Application to regenerator

Regenerators are unsteady heat flow system to which steady state heat, flow is not strictly applicable. For most engineering applications, a regenerator can be considered in terms of heat flow analogous to a continuous recuperator as 

and to  deal with average temperature to eliminate time. By this analogy brick surfaces are at higher temperature during flue gas cycle than during cold gas cycle and temperature difference corresponds to that across the separating wall in a recuperator. Also heat flow in and out from brick is equivalent to resistance to heat flow across the separating wall in a recuperator. With this analogy we can define the overall heat transfer coefficient as applicable to regenerator as

(18)

 and  are heat transfer coefficient from flue gas to brick surface and from brick surface to air respectively.  is the thermal resistance of the separating wall which is analogous to that of brick in the regenerator.
   

Estimation of   is relatively difficult to estimate in unsteady state flow. The equivalent thermal resistance varies with the thickness of the brick and the time of contact. Its contribution is 15 to of the total resistance to flow of heat from hot to cold stream. Equation 17 can be used for regenerators keeping in mind the above limitations.

References:
D. R. Poirier and G.H.Geiger: Transport: Transport Phenomena is materials processing 1994.
R. Schuhmann: metallurgical Engineering, vol .1 Engineering principles