The Mass and Heat Balance Model

Non-Isothermal Mass and Heat Balance Model of the Catalytic Pellet BVP with Finite External Mass and Heat Transfer Resistance 

In this section we consider the case where external mass and heat transfer resistances are not negligible, i.e., when both Sh and Nu are finite. In this case we need to solve the nonlinear material and energy balance equations simultaneously and this must be done for a coupled BVP in four dimensions. 

Here the system is modeled by two coupled second-order boundary value differential equations, one for the heat and the other for the mass balance. As usual, we will transform the two second-order DEs into one joint singular first-order four-dimensional BVP and solve it as before via MATLAB. 

The solution functions xa u) and y(w) to (5.68) and (5.69) must satisfy the four boundary conditions 

Here Sh denotes the dimensionless Sherwood number for mass transfer and Nu is the dimensionless Nusselt8 number for heat transfer. 

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