Relaxation of the Temperature of a Plate Placed in a Medium with a Lower Temperature
The present study considers the problem of cooling a perfectly heat-conducting plate in thermal contact with a stationary medium with uniform distribution of lower temperature than the initial plate’s temperature. An integral equation is obtained that describes the relaxation of the dimensionless plate temperature and depends only on one self-similar variable. An exact analytic solution of the integral equation is found, from which asymptotic formulas valid for small and large values of the dimensionless time are obtained with controlled accuracy. The analysis of graphs obtained with the help of an analytical solution and asymptotic formulas is performed. An exact analytical solution describing the temperature field of the medium around the plate is examined.