A transient, two-dimensional theoretical analysis of combined heal and mass transfer in the presence of adsorption/desorption is developed to study the fundamentals of heat and mass transfer dynamics. A parallel-plate rectangular channel is used as a model system. Appropriate surface boundary conditions for heat and mass transfer and adsorption/desorption interactions are formulated. A scale analysis of the governing equations is performed in order to identify the dimensionless physical parameters governing the process and to obtain the order-of-magnitude estimates for characteristic time constants of the system dynamics. Predictions of the scale analysis are validated against the results of the parametric study obtained through the numerical solutions of the governing equations. The findings demonstrate that the scale analysis is a very powerful analytical tool which allows one to evaluate the effects of different process parameters on heat and mass transfer dynamics in the presence of adsorption without performing the exhaustive numerical calculations.