Integral transforms in the two‐dimensional non‐linear formulation of longitudinal fins with variable profile

Abstract

The integral transform method is employed for the hybrid numerical‐analytical solution of two‐dimensional, steady‐state heat conduction within extended surfaces of variable longitudinal profile and temperature dependent thermal conductivity. Numerical results are then obtainable with automatic accuracy, allowing for the establishment of benchmark results and for the validation of approximate solutions. Convergence rates are illustrated for longitudinal fins with trapezoidal and parabolic profiles, and for different values of the governing parameters, Biot number and aspect ratio. In addition, the classical one‐dimensional approximate solutions are critically examined for these typical non‐straight profiles, and the applicability limits are investigated.

Citation

Cotta, R.M. and Ramos, R. (1998), "Integral transforms in the two‐dimensional non‐linear formulation of longitudinal fins with variable profile", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 8 No. 1, pp. 27-42. https://doi.org/10.1108/09615539810197916