s What is thermal energy storage? How does it differ from thermal energy generation? What role do the terms play in a surface energy balance? 4nergy generated- 4g < at an instant 4nergy storage- over a CH%n the general formulation of !ouriers #aw what are the vector and scalar .uantities? Why is there a minus sign on the right hand side of the e.uation? ouriers law has scalar temperature field and heat flux vector The minus sign is necessary because heat is always transferred in the direction of decreasing temperature What is an isothermal surface? What can be said about the heat flux at any location on this surface? The direction of heat flow will always be normal to a surface of constant temperature, the direction of ! is normal to the cross sectional area What form does fourier"s law ta/e for each of the orthogonal directions of Cartesian cylindrical and spherical coordinate systems? %n each case what are the units of the temperature gradient? Can you write each e.uation from memory? Cartisian Cylinderical
&pherical 0n important property of matter is defined by !ourier"s law What is it? What is its physical significance? What are its units? k, thermal conductivity, "# m', w#o k all materials that have the same 9, =T, =x would technically be the same What is isotropic material? 9 material where thermal conductivity is independent of the coordinate direction Why is the thermal conductivity of a solid generally larger than that of a li.uid? Why is the thermal conductivity of a li.uid generally larger than that of a gas? Thermal conductivity is greater in solid than l iuid and liuid than gas because the heat fluxes are higher Why is the thermal conductivity of an electrically conducting solid generally larger than that of a non conductor? Why are materials such as beryllium oxide, diamond, and silicon carbide exceptions to this rule? 7n pure metals, the electron contribution to conduction heat transfer dominates, while non-conductors and semiconductors, the phonon contribution is dominant because they have high thermal conductivity %s the effective thermal conductivity of an insulation system a true manifestation of the efficacy with which heat is transferred through the system by conduction alone? +o, heat is also transferred due to surface radiation and the nature of the volumetric fraction of the air or void space Why does the thermal conductivity of a gas increase with increasing temperature? Why is it approximately independent of pressure? Thermal conductivity of as gas increase w# increasing temperature because > increases with increasing temperature and decreasing molecular weight ?ecause @ and Amfp are directly and i nversely proportional to the gas pressure What is the physical significance of the thermal diffusivity? How is it defined and what are its units? Thermal diffusivity, B, it measures the ability of a material to conduct thermal energy relative to its ability t o store thermal energy m%#s !or a chemically reacting medium, what /ind of reaction provides a source of thermal energy . 23)? What /ind of reaction provides a sin/ for thermal energy . 43)? 7 0 a source if thermal is bei ng generated in the material at the expense of some other energy form 7f D0 a sink if thermal energy is being consumed CH 5 6nder what conditions may it be said that the heat flux is a constant, independent of the direction of heat flow? !or each of these conditions, use physical considerations to convince yourself that the heat flux would not be independent of direction if the conditions were not satisfied Heat flux is constant and independent of the direction of heat flow or a E-F GG in a plane wall with no heat generation !or one dimensional steady state conduction in a cylindrical or spherical shell without heat generation, is the radial heat flux independent of radius? %s the radial heat rate independent of radius? He flux is independent heat rate is dependant !or one dimensional stead state conduction without heat generation, what is the shape of the temperature distribution in plane wall? %n a cylindrical shell? %n a spherical shell?
What is the thermal resistance? How is it defined? What are its units? Thermal resistance is the ratio of a driving potential to the corresponding transfer rate '#" !or conduction across a plane wall, can you white the expression for the thermal resistance from memory? &imilarly can you write expressions for the thermal resistance associated with conduction across cylindrical and spherical shells? !rom memory can you express the thermal resistances associated with convection from a surface and net radiation exchange between the surface and large surroundings? "all Rtcond ) #k9 Rtconv ) E#h9 Rtrad ) E#hr9 Cylinder Rtcond ) ln (r%#rE*#%Ik Gphere Rt cond ) E#(5Ik*(E#rE < E#r%* what is the physical basis for existence of a critical insulation radius? How do the thermal conductivity and the convection coefficient affect its value? Jaximi.es heat transfer that is below which K increases with increasing r and above which K decreases with increasing r Rcr ) k#h h does not eual 0
How is the conduction resistance of a solid affected by its thermal conductivity? How is the convection resistance at a surface affected by the convection coefficient? How is the radiation resistance affected by the surface emissivity? Rt cond ) #k9 so the greater k is the lower Rtcond Rtconv L Rtrad is the higher h or hr the l ower the resistance %f heat is transferred from a surface by convection and radiation how are the corresponding thermal resistances represented in a circuit?
Can a thermal conduction resistance be applied to a solid cylinder or sphere? +o r does not eual 0 What is a contact resistance? How is it defined? What are its units for an interface of prescribed area? What are they for a unit area? Rtc < the temperature drop across the interface between materials may be appreciable Rtc ) T-To # ! m$% '# " What purpose is served by attaching fins to a surface? ins are used to increase the heat transfer from a surface by increasing the effective surface area What is the fin effectiveness? What is its range of possible values? 6nder what conditions are fins most effective? The ratio of find heat transfer rate to the heat transfer rate that would exists with out the fin M f % thin with close spacing what is the fin efficiency? What is its range of possible values? 6nder what conditions will the efficiency be large? N ) f # max ) f # h9 Ob values from 0-E for a maximum max ) f CH7 What is an isotherm? What is a heat flow line? How are the two lines related geometrically? "hen local heat flux in the solid is a vector that is everywhere perpendicular to the li nes of constant temperature ines that represent the directions of the heat flux vector They are perpendicular to each other What is an adiabatic? How is it related to a line symmetry? How is it intersected by an isotherm? 9 line where no heat can be conducted across 9diabatic surfaces are heat flow lines perpendicular What parameters characterie the effect of geometry on the relationship between the rate and the overall temperature difference for steady conduction in a -'8 system? How are these parameters related to the conduction resistance? The average temperature of a certain region What is represented by the temperature of a nodal point, and how does the accuracy of a nodal temperature depend on prescription of the nodal between? The larger the grid the finer the mesh, the more accurate CH 9 6nder what conditions may the lumped capacitance method be used to predict the transient response of a solid to a change in its thermal environment? ?i D E What is the physical interpretation of the (iot $umber? Ratio of internal and eternal thermal resistances %s the lumped capacitance method of analysis li/ely to be more applicable for a hot solid being cooled by forced convection in air or in water? (y forced convection in air or natural convection in air? 9ir, 9ir %s the lumped capacitance method of analysis li/ely to be more applicable for cooling of a hot solid made of copper or aluminum? !or silicon nitride or glass? Copper What parameters determine the time constant associated with the transient thermal response of a lumped capacitance solid? %s this response accelerated or decelerated by an increase in the convection coefficient? (y an increase in the density or specific heat of the solid? @cvh9 accelerated decelerated CH : What is the difference between a local convection heat transfer coefficient and average coefficient? What are their units? ocal at any distance x from the leading edge, average is the entire surface "#mP%'
What are the forms of $ewton"s law of cooling for a heat flux and a heat rate !)hQT K)h9QT QT) Ts-T What are the velocity and thermal boundary layers? 6nder what conditions do they develop 9 thin layer in which velocity gradients and shear stresses are larger, a thing fluid laying in which temperature gradients are present Selocity develops when there is a fluid flow over a surface, thermal develops if the flui d is free stream and the surface temp differs What .uantities change with location in a velocity boundary layer? 0 thermal boundary layer? Selocity boundary layer thickness surface shear stress U Thermal boundary layer thickness magnitude dT#dyVy)0 decreases as x increases ! and h decrease when x increases ;ecogniing that convection heat transfer is strongly influenced by conditions associated with fluid flow over a surface, how is it that we may determine the convection heat flux by applying fouriers law to the fluid at the surface? hQT)-kdT#dyVy)0 h)-k dT#dyVy)0#QT QT ) Ts-T 8o we expect heat transfer to change with transition from a laminar to a turbulent boundary layer? How? Wes,, 7ncreases What physical processes are represented by the terms of the x'momentum e.uation :1:)? (y the energy e.uation :1<)? Represents he net outflow of mass in the x X y directions, the sum of which must be .ero for GG eft side represents the net rate at which x-momentum leaves the CS due to fluid motion across its boundaries Right side represents the net pressure force and the net forces due to viscous shear stress What special approximations may be made for conditions within theis velocity and thermal boundary layers? uv du#dydu#dy(@v#dx* dt#dydt#dx How is the ;eynolds = defined? What is it physical interpretations? What role is played by the critical? Re) Sx#Y ratio of inertial and viscous forces calculates the boundary layer behavior What is the >randtl =? How does its value affect relative growth of the velocity and thermal boundary layers for laminar flow over a surface? What representative room temperature values of the >randtl = for a li.uid metal a gas water and oil &r) Y#B ratio of the momentum and thermal diffusivities &randtl Z for different fluids is different, for energy and momentum transfer by diffusion rate is as follows6 gases its comparable, liuid metal < energy exceeds momentum diffusion rate and oils are opposite of liuid metal What is the coefficient of friction? *he $usselt =? !or flow over a prescribed geometry what are the independent parameters that determine local and average values of these .uantities? Fimensionless surface shear stress Cf) Us#@vP%#% The ratio of convection to pure conduction heat transfer rates +u) h#k 6nder what conditions may velocity and thermal boundary layers be termed analogous? What is the physical basis of analogous behavior? 7f two or more processes are governed by dimensionless euations of the same form riction and heat transfer relations for a particular geometry are interchangeable What important boundary layer parameters are lin/ed by the ;eynolds analogy? Selocity parameter- if known the analogy may be used to obtain the heat transfer parameter and vice versa What physical features distinguish a turbulent flow from a laminar flow? aminar- fluid flow is highly ordered and you could identify streamlines along which fluid particles move Turbulent- fluid flow highly irregular and is characteri.ed by random, [-d motion of relatively large parcels CH< What is an external flow? ?oundary layers that develop freely without constraints imposed by ad;acent surfaces How does the velocity boundary layer thic/ness vary with distance from the leading edge for laminar flow over a flat plat? !or turbulent flow? What determines the relative velocity and thermal boundary layer thic/ness for laminar flow? !or turbulent flow? 7ncreases proportionally to x$E#% 7ncreases proportionally to x$5#\ &r- momentum and thermal diffusivity ratio ?oundary layer development is influenced by random fluctuations in fluid in the fluid and not by molecular diffusion How does the local convection heat transfer coefficient vary with distance from the leading edge for laminar flow over a flat plat? !or turbulent flow? !or flow in which transition to turbulence occurs of the plate Fecrease proportionally to x$-E#% from Fecrease proportionally to x$5#\
Fecrease in a range from xlamDxDxturb How does the local heat transfer from the surface of a flat plate affected by the existence of an unheated starting length There is no heat transfer for 0DxD] What are the manifestations of boundary layer separation from the surface of a circular cylinder in cross flow? How is separation influenced by whether the upstream flow is laminar or turbulent? "ake and vortices formation Geparation occurs later if turbulent How is the variation of the local convection coefficient on the surface of a circular cylinder in cross flow affected by boundary layer separation? (y boundary layer transition? Where do local max and min in the convection coefficient occur on the surface? ocal convection increase with increasing +u and vice versa 7s a result of part a, from the value at the stagnation point is due to boundary layer development but the sharp increase that occurs between ^0 and E00 degrees is now due to boundary transition to t urbulent ?etween ^0 and E00 degrees CH What are the salient features of a hydrodynamic entry region? 0 thermal entry region? 0re hydrodynamic and thermal entry lengths e.uivalent? %f not on what do the relative lengths depend on? luid enters with uniform velocity but coverage to a parabolic fully developed velocity profile luid enters at a uniform temp but converges to a parabolic fully devel oped thermal boundary layer +o, the hydrodynamic boundary layer develops first Hydrodynamic < Re, Thermal < &r, and Re What are the salient hydrodynamic features of fully developed flow? How is the friction factor for fully developed flow affected by wall roughness? Radial velocity component and gradient of axial velocity component are .ero everywhere, axial velocity component depends on r, u(x,r* ) u( r * *o what important characteristic of an internal flow is the mean or bul/ temperature lin/ed? *he rate at which thermal energy is affected What are the thermal features of fully developed flow? The local convection coefficient is a constant and T(r * is a function of x %f fluid enters a tub at a uniform temperature and there heat transfer to or from the surface of the tube, how does the convection coefficient vary with distance along the tube? Fecreases exponentially until fully developed conditions when it becomes constant !or fluid flow through a tube with a uniform surface heat flux, how does the mean temperature of the fluid vary with distance from the tube entrance in the entrance region? *he fully developed region? How doest he surface temperature vary with distance in the entrance and fully developed regions 7ncreases linearly 4xponentially in the entrance and linearly in the fully developed !or heat transfer to or from a fluid flowing through a tube with a uniform surface temperature, how does the mean temperature of the fluid vary with distance from the entrance? How does the surface heat flux vary with distance from the entrance? 4xponentially ,,,,,,,,,, the heat flux decreases Why is a log mean temperature difference rather that an arithmetic mean temperature difference used to calculate the total rate of heat transfer to or from a fluid flowing through a tube with a constant surface temperature ?ecause the exponential nature of the temperature decay What two e.uations may be used to calculate the total heat rate to a fluid flowing through a tube with a uniform surface heat flux? _conv) m(cp*(Tmo-Tmi* ) h9 (QT * 6nder what conditions is the nusselt number associated with internal flow e.ual to a constant value independent of the ;eynolds number and >randtl number? aminar fully developed conditions with constant surface temperatures %s the average nusselt number associated with flow through a tube larger than, e.ual to, or less than the nusselt number for fully developed conditions? Why? arger than This is because you are taking values from entire region both entry and exit How is the characteristic length defined for a non circular tube? 7t is termed the hydraulic diameter and is defined as F) 59#& CH @ What is an extensive fluid? Auiescent fluid? 4xtensive < an infinite fluid
_uiescent < a fluid that is at rest What conditions are re.uired for a buoyancy driven flow? Temperature gradient exceeds a critical value conditions are unstable and buoyancy forces take over and overcome viscous force How does the velocity profile in the free convection boundary layer on a heated vertical plate differ from the velocity profile in the boundary layer associated with forced flow over a parallel plate? Sertical plate has a parabolic velocity profile What is the general form of the buoyancy term in the x'momentum e.uation for a free convections boundary layer? How may it be approximated if the flow is due to temperature variations? What is the name of the approximation?
:rashof +umber What is the physical interpretation of the Brashof $umber? What is the ;ayleigh number? how does each parameter depend on the characteristic length? Ratio of buoyant forces to viscous forces Ra ) :r(&r* Ra ) u#Y :r ) g`(Ts-T*#Y &r ) Y#B !or a heated horiontal plate in .uiescent air, do you expect heat transfer to be larger for the top or bottom surface? Why ? for a cooled horiontal plate in .uiescent air, do you expect heat transfer to be larger for the top or bottom surface? Why? or uiescent flow heat transfer would be greater at the top due to the heat rising and cold falling or cold it is at the top because flow must go hori.ontally before passing by the plate Chapter 13 Pool boiling - liuid is uiescent and its motion near the surface is due to free convection and to mixinig induced by bubble growth and detachment Forced Convection boiling 'luid motion is induced by external means, as well as by free convection and bubble induced mixing Subcooled boiling ' the temperature of the liuid is below the saturation temperature and bubbles at the surface may be condensed in the liuid Saturated ' the temperature of the liuid slightly exceeds the saturation temperature Excess Temperature' delta Temperature(excess*) T(surface*-T(sat* Sketch the boiling curve and identify key regimes and feature.G!P" G!P" G!P" Critical heat flux# maximum heat flux $eidenfrost ' heat flux is a minimum and surface is completely covered by vapor blanket "o% does progression along the boiling curve occur if the surface heat flux is controlled& 9t the critical point, there is a sharp departure from the boiling curve where surface conditions change from Temp(4,C* to T(e,4* 7f T(s,4* exceeds melting point of solid, system will fail "ysteris effect# Surface temp controlled#&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& "o% does heat flux depend on the excess temperature in the nucleate boiling regime. Heat flux is approx proportional to Felta T(excess*$[ 'hat modes of heat transfer are associated %ith film boiling& Conduction,radiation "o% is the amount of li(uid subcooling defined 1 FeltaT(sub*)T(sat*-T(* To %hat extent is the boiling heat flux influenced by the magnitude of the :ravitational field- for low gravity effects :$%\ 7n nucleate boili ng heat flux is 7s nearly independent of gravity iuid subcooling- heat flux i ncreases typically as (T(s*-T(**$E%\ 7n nucleate ?oiling influence of subcooling is considered to be neglible or film boiling Heat flux increases strongly Gurface Roughness-heat flux is neglible for film boi ling 7ncreased surface roughness can cause large increase in heat flux for nucleate boiling
Chapter 11 'hat are t%o possible arrangement for a concentric tube heat exchanger& &arallel and counter flow 'hat are the restrictions associated %ith the fluid outlet temperatures& 7n parallel the final temperatures approach each other 7n counter flow, Temperature cold final can be higher than T(ho* For cross#flo% heat exchanger) %hat is meant by the terms mixed and unmixed& 8;0W%$B????????????????????????????? *n %hat sense are they ideali+ations of actual conditions& The two configurations are typically differentiated by an ideali.ation that treats fluid motion over the tubes as unmixed or mixed 'hy are baffles used in a shell#and#tube heat exchanger& ?affles are usually installed to increase the convection coefficient of the shll-side fluid by inducing turbulence and a cross flow velocity component Compact heat exchanges# These devices have dense arrays of finned tubes or plates and are typically used when at least one of the fluids is a gas and is hence characteri.ed by a small convection coefficient Fouling Factor#R,f- during normal heat exchanger operation, surfaces are often eub;ect to 87+: by fluid impurity,rust, or other reactions b#w the fluid and the wall increase the resistance to heat transfer b#w the fluids This effect can be treated by introducing an additional thermal resistance Finned surfaces' by increasing the area, they reduce the resistance to convection heat transfer "hen surface area is in need of increase 'hen can the overall heat transfer coefficient be expressed as ,-hi/#0 1 "o/#02/#0 ?when you have two tubes, that cool one another 'hat is the appropriate form of the mean temp differ. For the t%o fluids of a parallel or counter#flo% heat exchanger& #+0+ &>0C+ *D W;%*+ D6* #+0+ &>0C+ *D W;%*+ D6* #+0+ &>0C+ *D W;%*+ D6* #+0+ &>0C+ *D W;%*+ D6* #+0+ &>0C+ *D W;%*+ D6*
'hat can be said about the change in temp of a saturated fluid undergoing evaporation or condensation in a heat exchanger& 7f condensing hot temp stays constant and cold fluid increases 7 evaporating liuid cold temp stays constant and hot fluid decreases
'ill the fluid have the min or max heat capacity rate experience the largest temp change in a heat exchanger& Jin 'hy is the maximum possible heat rate for aheat exchanger not e(ual to CmaxThi#Tci2& 7f a fluid having the larger heat capacity rate were to experience the maximum possible temperature change, conservation "R7T4 8T would reuire that the other fluid experience yet a larger temperature change 7f Cmax)Cc and one F8: 7 :T T 9G' W8 9?8T +4 TH7+: H4R4 Can the outlet temperature of the cold fluid ever exceed the inlet temperature of the hot fluid& + *o define the effectiveness of a heat exchanger of a heat transfer, we must first determenin the maximum determine the max possible heat transfer rat, .max, for the exchanger +, the ratio of actual heat transfer rate for a heat exchanger to the maximum possible heat transfer rate +.E.max CH0>*+; 1What is the nature of radiation? ' the propagation of a collection of particles termed photons or uanta What two important features characterie radiation? ' freuency#wavelength and directionality What is the physical origin of radiation emission from a surface?
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thermal euilibrium w# thermally excited conditions within the matter How does this emission affect the thermal energy of a material? ' if TsTsurr, the net heat transfer rate by radiation rad,net is from the surface will continue to cool until Ts reaches Tsurr What region of the electromagnetic spectrum is thermal radiation concentrated? ' E0-E thru E0% What is the spectacle intensity of radiation emitted by a surface? ' the rate at which radiant energy is emitt ed at the wavelength in the (,* direction, per unit area of the emitting surface normal to its direction per unit solid angle about this direction, and per unit wavelength interval dA about A What are the depending variables? ' - ,, A How can this be used to determine the rate at which matter loses thermal energy due to emission from its surface? ' because it is used to find dA in, dA ) 7A,e(,, A* d9E cos d What is steradian? ' the units of a solid angle, analogous to radians for plane angles How many steradians are associated with the hemisphere? ' % What is the distinction between spectral and total radiation? ' the total is the rate at which radiation is emitted per unit area at all possible wavelengths and in all possible directions ' Gpectral is the rate at which radiation of wavelength, A, is emitted i n all directions from a surface per unit wavelength What is the distinction between directional and hemispherical radiation? ' 7n hemisphere, you integrate between )0 to )% ' 7n directional, you integrate between )0 to ) #% What is total emissive power? ' 4 emission in all directions What role does it play in the surface energy balance? ' it is redundant and is often dropped What is a diffuse emitter? ' surface for which the intensity of the emitted radiation is independent of direction1 How is the intensity related to the total emissive power? ' 4 ) 7e What is irradiation? ' the intensity of the incident radiation may be related to an important radiative flux How is it related to the intensity of incident radiation? ' radiation from all directions What is radiosity? ' accounts for all radiation leaving the surface What role does it play in the surface energy balance? ' related to the intensity associated with emission and reflection What are the characteristics of (lac/body? ' it absorbs all incident radiation, regardless of wavelength and direction ' for a prescribed temperature and wavelength, no surface can emit more energy than a blackbody ' although the radiation emitted by a blackbody is a function of wavelength and temperature, it is independent of direction That is, the blackbody is a diffuse emitter 8oes such a thing exist in nature? ' no, it has to be man made What is the principle role in blac/body behavior in radiation analysis? ' blackbody exists within the cavity irrespective of whether the cavity surface is hi ghly reflective or absorbing What is >lanc/"s 8istribution? ' eu E%%[
What is Wien"s 8isplacement #aw?
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What is &tefan'(oltmann #aw? ' ' σ = 9:< x 13 How would determine the total intensity of radiation emitted by a blac/body at a prescribed temperature? ' it enables the calculation of the amount of radiation emitted in all directions and over all wavelengths
