In a typical shell and tube membrane humidifier module, heat and moisture are exchanged between the wet and dry fluids flowing on either side of the membrane. Now, is there a correlation that governs the co-dependence of heat transfer on mass transfer?
Yes, I do believe that the heat and mass transfer is co-dependent in evaporation and condensation, related to humidification and de-humidification phenomena. In fact the world of vapor compression refrigeration is only depended on this effect to through the heat to atmosphere and extract the heat from the closed interior in air conditioning and otherwise also in heat pump applications. Marvelous invention.
There is a well-documented dependence of heat and mass transfer on the net mass transfer rate that variously goes by the names Stefan flow or the blowing factor. Generally, a net mass transfer into a surface (condensation, absorption, some forms of catalysis and combustion) increases both the heat and mass transfer coefficient relative to what it would be with no net mass transfer. Similarly, a net mass transfer out of a surface (vaporizatoin, desorption, some forms of catalysis and combustion) decreases both the heat and mass transfer coefficient relative to what it would be with no net mass transfer.
Thank you so much Prof. Baxter. Would you recommend any specific article or book which I should refer to understand more about this in detail?
Regards
Ramendra
Heat transfer and evaporation/condensation can be described by Lewis number.
In case of diffusion - such as in catalysts - increased heat transfer coefficient does NOT increase the chemical reaction.
For the calculation of the convective mass transfer coefficient in the gas phase the analogy between heat and mass transfer can be applied. If a correlation f is known for heat transfer Nu= f ( Re, Pr ), the same correlation is applicable for mass transfer in which Nu has to be replaced by Sh and Pr by Sc.: Sh = f ( Re, Sc ). Sc and Pr are functions of the composition of the fluid mixture. Depending on the boundary conditions additional corrections may be necessary. Sh=Sheerwood number= (mass transfer coefficient) (characteristic length)/ (diffusion coefficient) . Sc=Schmidt number =(kinematic viscosity)/ (diffusion coefficient). Pr= Prandtl number=(kinematic viscosity)/ (thermal diffusivity). Nu=Nußelt number= (heat transfer coefficient ) (characteristic lengt)/(thermal conductivity).
The ratio Sc/Nu may be expressed as a function of the ratio Sc/Pr=Le=Lewis number. For turbulent flow the function ln(Sc/Nu) = 1/3 ln(Le) should be applicable. As a rough approximation one could assume Le=1. Then Sc=Nu and (mass transfer coefficient)=(heat transfer coefficient)(diffusion coefficient)/ (thermal conductivity).
And finally: (mass transfer coefficient) = (heat transfer coefficient)/ (density)(isobaric specific heat capacity).
Dear Prof. Roetzel,
Thank you so much for the detailed response. As you had mentioned that the mass transfer coefficient can be derived from the heat transfer coefficient in case of Le=1. Now, does this suffice to couple the heat and mass transfer processes or is there a need to introduce a correction factor to predict the behavior of such systems?
Regards
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