Charts of heat conduction for the stepwise change of surface convection or radiation conditions

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The temperature distribution for non-steady heat conduction in solids, where the initial temperature distribution is parabolic and the surface heat flux is controlled by fluid convection or radiation, can be expressed in the following equation, regardless of solid shapes of plates, cylinders and spheres. [numerical formula] E and E' were expressed in Equations (8)～(13) for each solid shape in Table 1 and calculated by the computer for various values of parameters such as αθ/R^2, λ/Rh, and r/R. If the initial temperature distributions were uniform, temperature curves in solids were found to be parabolic at any time for dimensionless time αθ/R^2>0.2, regardless of solid shapes. E and E' for the center and surface of solids were shown in the charts for each solid shape. If these charts are used repeatedly with Equations (4) and (7), temperature distribution histories can be calculated easily for the case that the surface convection or radiation conditions (heat transfer coefficients and equilibrium temperatures) are changed stepwisely. Charts for E_<αυ> and E'_<αυ>, which serve to obtain the average temperatures, were also given. For the extreme case that the heat transfer coefficient tended toward infinity and the surface temperature became closer to the equilibrium temperature, the charts for the average temperature were shown.
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