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and we relate the enthalpy change in the tubes to the interfacial energy flux using air Ft ytw(i+1) air −Ft tw(i+1) ytw(i) + CpaMa (6.25) CpwMw 1 − y Tt(i+1) − Tref Tt(i) − Tref + CpaMa CpwMw 1 − y = − energy balance, equations 6.16 and 6.25, to give air Ft air Ft ytw(i+1) ytw(i) − 1 − y = −ηM tw(i) A J1 dA (6.28) (6.29) tw(i) q1 dAid We introduce overall efficiency terms into our models for mass and energy transport to account for any flow maldistributions by AηM =Aid (6.26) and AηT =Aid (6.27) where A is the actual surface area utilized accounting for poor flow distribution. Equations 6.26 and 6.27 are substituted into the corresponding tube-side mass and Aid and air −Ft tw(i+1) ytw(i) Tt(i) − Tref 1 − y CpwMw 1 − y tw(i+1) CpwMw 1 − y = −ηT + CpaMa ytw(i+1) Tt(i+1) − Tref + CpaMa tw(i) q1 dA 6.4 Results and Discussion In order to characterize the performance of the NafionT M shell and tube mem- brane module from our experiments, we solve the coupled mass and energy equations numerically with the aid of a generalized nonlinear equation solver that applies a modified Powell method.1 We model the membrane module in Figure 6.2 as a set of 113 APDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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