General non-isothermal case

If there is heat exchange with the surroundings, then Q 0 and an iterative solution of the coupled mass and energy equations is necessary. The usual procedure takes the following path. 

Cooper and Jeffreys [3] give a worked example in which an endothermic reaction carried out with various heating rates is considered in some detail. 

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When a chosen adsorber input x is modulated periodically in the quasi-stationary state, all the output variables of the adsorber become periodic functions of time as well. In the general non-isothermal case, four adsorber outputs can be defined pressure P and temperature Tg of the gas... 

The Classical Correspondence Principle was enunciated in reasonably general form by Read (1950) and Lee (1955) among others and discussed rigorously by Sternberg (1964) for the more general non-isothermal case. Sternberg (1964) reviews the older literature in some detail. Tao (1966) discusses correspondences between elastic and viscoelastic inertial problems in terms of Laplace transforms, essentially generalizing the work of Lee (1955). 

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