SIMPLIFIED CALCULATION OF HEAT ON A FLAT SURFACE

Abstract

When building physical models of many processes are used information about the magnitude of the temperature of the structure surface and the heat flux into the design, you must have the foreseeable analytical expressions. Existing solutions to the heat equation for plates and semi-infinite space, hard understand as expressed through an infinite series of special functions or tabulated. Unfortunately, members of series are defined by the tables or graphes. In the proposed work an attempt was made to get the final expressions to determine the surface temperature and the magnitude of the heat flow directed inside design. These expressions must include values that define the decision problem - the initial and boundary conditions. If the task addresses the following options: • design is thermally thin body, when the Bio number is small (Bi < 0.14); • design is thermally thick body, when the Fourier number Fo < 0.5, the condition means that the thermal perturbation has not reached the opposite border; • body is not thermally thick, as Fo > 0.5, but is not thermally thin, because Bi > 0.14. For a thermally thin body design temperature thickness has a constant value. For thermally thick body Fo < 0.5 there are defined three ranges of surface temperature determination. The first mode is determined by the product of FoBi < 0.01 (ofFo < 0.5). The second mode is limited by the condition of 0.01 < FoBi² < 8, a third mode is realized under condition FoBi² <8. As result there are derived the final expressions for determining surface temperature and heat flux inside the structure, which includes initial and boundary conditions, and does not require other additional information.