The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer

Kreith, F.; Boehm, R.F.; et. al. “Heat and Mass Transfer”Mechanical Engineering HandbookEd. Frank KreithBoca Raton: CRC Press LLC, 19991999 by CRC Press LLCcHeat and Mass TransferFrank KreithUniversity of ColoradoRobert F. BoehmUniversity of Nevada-Las Vegas4.1Introduction • Fourier’s Law • Insulations • The Plane Wall atSteady State • Long, Cylindrical Systems at Steady State • TheOverall Heat Transfer Coefficient • Critical Thickness ofInsulation • Internal Heat Generation• Fins • Transient Systems• Finite-Difference Analysis of ConductionGeorge D. RaithbyUniversity of WaterlooK. G. T. HollandsUniversity of WaterlooN.

V. Suryanarayana4.24.3Van P. CareyJohn C. Chen4.44.5Heat Exchangers ..........................................................4-1184.6Temperature and Heat Transfer Measurements...........4-182Compact Heat Exchangers • Shell-and-Tube Heat ExchangersUniversity of PennsylvaniaRam K. ShahTemperature Measurement • Heat Flux • Sensor EnvironmentalErrors • Evaluating the Heat Transfer CoefficientDelphi Harrison Thermal SystemsKenneth J. Bell4.7Oklahoma State UniversityStanford UniversityUniversity of California at Los Angeles4.8Larry W.

SwansonHeat Transfer Research InstituteVincent W. AntonettiPoughkeepsie, New YorkApplications..................................................................4-240Enhancement • Cooling Towers • Heat Pipes • CoolingElectronic EquipmentArthur E. BerglesRensselaer Polytechnic InstituteMass Transfer ...............................................................4-206Introduction • Concentrations, Velocities, and Fluxes •Mechanisms of Diffusion • Species Conservation Equation •Diffusion in a Stationary Medium • Diffusion in a MovingMedium • Mass ConvectionRobert J. MoffatAnthony F. MillsPhase-Change .................................................................4-82Boiling and Condensation • Particle Gas Convection • Meltingand FreezingLehigh UniversityNoam LiorRadiation ........................................................................4-56Nature of Thermal Radiation • Blackbody Radiation •Radiative Exchange between Opaque Surfaces • RadiativeExchange within Participating MediaPennsylvania State UniversityUniversity of California at BerkeleyConvection Heat Transfer ..............................................4-14Natural Convection • Forced Convection — External Flows •Forced Convection — Internal FlowsMichigan Technological UniversityMichael F.

ModestConduction Heat Transfer................................................4-24.9Non-Newtonian Fluids — Heat Transfer ....................4-279Introduction • Laminar Duct Heat Transfer — Purely Viscous,Time-Independent Non-Newtonian Fluids • Turbulent DuctFlow for Purely Viscous Time-Independent Non-NewtonianFluids • Viscoelastic Fluids • Free Convection Flows and HeatTransferThomas F.

Irvine, Jr.State University of New York, Stony BrookMassimo CapobianchiState University of New York, Stony Brook© 1999 by CRC Press LLC4-14-2Section 44.1 Conduction Heat TransferRobert F. BoehmIntroductionConduction heat transfer phenomena are found throughout virtually all of the physical world and theindustrial domain. The analytical description of this heat transfer mode is one of the best understood.Some of the bases of understanding of conduction date back to early history. It was recognized that byinvoking certain relatively minor simplifications, mathematical solutions resulted directly.

Some of thesewere very easily formulated. What transpired over the years was a very vigorous development ofapplications to a broad range of processes. Perhaps no single work better summarizes the wealth of thesestudies than does the book by Carslaw and Jaeger (1959). They gave solutions to a broad range ofproblems, from topics related to the cooling of the Earth to the current-carrying capacities of wires.

Thegeneral analyses given there have been applied to a range of modern-day problems, from laser heatingto temperature-control systems.Today conduction heat transfer is still an active area of research and application. A great deal ofinterest has developed in recent years in topics like contact resistance, where a temperature differencedevelops between two solids that do not have perfect contact with each other. Additional issues of currentinterest include non-Fourier conduction, where the processes occur so fast that the equation describedbelow does not apply. Also, the problems related to transport in miniaturized systems are garnering agreat deal of interest. Increased interest has also been directed to ways of handling composite materials,where the ability to conduct heat is very directional.Much of the work in conduction analysis is now accomplished by use of sophisticated computercodes.

These tools have given the heat transfer analyst the capability of solving problems in nonhomogenous media, with very complicated geometries, and with very involved boundary conditions. It is stillimportant to understand analytical ways of determining the performance of conducting systems.

At theminimum these can be used as calibrations for numerical codes.Fourier’s LawThe basis of conduction heat transfer is Fourier’s Law. This law involves the idea that the heat flux isproportional to the temperature gradient in any direction n. Thermal conductivity, k, a property ofmaterials that is temperature dependent, is the constant of proportionality.qk = - kA¶T¶n(4.1.1)In many systems the area A is a function of the distance in the direction n. One important extension isthat this can be combined with the first law of thermodynamics to yield the heat conduction equation.For constant thermal conductivity, this is given asÑ2T +q˙ G 1 ¶T=a ¶tk(4.1.2)In this equation, a is the thermal diffusivity and q̇G is the internal heat generation per unit volume.Some problems, typically steady-state, one-dimensional formulations where only the heat flux is desired,can be solved simply from Equation (4.1.1).

Most conduction analyses are performed with Equation(4.1.2). In the latter, a more general approach, the temperature distribution is found from this equationand appropriate boundary conditions. Then the heat flux, if desired, is found at any location usingEquation (4.1.1). Normally, it is the temperature distribution that is of most importance. For example,© 1999 by CRC Press LLC4-3Heat and Mass Transferit may be desirable to know through analysis if a material will reach some critical temperature, like itsmelting point.

Less frequently the heat flux is desired.While there are times when it is simply desired to understand what the temperature response of astructure is, the engineer is often faced with a need to increase or decrease heat transfer to some specificlevel. Examination of the thermal conductivity of materials gives some insight into the range of possibilities that exist through simple conduction.Of the more common engineering materials, pure copper exhibits one of the higher abilities to conductheat with a thermal conductivity approaching 400 W/m2 K.

Aluminum, also considered to be a goodconductor, has a thermal conductivity a little over half that of copper. To increase the heat transfer abovevalues possible through simple conduction, more-involved designs are necessary that incorporate a varietyof other heat transfer modes like convection and phase change.Decreasing the heat transfer is accomplished with the use of insulations.

A separate discussion ofthese follows.InsulationsInsulations are used to decrease heat flow and to decrease surface temperatures. These materials arefound in a variety of forms, typically loose fill, batt, and rigid. Even a gas, like air, can be a goodinsulator if it can be kept from moving when it is heated or cooled. A vacuum is an excellent insulator.Usually, though, the engineering approach to insulation is the addition of a low-conducting material tothe surface.

While there are many chemical forms, costs, and maximum operating temperatures ofcommon forms of insulations, it seems that when a higher operating temperature is required, many timesthe thermal conductivity and cost of the insulation will also be higher.Loose-fill insulations include such materials as milled alumina-silica (maximum operating temperatureof 1260°C and thermal conductivities in the range of 0.1 to 0.2 W/m2 K) and perlite (maximum operatingtemperature of 980°C and thermal conductivities in the range of 0.05 to 1.5 W/m2 K).

Batt-typeinsulations include one of the more common types — glass fiber. This type of insulation comes in avariety of densities, which, in turn, have a profound affect on the thermal conductivity. Thermal conductivities for glass fiber insulations can range from about 0.03 to 0.06 W/m2K. Rigid insulations showa very wide range of forms and performance characteristics. For example, a rigid insulation in foamform, polyurethane, is very lightweight, shows a very low thermal conductivity (about 0.02 W/m2 K),but has a maximum operating temperature only up to about 120°C.

Rigid insulations in refractory formshow quite different characteristics. For example, high-alumina brick is quite dense, has a thermalconductivity of about 2 W/m2 K, but can remain operational to temperatures around 1760°C. Manyinsulations are characterized in the book edited by Guyer (1989).Often, commercial insulation systems designed for high-temperature operation use a layered approach.Temperature tolerance may be critical. Perhaps a refractory is applied in the highest temperature region,an intermediate-temperature foam insulation is used in the middle section, and a high-performance, lowtemperature insulation is used on the outer side near ambient conditions.Analyses can be performed including the effects of temperature variations of thermal conductivity.However, the most frequent approach is to assume that the thermal conductivity is constant at sometemperature between the two extremes experienced by the insulation.The Plane Wall at Steady StateConsider steady-state heat transfer in a plane wall of thickness L, but of very large extent in both otherdirections.

The wall has temperature T1 on one side and T2 on the other. If the thermal conductivity isconsidered to be constant, then Equation (4.1.1) can be integrated directly to give the following result:qk =kA(T - T2 )L 1This can be used to determine the steady-state heat transfer through slabs.© 1999 by CRC Press LLC(4.1.3)4-4Section 4An electrical circuit analog is widely used in conduction analyses. This is realized by considering thetemperature difference to be analogous to a voltage difference, the heat flux to be like current flow, andthe remainder of Equation (4.1.3) to be like a thermal resistance. The latter is seen to beRk =LkA(4.1.4)Heat transfer through walls made of layers of different types of materials can be easily found by summingthe resistances in series or parallel form, as appropriate.In the design of systems, seldom is a surface temperature specified or known.