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Analytical Solution for Temperature Distribution in a Coated Solid Substrate: An Effective Boundary Condition Approach
H. M. Al-Qahtani and B. S.Yilbas

Heat conduction in a two-layer assembly consisting of a coating and a base substrate was considered in this work. An analytical solution for temperature distribution in the assembly was obtained for a step input heating pulse at the coating surface. Since the coating thickness is considerably smaller than the thickness of the base-substrate, an effective boundary condition was introduced through two approaches in order to resemble the coating at the base-substrate surface. The effective boundary condition simplified the analysis and minimized the mathematical complications at the coating and base-substrate interface. The resulting analytical solution was simulated to obtain temperature variation at the coating and base-substrate interface for a Ni coating at differing thicknesses. The simulation was extended to include the effects of the coating material and the heat source pulse length on the temperature distribution. It was found that both approaches of effective boundary conditions gave identical temperature distributions at the coating and base-substrate interface. The rise and fall in temperature at the interface was faster in the early heating and early cooling periods, respectively. This became more pronounced for short pulse lengths.

Keywords: Analytical solution, heating, two layers, coating, temperature.

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