Exact Analytical Solution for Two-Dimensional Heat Transfer Equation through a Packed Bed Reactor

Heat transfer through packed bed reactors with chemical reactions can play a crucial role in determining the performance of such systems. To explain the effects of temperatures profiles on packed bed reactors, an exact analytical model has been derived by using Hankel and Laplace transform methods. The analysis is based on a transient two-dimensional model of cylindrical coordinates in which the energy equation is solved to yield the transient parameters of a packed bed flow. The model has been used to investigate the axial, radial and time temperature profiles and the effects of superficial velocity on the analytical solution. Comparisons with the experimental results and previous works are presented and show reasonable agreement with the analytical results. The model can be used to derive simple operating maps that would help to identify the effects heat transfer parameters on axial, radial and time temperature profiles.