A finitedifference formulation of the equation of heat conduction in generalized coordinates
Abstract
The equations of transient heat conduction are developed for a generalized curvilinear coordinate system in Euclidean space. The equation is then specialized for the case of twodimensional heat flow. The equations are applicable not only to planar problems but also to problems for thin surfaces. A compact finitedifference formulation for surface heat flow is given that permits variable mesh spacing, variable thickness, properties that vary spatially and with temperature, nonlinear boundary conditions, and volumetric heat generation. Example problems in nonorthogonal planar coordinates are given along with a problem for a thin curved surface.
 Publication:

Numerical Heat Transfer
 Pub Date:
 March 1979
 Bibcode:
 1979NumHT...2...61R
 Keywords:

 Conductive Heat Transfer;
 Finite Difference Theory;
 Two Dimensional Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Coordinates;
 Curves (Geometry);
 Integral Equations;
 Temperature Effects;
 Thickness;
 Transient Response;
 Fluid Mechanics and Heat Transfer