A study about one-dimensional steady state heat transfer in cylindrical and spherical coordinates

Numerical Simulation of 1D Heat Conduction in Spherical and Cylindrical Coordinates by Fourth-Order Finite Difference Method

“…Before starting the spatial discretization, here it will be realized a reorganization of Equations (3)(4), respectively, as follows (adopting…”

“…To analyze the numerical efficiency of the formulation presented in this work will be presented two applications. The first makes a comparison of numerical results with the presented in [3] while the second application presents an exact solution to analyze the numerical efficiency. In both applications it was considered α = 1 and v r = 1.…”

“…This proposal is a numerical evolution in the work proposed in [3] where the Second Order Finite Difference Method is used to solve the problems governed by Equations (3)(4). It is important to emphasize that the idea of using the Fourth Order Finite Difference Method has already been successful in [4][5][6][7][8] for problems in cartesian coordinates, and thus, the same idea of solution to problems in cylindrical and spherical coordinates is now proposed.…”