Heat and Mass Transfer Principles

For any system or process, the law of conservation of mass enables a mathematical expression of the operation by a series of equations derived from a total or overall material balance and a material balance for individual components within the system. The energy balance provides an additional independent overall expression. This often represents the additional tool by which systems or unknown parameters can be solved for. 

Before developing specific relationships to describe cooling tower operations, it is worthwhile to review some elementary principles in developing material and energy balances. In addition, we need to review heat and mass transfer analogies before tackling design problems. The more experienced reader may wish to proceed to Chapter 4 or try the example problems at the end of the chapter as a refresher. 

---

For the control volume, the heat flux at the boundary is given as if = hc(T — T. ). The diffusion mass flux supplying the reaction is given as m" = hm(yFj00 — yF ), where from heat and mass transfer principles hm — hc/cv. Let Vand S be the volume and surface area of the control volume. The reaction rate per unit volume is given as m " — AYf E ilRT] for the fuel in this problem. 

Microscopic Balance Equations Partial differential balance equations express the conservation principles at a point in space. Equations for mass, momentum, totaf energy, and mechanical energy may be found in Whitaker (ibid.). Bird, Stewart, and Lightfoot (Transport Phenomena, Wiley, New York, 1960), and Slattery (Momentum, Heat and Mass Transfer in Continua, 2d ed., Krieger, Huntington, N.Y., 1981), for example. These references also present the equations in other useful coordinate systems besides the cartesian system. The coordinate systems are fixed in inertial reference frames. The two most used equations, for mass and momentum, are presented here. 

Some of the principles of free surface model proposed by Happel (H10, P7, P8) for studying the rate of sedimentation of solid particles may be adopted for studying heat and mass transfer in gas-liquid dispersions (R9). 

In addition to the effects of formulation factors on freeze-drying behavior, it is important for the pharmaceutical scientist to understand basic principles of heat and mass transfer in freeze-drying [29,30]. Because of the high heat input required for sublimation (670 cal/g), transfer of heat from the heated shelf to the sublimation front is often the rate-limiting step in the coupled heat... 

Aguilera, J.M. and Stanley, D.W. 1990. Simultaneous heat and mass transfer Dehydration. In Microstructural Principles of Food Processing and Engineering (J.M. Aguilera and D.W. Stanley, eds), pp. 291-329. Elsevier Applid Science, London. 

The principles of separation have been discussed using equilibrium theory. Finite resistances to heat and mass transfer will reduce the separation achieved. 

Rapid evaporation introduces complications, for the heat and mass transfer processes are then coupled. The heat of vaporization must be supplied by conduction heat transfer from the gas and liquid phases, chiefly from the gas phase. Furthermore, convective flow associated with vapor transport from the surface, Stefan flow, occurs, and thermal diffusion and the thermal energy of the diffusing species must be taken into account. Wagner 1982) reviewed the theory and principles involved, and a higher-order quasisteady-state analysis leads to the following energy balance between the net heat transferred from the gas phase and the latent heat transferred by the diffusing species ... 

Due to the severe operating conditions (high temperature and high flow rates), typical of short contact time reactions, heat and mass transfer properties are expected to play a decisive role in the behavior of the reactor. Thus, in principle, the choice of catalyst support can greatly affect the reactor performance [69]. 

These ordered array materials find interest not only in catalysis, but in several other applications, from optical materials, sensors, low-k materials, ionic conductors, photonic crystals, and bio-mimetic materials.Flowever, with respect to these applications, catalysis requires additional specific characteristics, such as the presence of a thermally stable nanostructure, the minimization of grain boundaries where side reactions may occur, and the presence of a porous structure which guarantees a high surface area coupled to low heat and mass transfer limitations. An ordered assembly of ID nanostructures for oxide materials could, in principle, meet these different requirements. 

On the theoretical side, Dmitriev and Bonchkovskaya (D8) have shown that in principle turbulence should spread from waves. Kapitsa (K9) has calculated a general tensor quantity, termed the coefficient of wavy transfer, which is applicable to any flow with periodic disturbances, such as pulsations or surface waves. This treatment predicts an appreciable increase in the rates of heat and mass transfer in wavy films, though this increase does not appear to be as large as that observed experimentally under certain conditions. 

At the present time, three-phase fluidised-beds are not often chosen for gas-liquid-solid reactions despite their advantages of good heat and mass transfer and, in principle, freedom from the blockages that can occur with fixed-beds(30). The reason may be that, because of the pronounced hydrodynamic interactions between the phases as indicated in Fig. 4.16, development of a three-phase fluidised-bed... 

Heat and Mass Transfer in Packed Beds, NWakao S Kaguei Three-Phase Catalytic Reactors, P A Ramachandran R V Chaudari Drying Principles, Applications and Design, by Cz Strumillo T Kudra... 

In principle, gas-continuous impinging streams (GIS) can be applied for the combustion of gases, powdery solids and sprayed liquids. Since gas-combustion is relatively simple and the process is essentially independent of the major feature of GIS, i.e., that it significantly enhances heat and mass transfer between phases, the discussions in this chapter will focus on the combustion of the latter two kinds of fuels. 

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. 

---