Improving convergence of summations in heat conduction (Q860071)

This paper is concerned with the study of transient heat-conduction solutions in two-dimensional rectangles heated at the \(x=0\) surface. In this case the solution is obtained by means of a double-summation formula. From the double-summation, two alternate single-sum solutions are constructed by studying a one-dimensional transient problem, first along the homogeneous \(y\)-direction, and second along the non-homogeneous \(y\)-direction. The solutions developed in this paper can be used along with the standard solutions obtained by separation of variables for checking of numerical values, in regions where both solutions are convergent.