Thermal transport general energy equation

Mass and energy transport occur throughout all of the various sandwich layers. These processes, along with electrochemical kinetics, are key in describing how fuel cells function. In this section, thermal transport is not considered, and all of the models discussed are isothermal and at steady state. Some other assumptions include local equilibrium, well-mixed gas channels, and ideal-gas behavior. The section is outlined as follows. First, the general fundamental equations are presented. This is followed by an examination of the various models for the fuel-cell sandwich in terms of the layers shown in Figure 5. Finally, the interplay between the various layers and the results of sandwich models are discussed. 

A fundamental fuel cell model consists of five principles of conservation mass, momentum, species, charge, and thermal energy. These transport equations are then coupled with electrochemical processes through source terms to describe reaction kinetics and electro-osmotic drag in the polymer electrolyte. Such convection—diffusion—source equations can be summarized in the following general form... 

In addition to the equation of state, it will be necessary to describe other thermodynamic properties of the fluid. These include specific heat, enthalpy, entropy, and free energy. For ideal gases the thermodynamic properties usually depend on temperature and mixture composition, with very little pressure dependence. Most descriptions of fluid behavior also depend on transport properties, including viscosity, thermal conductivity, and diffusion coefficients. These properties generally depend on temperature, pressure, and mixture composition. 

Generally speaking, we prefer to use the equations in the form of Eqs 6.40 and 6.41, rather than transform to the F form. For the numerical solutions used here, there is no advantage to the single third-order equation compared to the system of equations. Furthermore the F equation has lost any clear physical meaning. The physical form of the equations can accommodate variable densities or viscosities without difficulty, but the F form of the equations loses its appeal in this case. Finally, the overall objective is to include variable properties, as well as to consider the coupled effects of thermal energy and species transport. Therefore the discussion on the F form of the equations is included here mainly for historical perspective. 

General molecular transport equation. All three of the molecular transport processes of momentum, heat or thermal energy, and mass are characterized in the elementary sense by the same general type of transport equation. First we start by noting the following ... 

Equations (2.3-11) and (2.3-12) are general equations for the conservation of momentum, thermal energy, or mass and will be used in many sections of this text. The equations consider here only molecular transport occurring and the equations do not consider other transport mechanisms such as convection, and so on, which will be considered when the specific conservation equations are derived in later sections of this text for momentum, energy, or mass. 

In this chapter, we briefly describe fundamental concepts of heat transfer. We begin in Section 20.1 with a description of heat conduction. We base this description on three key points Fourier s law for conduction, energy transport through a thin film, and energy transport in a semi-infinite slab. In Section 20.2, we discuss energy conservation equations that are general forms of the first law of thermodynamics. In Section 20.3, we analyze interfacial heat transfer in terms of heat transfer coefficients, and in Section 20.4, we discuss numerical values of thermal conductivities, thermal diffusivities, and heat transfer coefficients. 

---