Engineering method of calculation temperature fields and thermal stresses in the initial stage of radiation convection heating (cooling) body with variable heat transfer coefficient, and the temperature at environment

Existing solutions of radiant and convective heating (cooling) body problems at the initial stage at unsteady heat transfer coefficients and temperatures are rather cumbersome. The purpose of this work is getting simpler dependencies. Decisions are based on the analysis of relations between the cause (heat flow) and the effect (surface temperature) in the initial period of heating. Two simple and effective engineering methods of calculation of unsteady temperature fields, and axial thermal stresses at the initial stage of heating (cooling) of body of canonical form for both convection and radiation heat transfer at variable ambient temperature and environmental factors have been developed. Some of the solutions are generic in nature, which allows significantly reducing the number of variables and thus using the graphical method of problem solving. The formulas for calculating the bulk and central temperature in the initial stage are provided; other researchers of nonlinear heat conduction problems did not usually do this. It has been found that the axial thermal stresses are determined entirely by the heat flow on the surface. The adequacy of the developed techniques is based on five cases of calculation of heating (cooling) plates under various conditions of its thermal loading. It is shown that the error in determining the surface temperature does not exceed 6%, and that the developed method can be used up to Fourier numbers.