How to Deal with Heat of Adsorption in Microscopic Mathematical Modeling of Adsorbent–Fluid Systems?

The placement of the heat of adsorption term in microscopic mathematical models significantly influences predicted transport behavior and system performance. This term may be incorporated either in the thermal energy equation or in the boundary condition at the adsorbent–fluid interface. In this study, the implications of these two formulations were investigated for adsorption heat pumps applications utilizing adsorbent coatings. Results showed that, generally, longer heat pump cycle durations were observed when the heat of adsorption term was included in the boundary condition at the adsorbent–fluid interface. Characteristics of water adsorption isotherms of the adsorbents, including their regeneration temperatures, had notable impact on the results. A dimensionless analysis based on the Fourier/Lewis (Fo/Le) ratio was introduced to interpret the results in terms of underlying transport regimes. It was shown that the discrepancy between the two formulations depended strongly on this ratio, which reflected the relative effectiveness of mass diffusion over the coating thickness. At low Fo/Le values, where mass transfer resistance dominated, the predictions of the two formulations remained relatively close. In contrast, at moderate to high Fo/Le values, the adsorption process became increasingly sensitive to surface thermal conditions, leading to significant divergence between the two approaches. Validation was performed using experimental data for zeolite NaA, based on optimum coating thickness derived from adsorption kinetics. The formulation incorporating the heat of adsorption in the boundary condition was found to provide significantly better agreement with experimental observation, while the other formulation overpredicted the optimum thickness.