ANALYTICAL TEMPERATURE DISTRIBUTION FOR MULTIDIMENSIONAL BODIES EXPOSED TO A CONSTANT SURFACE HEAT FLUX

For many decades, solutions for transient temperature distributions in multidimensional objects were determined by combining as a product the solutions of one-dimensional objects necessary to delimit the contour of these multidimensional objects. These product solutions are usually restricted to two types of boundary conditions: a constant wall temperature and a constant heat transfer coefficient

This paper considers the case of an object exposed to a constant surface heat flux. It is shown that when the surface of multidimensional object is submitted to a constant heat flux density, its temperature distribution can be obtained by the simple addition of one-dimensional temperature distributions. Only three one-dimensional solutions are necessary to solve all possible multidimensional problems. These are the solutions for a semi-infinite slab, an infinite plate and an infinite cylinder. The equations describing the temperature profile within each of these one-dimensional objects are presented as well as their graphical representations in a generalized form for rapid determination of temperatures.