Counter-current parallel-plate moving bed heat exchanger: An analytical solution

Counter-flow moving bed heat exchangers provide thermal and economic advantages over their co-current counterparts. Recently, Laplace transforms were used to develop an analytical solution for the set of coupled non-homogeneous equations governing co-current systems. In this work, an extension of the analysis for counter-flow configurations is presented, revealing an important dependency on the capacity ratio. The steady-state energy equations for a plate system are formulated and nondimensionalized, and an analytical solution is presented. Temperature functions, and the associated transcendental equations, for the solids and fluid are presented. The analytical expressions depend on the capacity ratio due to its influence on the location and multiplicity of roots in the Laplace domain solution. Limiting cases are explored and contrasted with expressions in the literature. A graphical analysis further depicts some of the representative behaviors of the solution.