Determination of heat exchange coefficient in heat conductivity problems with asymmetric boundary conditions

This paper depicts an approximate analytical solution of the non-stationary heat conduction problem for an infinite plate under asymmetric boundary conditions of the third kind according to the heat balance integral method. The solution is a simple, engineering-friendly product of exponential and coordinate functions. The coordinate functions are found by the method of undetermined coefficients so that the asymmetric boundary conditions of the third kind meet the main criteria primarily. Satisfactory accuracy of the obtained solution for engineering use is provided by residual orthogonality condition abidance of the differential equation to the coordinate function obtained in this research. This method allows for errors by no more than 1% in the second approximation, in the range 1.0 < Fo < ∞ for Bi = 0 and Bi₂ = 0.1. The heat transfer coefficient was determined a plate surface using the named solution along with data on the temperature change at a fixed plate spot, thus solving the inverse heat conductivity problem. (paper)