Author(s)

K.M. Al-Suleiman

Abstract

Accuracy and stability of a series solution for a horizontal thermal layer K.M. Al-Suleiman Institute of Atomic Energy Research, King Abdulaziz City for Science and Technology Saudi Arabia ABSTRACT A series solution to a one dimensional transient heat conduction problem, insulated from below and subjected to connective conditions at the top boundary, is computed. The accuracy and stability of the solution is investigated. Also, the steady state version of the series solution is compared to the corresponding analytical initial temperature distribution. INTRODUCTION Since the density of a fluid decreases with increasing temperature, an unstable situation may occur when denser fluid layers lie above less dense fluid layers. Heating of the fluid from below or internally will produce such situations. Such cases are encountered in nuclear reactor design and safety problems, as well as problems of convection in the earth's mantle. The problem

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