Abstract
A simple and efficient finite-difference technique using the generalized finite-difference (GFD) discretization is presented for two-dimensional heat transfer problems of irregular geometry. A finite number of nodal points are distributed in the problem domain. At every interior node the spatial derivatives of a field equation are approximated by functional values at neighboring nodes after introducing a family of shape functions for the dependent variables. The resulting simultaneous algebraic equations are solved in a usual manner. The results of two examples, a steady-state heat conduction and a steady natural convection problem, are compared with results of the finite-element and conventional finite-difference method, respectively. The present study demonstrates that, if well implemented, this method will become a handy yet efficient tool for solutions to any field problems since its mathematical concept is simple and the problem formulation is straightforward.
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