One-dimensional transient heat conduction in a bilayer finite slab: A case study in the printing process

In this work, a typical case of heat distribution is examined during a paper printing process, based on one-dimensional transient heat conduction in two-layer finite slabs with an insulated free surface, and a constant temperature free surface. Analytical solutions were obtained in non-dimensional form. Various examples of applying these solutions are presented. The accuracy of the solutions, with respect to time, is analyzed considering the eigenvalues of their infinite solutions. It is observed that the larger the number of eigenvalues in consideration, the better the accuracy of the solutions. The model related to a two-layer slab describes the simplified case in which all heat transfer occurs only by conduction. The solutions obtained are finally compared with the solutions for heat conduction in two semi-infinite solids. The comparison between the two solutions shows that results are in good agreement only during short time scales. The heat distribution study is expected to be helpful in knowing the effectiveness of various mediums to be used as the reciever during the printing process; however, there is scope for development of more robust models.