Plain correlation asymptotes to predict the center and mean temperatures and total heat transfer in simple solid objects with uniform surface temperature at limiting small-time conditions

Abstract

Within the platform of unsteady, one-dimensional heat conduction in simple solid objects (large plate, long cylinder and sphere) cooled/heated with uniform surface temperature, the three important thermal quantities that need to be quantified are: the center temperature, the mean temperature and the total heat transfer. One objective of the study is the accurate determination of new dimensionless critical times for the mean and center temperatures that describe the large time sub-domain using a symbolic algebra software. Another objective of the study is to use regression analysis to construct plain correlation asymptotes for the center temperature, the mean temperature and the total heat transfer in the small time sub-domain using as input data the exact, analytical temperature distributions for the plate, cylinder and sphere expressed by infinite series for all time. Excellent agreement for the center temperature, mean temperature and total heat transfer are achieved in the small time sub-domain using the two different computational procedures.