Moving bed heat exchangers have found a role in numerous industrial processes. However, analytical solutions for such systems, applicable in sizing and thermal performance analysis, have yet to be presented. In this work, the formulation and nondimensionalization of the steady-state energy equations for a co-current parallel-plate system is presented. A novel analytical solution is obtained through Laplace transforms and the expansion theorem. Temperature functions for the solids and fluid are presented, along with an exploration of limiting cases. Decreasing the Biot number and capacity ratio yields agreement with existing expressions in the literature. A graphical analysis, including contour and axial plots, depicts typical behaviors of the solution. (C) 2015 Elsevier Ltd. All rights reserved.