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where the subscript i denotes axial position, Mw and Ma are the molecular weights of water and dry air, and Cpw and Cpa are the specific heats of water and dry air respectively. The conversion of mass flow rates to molar flow rates and substitution of equations 6.18 and 6.19 in equation 6.17 yields NtFt −NtFt air Fs air −Fs Tt(i+1) − Tref air ytw(i+1) CpwMw 1 − y air + CpaMa tw(i+1) ytw(i) CpwMw 1 − y ysw(i) = + CpaMa Tt(i) − Tref Ts(i) − Tref CpwMw 1 − y + CpaMa tw(i) + CpaMa (6.20) CpwMw 1 − y sw(i) ysw(i+1) Ts(i+1) − Tref sw(i+1) where Tref is a reference temperature set equal to 298 K. We use an analogous 3 resistance model to describe the energy flux from the bulk phases to the membrane interfaces and through the membrane itself. Rate equations are (6.21) (6.22) (6.23) where Tmt and Tms are the interfacial membrane temperatures. We use analogous correlations that parallel those for mass transfer to calculate the convective heat transfer coefficients in the shell and tube, hs and ht, respectively. We assumed a constant value for the membrane thermal conductivity, km, ascertained by Khandelwal and Mench.3 Similarly to mass transfer, the steady state rates of enthalpy transfer are set equal, i.e., q1dA1 = q2dA2 = q3dA3 (6.24) q1 = −ht (Tt − Tmt) q2 = −km (Tmt − Tms) lm q3 = −hs (Ts − Tms) 112PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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