Reproducing Kernel Method to Detect the Temperature Distribution for Annular Fins with Temperature-Dependent Thermal Conductivity

摘要

The efficiency of convective straight fins with temperature dependent thermal conductivity is determined by means of the reproducing kernel (RK) method. The RK space W3[0,λ ?1] is constructed so thatevery function satisfies the boundary conditions of the problem. Therepresentation of the exact solution is given in the form of a seriesand the approximation is obtained by its truncation. The paper (i)derives the error estimates, (ii) proves the convergence and (iii) develops an iterative algorithm for obtaining the solution in the spaceW3[0,λ ?1]. The results obtained by the proposed method are compared with those given by schemes in previous works demonstratinga fast convergence and high precision.