A physical approach to the finitedifference solution of the conduction equation in generalized coordinates
Abstract
A finitedifference formulation is presented for modeling conduction heat transfer in a generalized nonorthogonal curvilinear coordinate system. A control volume energy balance approach is taken in this work, and this leads to a formulation that permits direct physical interpretation. The inclusion of a convective boundary condition is demonstrated by example, and it is shown that this condition can be used to implement convective, Neumann, adiabatic, and Dirichlet boundary constraints. Three examples are examined to demonstrate the application of the generalized nonorthogonal formulation. For the three examples examined, the results agree well with previous solutions, where they are available. The examples are also used to provide the first application of the modified strongly implicit procedure for solving the algebraic equation system of a nonorthogonal coordinate formulation. The procedure is observed to perform well on three test problems.
 Publication:

Numerical Heat Transfer
 Pub Date:
 March 1982
 Bibcode:
 1982NumHT...5....1Z
 Keywords:

 Boundary Value Problems;
 Conductive Heat Transfer;
 Coordinate Transformations;
 Finite Difference Theory;
 Temperature Distribution;
 Thermodynamics;
 Adiabatic Conditions;
 Boundary Conditions;
 Constraints;
 Convective Heat Transfer;
 Convergence;
 Dirichlet Problem;
 Fluid Mechanics and Heat Transfer