The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 50
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The inner (uniform) and outer (measured) temperature distributions are thenused as boundary conditions to a three-dimensional conduction solver which calculates the total heatflux at each point on the surface. The total heat flux is corrected for radiation to yield the net convectivetransport at each point, from which h can be determined.This method appears to have an advantage in accuracy over the heated foil technique because of themore accurate handling of substrate conduction.Transient Lumped Parameter Systems.
In the lumped parameter transient method, the specimen isassumed to be uniform in temperature at every instant through the transient. The power, e˙in , in Equation(4.6.16) is usually zero, although that is not necessary (one could simply change the power level at timezero to initiate the transient). At time zero, a transient is initiated, and the response curve recorded.The data can be interpreted, and the validity of the first-order assumption tested at the same time byplotting (T– Tfinal)/(Tinitial – Tfinal) on the log scale of semilog coordinates, with time on the algebraic scale.If the line is straight, then the system is first order and the characteristic time can be determined fromany two points on the line byt=where tt1t2T1T2Tfin======(t2 - t1 )ì T - T1 üln í finýî Tfin - T2 þ(4.6.17)characteristic time, Mc/hA, sectime at the first instanttime at the second instantspecimen temperature at the first instant, °Cspecimen temperature at the second instant, °Cspecimen temperature after a long time (fluid temperature), °CThe heat transfer coefficient is extracted from the time-constant definition.Indirect MethodsAn increasingly popular method is the extraction of h from surface-temperature variations after a stepin flow temperature using an inverse calculation method (see the section on inferential methods of heatflux measurement).
The simplest inverse method assumes one-dimensional conduction into an infinitelythick plate of constant material properties. Even highly irregular geometries can be studied with thistechnique, if the streamwise extent of the specimen is small and the testing time is short. A short timeinterval is necessary so the penetration of the thermal wave is limited to a thin layer near the surface.The short streamwise extent is necessary so the temperature response of the surface upstream does notalter the thermal step applied to the downstream surface.
This technique has been used to determine theheat transfer coefficient distribution on the inside walls of passages of irregular shape, by making thepassage in a transparent material.Naphthalene Sublimination. The equations for mass diffusion are similar to those for heat transfer,except for replacing the Prandtl number in the heat transfer equation by the Schmidt number in thediffusion equation. Thus, one could expect that the distribution of the mass transfer coefficients on asurface would mimic the distribution of the heat transfer coefficients.The most commonly used analog technique is naphthalene sublimination. As early as 1940, the masstransfer/heat transfer similarity was used to estimate the heat transfer coefficient distribution. Naphthalene© 1999 by CRC Press LLC4-204Section 4is a solid material which sublimes at a reasonable rate in air at ambient temperature.
Specimens can becast in naphthalene with good precision, and the recession of the surface mapped as a function of positionand time using automated or semiautomated measuring equipment. The surface recession over a knowninterval of time is a measure of the mass transfer rate, from which the mass transfer coefficient can bededuced.Naphthalene experiments are generally done at uniform temperature; hence, a uniform vapor pressureexists at the surface. This corresponds to the heat transfer situation of heat transfer from a uniformtemperature surface. No counterpart of the uniform heat flux situation has been produced using naphthalene, nor have there been experiments corresponding to variable wall temperature.Naphthalene sublimation experiments do not suffer from any counterpart of the conduction heattransfer in the substrate.
Conduction makes it difficult to work near discontinuities in wall temperaturein a heat transfer experiment. Details of the fine structure of mass transfer near obstructions anddiscontinuities can be resolved in naphthalene experiments, but those details might not exist in a heattransfer process. The Prandtl number of air is much lower than the Schmidt number of naphthalenediffusing in air; hence, thermal conduction would tend to blur out sharp gradients in the temperaturefield more than diffusion would blur out gradients in naphthalene concentration.The Schmidt number of naphthalene in air is about 2.5, far different than the Prandtl number of air(0.71); hence, the mass transfer coefficient deduced from a naphthalene experiment is not numericallyequal to the heat transfer coefficient which would have existed at those conditions.
The usual recommendation is to adjust for the Prandtl number of Schmidt number using a relation of the form:St Pr 2 3 = f {Re} = Sh j Sc 2j 3(4.6.18)based on laminar results. That recommendation has not been seriously tested by experiments in turbulentand separated flows. By using nominal values of the Schmidt number and Prandtl number, the heattransfer Stanton number would be 2.3 times higher than the measured Sherwood number and anuncertainty of 10% in that ratio would alter the inferred heat transfer coefficient by 23%.System Performance Matching.
Sometimes the “effective average heat transfer coefficient” for a systemis inferred from the overall behavior of the system, e.g., estimating h from the effectiveness of a heatexchanger. Values deduced by this means cannot be expected to agree well with direct measurementsunless a very sophisticated system description model is used.ReferencesMoffat, R.J., The gradient approach to thermocouple circuitry, Temperature, Its Measurement and Controlin Science and Industry, Rienhold, New York, 1962.Steinhart, J.S. and Hart, S.R., Calibration curves for thermistors, Deep Sea Res., 15, 497, 1968.Rhee, H.S., Koseff, J.R., and Street, R.L., Flow visualization of a recirculating flow by rheoscopic liquidand liquid crystal techniques, Exp. Fluids, 2, 57–64, 1984.Hollingsworth, K., Boehman, A.L., Smith, E.G., and Moffat, R.J., Measurement of temperature and heattransfer coefficient distributions in a complex flow using liquid crystal thermography and truecolor image processing, in Coll.
Pap. Heat Transfer, ASME HTD, 123, 35–42, Winter AnnualMeeting, 1989.Cooper, T.E., Field, R.J., and Meyer, J.F., Liquid crystal thermography and its application to the studyof convective heat transfer, J. Heat Transfer, 97, 442–450, 1975.Hippensteele, S.A., Russell, L.M., and Torres, F.J., Local Heat Transfer Measurements on a Large ScaleModel Turbine Blade Airfoil Using a Composite of a Heater Element and Liquid Crystals, NASATechnical Memorandum 86900, March 1985.© 1999 by CRC Press LLCHeat and Mass Transfer4-205den Ouden, C. and Hoogendoorn, C.J., Local convective heat transfer coefficients for jets impinging ona plate: experiments using a liquid crystal technique, in Proc.
of the 5th Int. Heat Transfer Conf.,Vol. 5, AIChE, New York, 1974, 293–297.Personal Communication from Erwin Meinders, March 1996. Work in progress at the Technical University of Delft under Prof. Hanjalic.Akino, N. and Kunugi, T., ASME HTD, Vol. 112, 1989.© 1999 by CRC Press LLC4-206Section 44.7 Mass TransferAnthony F. MillsIntroductionMass transfer may occur in a gas mixture, a liquid solution, or a solid solution. There are several physicalmechanisms that can transport a chemical species through a phase and transfer it across phase boundaries.The two most important mechanisms are ordinary diffusion and convection.
Mass diffusion is analogousto heat conduction and occurs whenever there is a gradient in the concentration of a species. Massconvection is essentially identical to heat convection: a fluid flow that transports heat may also transporta chemical species. The similarity of mechanisms of heat transfer and mass transfer results in themathematics often being identical, a fact that can be exploited to advantage. But there are some significantdifferences between the subjects of heat and mass transfer. One difference is the much greater varietyof physical and chemical processes that require mass transfer analysis.
Another difference is the extentto which the essential details of a given process may depend on the particular chemical system involved,and on temperature and pressure.In the next subsection, concentrations, velocities, and fluxes are defined, and special attention is paidto phase interfaces where the concentration of a chemical species is almost always discontinuous. Fick’slaw of ordinary diffusion is introduced in the third section, where other diffusion phenomena are alsodiscussed.
The fourth section presents various forms of the species conservation equation. Results fordiffusion in a stationary medium are given in the fifth section, and include steady diffusion across aplane wall, transient diffusion in a semi-infinite solid, and diffusion in a porous catalyst. Results fordiffusion in a moving medium are given in the sixth section, and the Stefan flow is introduced fordiffusion with one component stationary.
Also considered are particle combustion, droplet evaporation,and combustion of a volatile liquid hydrocarbon fuel droplet. The last section deals with mass convection.Low mass transfer rate theory is presented and how to exploit the analogy between convective heat andmass transfer is shown. Particular attention is given to situations involving simultaneous heat and masstransfer associated with evaporation or condensation.
The section closes by presenting high mass transferrate theory for convection, and gives engineering calculation methods for boundary layer flows thataccount for variable property effects.Concentrations, Velocities, and FluxesDefinitions of ConcentrationsIn a gas mixture, or liquid or solid solution, the local concentration of a mass species can be expressedin a number of ways.
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