Heat Transport Equation

Develop the heat transport equation in cylindrical coordinates for temperature. 

Here the heat flux vector for species K, taken as positive for outward heat transport. Equation (37) can be transformed by the use of equation (20) with... 

In the following, steady state mass and heat transport equations are written for species j and reaction i in each of the regions depicted in Figure 10.1. Assumptions are made that ... 

Momentum and Heat Transport Equations for Incompressible Fluids... 

A commercial Computational Fluid Dynamics package (FIDAP Version 7.6, Fluid Dynamics International, Evanston, IL) based on the finite element method was used to solve the governing continuity, momentum and heat transport equations. A mesh was defined with more nodes near the wall and the entrance of the tubular heat exchanger to resolve the larger variations of temperature and velocities near the wall and the entrance. 

The code solves four main governing equations the equilibrium equation, the flow equation, the heat transport equation, and the solute transport equation. These four equations for deformable porous media are... 

The quantities D and S must be estimated (Section 2.1.3.2). In analogy to heat transport Equation (2.1-18b) is obtained with the Nusselt number Nu (see Section 2.3.1). 

Out of equilibrium there is no such rigorous principle. However, macroscopicaUy one can find a large variety of phenomenological equations for the time evolution which are based on macroscopic quantities alone, e.g., the diffusion equation, the heat transport equation, and the Navier-Stokes equations for hydrodynamics. A microscopic dynamical theory for the time evolution of slow variables such as the momentum density or the particle density with molecular spatial resolution is highly desirable. 

The volume basis for this simple model is the material of the fins or pillars between the channels or in the slits, respectively. This specific volume is responsible for transport through a stack of several catalytically modified microstructured plates without intermediate cooling or heating. Assumption for this simple solution of the heat transport equation is a temperature constant heat production rate, so that only small predicted gradients fit the experiment. The stack height without intermediate cooling/heating is... 

Here and below we consider AS of the ORR as a positive value. The respective term in the heat transport equation represents the rate of cell heating. 

The velocity of gas flow in the CL is very small this allows us to neglect the convective term in the heat transport equation. The heat balance in the CL is, therefore, given by... 

In this section, we derive exact analytical solutions to the heat transport equations in the catalyst layers and membrane of a PEFC (Kulikovsky, 2007b). The results are illustrated by two cases when the temperature on the outer sides of the MEA is kept fixed and when the cathode side of the MEA is thermally insulated. 

In view of Eq. (5.26), 1/e thanks to the smallness of e, parameter is large ( > 10, Table 5.2) and 10. Thus, the leading term in the heat transport equations is the rate of heat exchange between air in the channel and the stack. Due to this high rate, T and Tair are close to each other and their -dependencies are well described by a simple linear law. A numerical model (lora et al., 2005) supports this conclusion. 

A. A. Kulikovsky. Heat balance in the catalyst layer and the boundary condition for heat transport equation in a low-temperature fuel cell. J. Power Sources, 162 1236-1240, 2006d. 

The mass transfer-related term in the thermal heat transport equation (4.334) is also closed using the same approximation as applied by Lindborg [97] and Lathouwers and Bellan [89] ... 

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