Convection heat transfer general discussion

In the previous section we discussed wall functions, which are used to reduce the number of cells. However, we must be aware that this is an approximation that, if the flow near the boundary is important, can be rather crude. In many internal flows—where all boundaries are either walls, symmetry planes, inlets, or outlets—the boundary layer may not be that important, as the flow field is often pressure determined. However, when we are predicting heat transfer, it is generally not a good idea to use wall functions, because the convective heat transfer at the walls may be inaccurately predicted. The reason is that convective heat transfer is extremely sensitive to the near-wall flow and temperature field. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

Many different models and correlations have been proposed for the prediction of the heat transfer coefficient at vertical surfaces in FFBs. At time of this writing, no single correlation or model has won general acceptance. The following discussion presents a summary of some potentially useful approaches. It is helpful to consider the total heat transfer coefficient as eomposed of convective contributions from the lean-gas phase and the dense-particle phase plus thermal radiation, as defined by Eqs. (15) and (16). All eorrela-tions based on ambient temperature data, where thermal radiation is negligible, should be considered to represent only the convective heat transfer coefficient hr. 

Prior to a general discussion on specifics of thermophysical properties and forced convective heat transfer at critical and supercritical pressures, it is important to define special terms and expressions used at these conditions. For a better understanding of these terms and expressions, their definitions are listed below together with complementary (Figs. A3.1—A3.4). 

Because the mechanisms governing mass transfer are similar to those involved in both heat transfer by conduction and convection and in momentum transfer (fluid flow), quantitative relations exist between the three processes, and these are discussed in Chapter 12. There is generally more published information available on heat transfer than on mass transfer, and these relationships often therefore provide a useful means of estimating mass transfer coefficients. 

The transfer of heat by radiation in general can be said to occur simultaneously with heat transfer by convection and conduction. Transfer by radiation tends to become more important than that by the other two mechanisms as the temperature increases. It is useful to gain an appreciation of the basic definitions of the energy flux terms, the surface property terms and their relationships while discussing radiative heat transfer. With this objective, reference may be made to Table 3.4 in which these are presented. 

The advection—diffusion equation with a source term can be solved by CFD algorithms in general. Patankar provided an excellent introduction to numerical fluid flow and heat transfer. Oran and Boris discussed numerical solutions of diffusion—convection problems with chemical reactions. Since fuel cells feature an aspect ratio of the order of 100, 0(100), the upwind scheme for the flow-field solution is applicable and proves to be very effective. Unstructured meshes are commonly employed in commercial CFD codes. 

Eckert, E.R.G. and Soehnghen. E., "Interferometric Studies on the Stability and Transition to Turbulence of a Free-Convection Boundary Layer , Proc. of the General Discussion on Heat Transfer, pp. 321-323. ASME-1ME. London. 1951. 

In addition, the heat transport at the boundary between the fixed bed and the heat exchange surface is also decisive for the heat exchange. The latter heat transport is generally described by a wall heat-transfer coefficient otB.. It lumps the complex interplay between convective flow at the tube wall and conduction transport by contact between the fixed bed and the heat exchange surface. Heat transport in packed tubes has been investigated and discussed in detail [8, 21]. How-... 

We stait this chapter with one-dimensional steady heat conduction in a plane wall, a cylinder, and a sphere, and develop relations for thennal resistances in these geometries. We also develop thermal resistance relations for convection and radiation conditions at the boundaries. Wc apply this concept to heat conduction problems in multilayer plane wails, cylinders, and spheres and generalize it to systems that involve heat transfer in two or three dimensions. We also discuss the thermal contact resislance and the overall heat transfer coefficient and develop relations for the critical radius of insulation for a cylinder and a sphere. Finally, we discuss steady heat transfer from finned surfaces and some complex geometries commonly encountered in practice through the use of conduction shape factors. 

We start this chapter with a general physical description of the convection mechanism. We then discuss (he velocity and thermal botmdary layers, and laminar and turbitlent flows. Wc continue with the discussion of the dimensionless Reynolds, Prandtl, and Nusselt nuinbers, and their physical significance. Next we derive the convection equations on the basis of mass, momentiim, and energy conservation, and obtain solutions for flow over a flat plate. We then nondimeiisionalizc Ihc convection equations, and obtain functional foiinis of friction and convection coefficients. Finally, we present analogies between momentum and heat transfer. 

The foundations of an engineering discipline may be best understood by considering the place of that discipline in relation to other engineering disciplines. Therefore, our first concern in this chapter will be to determine the place of heat transfer among engineering disciplines. Next, we shall proceed to a review of the general principles needed for heat transfer. Finally, we shall discuss the three modes of heat transfer— conduction, convection, and radiation—and introduce a five-step methodology for an inductive formulation. 

Correlations for Post-CHF Heat Transfer in Forced Convective Boiling in Channels. Despite the complexity of the phenomena involved (as discussed earlier), there have been many attempts at providing general correlations. Here, we give two such correlations that serve as examples of this approach. The previously cited reviews should be consulted for further information. 

Of the three general categories of transport processes, heat transport gets the most attention for several reasons. First, unlike momentum transfer, it occurs in both the liquid and solid states of a material. Second, it is important not only in the processing and production of materials, but in their application and use. Ultimately, the thermal properties of a material may be the most influential design parameters in selecting a material for a specific application. In the description of heat transport properties, let us limit ourselves to conduction as the primary means of transfer, while recognizing that for some processes, convection or radiation may play a more important role. Finally, we will limit the discussion here to theoretical and empirical correlations and trends in heat transport properties. Tabulated values of thermal conductivities for a variety of materials can be found in Appendix 5. 

Radiation is frequently associated with that bad nuclear stuff. However, the general scientific meaning of this word is much broader. Back in chapter 4 we discussed the concept of heat, or the process by which energy is transferred from a hotter body to a colder one. What wasn t discussed was how energy gets exchanged between objects. Heat exchange can occur via conduction, convection, and radiation. 

When strong temperature gradients exist, natural convection may be primarily induced thermally or both heat and mass transfer may play comparable roles. In these cases the situation is more complex, because the number of parameters increases. In liquid metals and semiconductors the Schmidt number, v/Dl, is several orders of magnitude greater than the Prandtl number, v/a, and this enables one to solve for the concentration profile in a rather general way without great difficulty as will be discussed next. 

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