Quenching of a solid sphere in oil

Abstract

Abstract. Transient heat conduction in a solid sphere quenched in oil is studied. Specifically, the influence of radius and thermal conductivity of the sphere (Biot number) on the surface temperature is investigated. The problem is extremely nonlinear because the heat transfer coefficient is a strong function of the surface temperature. In the analysis, the transient heat conduction equation and boundary conditions are transformed into a singular nonlinear Volterra Integral equation of the second kind for the surface temperature. This equation is solved numerically by a modified successive approximation method and a separable kernel approximation. Results for a sphere initially at 1144 K and cooled to 317 K are obtained over a wide range of Biot numbers and are compared with the infinite thermal conductivity approximation. The maximum difference between the infinite thermal conductivity approximation and the exact results is 24 K, 64 K, and 144 K for Blot numbers 0.1, 1.0, 10.0, respectively.