Analytical solution of a heat transfer model for a tubular co-current diluted moving bed heat exchanger with indirect heating and thermal losses to the environment

A mathematical model for a co-current moving bed heat exchanger (MBHE) is presented. The bed is diluted and composed of spheres of uniform radius which are transported by a dragging fluid in plug flow. The gas-solid mixture is heated indirectly by a flue gas, which flows in a jacket around the MBHE. Intraparticle temperature gradients and thermal losses to the external environment are considered. The model is solved analytically by the Self-Adjoint Operator method (SAO) and numerically by a combination of the Finite Analytical (FA) and the Finite Difference (FD) method. The results show excellent agreement and the comparison with experimental data validates the model, enabling its use in the design and analysis of MBHEs for which thermal losses are a relevant factor. MBHE effectiveness is defined, and it is shown - for a selected case - that the addition of 5.0 cm thick glass wool raises it by 25.5%.