The Heat Balance Model

The Heat Balance Model Equations of the Catalytic Pellet BVP 

Note that the DE is singular at ui = 0 due to the term +(2/w) (dy/dui) on the left-hand side of (5.65). The term singular refers to the indeterminate value (2/0) 0 in (2/w) (dy/d,uj) when ui = 0 according to the required boundary condition. MATLAB can handle singular boundary problems easily. To do so, the user has to set up the differential operator dydt in a specific way. First we must rewrite (5.65) as a first-order two-dimensional system of DEs. 

Equation (5.66) contains the singular term —2 (y2(iv)/iv). This is singular for w = 0 since it asks for the division of 2/2(0) = 0 by zero there. To account for this in MATLAB and to avoid dividing by zero, we define the SingularTerm vector used in MATLAB s BVP solver as the coefficient matrix 

We can verify that this choice of S is correct by evaluating 

Once prepared, this singular BVP can be solved as before via our modified version bvp4cf singhouseqr. m of MATLAB s bvp4c.m boundary value problem solver. 

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