SPLINE COLLOCATION SOLUTION OF COMBINED RADIATION-CONVECTION IN THERMALLY DEVELOPING FLOWS WITH SCATTERING

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Abstract
A collocation method employing piece-wise cubic splines as approximating functions and Gaussian quadrature points as the collocation points provides a very convenient technique for the solution of thermally developing combined radiation-convection problems with and without radiation scattering. It is demonstrated that this method provides an alternative noniterative technique that with a small number of equations can produce a more accurate solution than the existing iterative methods. For the solution of these problems by the collocation method, one needs only the standard software available at any computing laboratory, thus considerably reducing the preparation time for successfully setting up the problem on the computer. It is shown that the existing solution for the case of thermally developing slug flow with radiation scattering suffers from inaccuracies.

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