An approach for determining surface temperature distributions of solid objects subjected to heating applications

This study presents a simple technique of determining surface temperature values and/or distributions of solid objects of various geometrical shapes (e.g. infinite slab, infinite cylinder, and sphere) during heating in a medium under natural or forced convection conditions. In the model, the boundary condition of the third kind (i.e., 0.1 < Bi < 100) in transient heat transfer, which is commonly encountered, is used. In many practical applications ranging from metallurgy to food engineering processes, the measurement of surface temperatures of such solid objects is a remarkable problem; however, centre temperature measurements are quite easy. For this reason, simple and accurate models are required for use in practice. The proposed model depends on the centre temperature and determines the surface temperatures using the centre temperature measurements. In order to test the present analytical model, an actual example for a slab object was given and the centre and surface temperature profiles were drawn. In addition, the centre and surface temperature distributions for infinite slab, infinite cylinder, and sphere were computed for the values of 0.1, 1, 10, and 100 of the Biot number and were exhibited as reference graphics. As a result, the present model is capable of determing surface temperatures of various geometrical objects heated in any medium using their centre temperature measurements in a simple and accurate manner.