SOLUTIONS TO FOURIERS EQUATION AND UNSTEADY HEAT-FLOW THROUGH STRUCTURES

The Fourier continuity equation for unsteady heat flow in one dimension underlies most solutions for unsteady heat flow in building structures and other situations. It can be solved numerically and it also leads to a number of families of analytical solutions in which distance x and time t variously appear: (i) in product form, (ii) independently and leading to two distinct situations, and (iii) in quotient form. These basic solutions are discussed for a homogeneous solid, of either finite oi semi-infinite thickness. Developments are indicated involving several slabs and/or surface films so as to include convection and radiation at exposed surfaces, their applications are discussed in the field of building heat transfer and a number of forms are provided for the ratio of heat flow to temperature at an exposed surface.