Abstract
AbstractThe present paper addresses unsteady, unidirectional heat conduction in regular solid bodies (vertical plate, horizontal cylinder, and sphere) that exchange heat by natural convection with a neighboring fluid. From thermal physics, natural convection constitutes a worst‐case scenario for forced convection cooling. Under the premises of natural convection heat transfer, the unsteady, 1‐dimensional heat conduction equation consists in a linear parabolic partial differential equation with a dominant natural convection boundary condition represented by the mean convective coefficient that depends upon temperature. As expected, the nonlinear unsteady, unidirectional heat conduction problem is complex and does not admit an exact, analytical solution. Instead, the nonlinear unsteady, unidirectional heat conduction problem forcibly necessitates approximate numerical treatment with the finite difference method. The computed dimensionless center, surface, and mean temperatures varying with dimensionless time are obtained numerically and are graphed for 3 solids: iron, aluminum, copper exposed to 3 fluids: air, water, oil; the 6 media are used in numerous engineering applications.
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