Temperature Polarization Coefficients - Essay Example

? Temperature polarization coefficients of a process can be calculated along with heat transfer coefficients, membrane surface temperatures and heat flux components of the process through heat transfer analysis using heat and mass transfer equations. The temperature polarization coefficient is directly proportional to feed flow rate and inversely proportional to feed temperature. The effective heat transfer of the system is exhibited by the high values of temperature polarization coefficient obtained in the range of 0.86-0.94. The heat transfer resistances are determined by the feed flow rate and feed concentration, feed temperature and other operating parameters. The system heat transfer is controlled by the heat transfer in the membrane the resistance of which is 27-46 times higher than that of feed stream. 1. Heat Transfer The total heat flux (Q), across the membrane is expressed by the following equation: (1) Where, U is the overall heat transfer coefficient is bulk temperature difference among the feed and permeate sides J is the trans-membrane mass flux is the latent heat of vaporization Under steady state conditions, derived from the heat balance, the heat transfer in the individual compartments of system is represented by the following equation: (2) On the basis of equation 8, and, or the temperatures on both sides of the membrane can be estimated using the following equations: (3) (4) Further the heat transfer coefficient of the membrane (hm) can be determined on the basis of thermal conductivities of the membraneand of the vapor that fills the pores, using the equation 5. (5) The heat transfer coefficients of the boundary layer and can next be estimated experimentally or can be calculated using empirical correlations of dimensionless groups, namely Nussselt number (Nu), Reynolds number (Re) and Prandtl number (Pr). These numbers can be calculated directly from the data available for aqueous NaCl solutions and water, using the equation 6. (6) Where a, b and c are correlation coefficients dependent upon specific hydrodynamic conditions. 2. Pure Water Experimental set ups involving use of pure water and aqueous sodium chloride (NaCl) solutions were used to determine the effect of operating parameters namely feed temperature, feed flow rate and feed concentration. The primary set up included pure water operated at four selected feed temperatures viz. 40, 50, 60 and 70?C. 3. Membrane distillation coefficient and pure water flux The vapor pressure differencewas calculated at the membrane surface temperaturesand, and plotted against the steady state fluxes obtained at selected feed temperatures as illustrated in Fig 4. On the basis of equation (1), it can be concluded that the slope of the straight line of the plot thus obtained gives the value of membrane distillation coefficient, (C= 0.0004 kg/m2.h.Pa or C= 1.11E-7 kg/m2.s.Pa). The membrane distillation coefficient remains constant for a specific membrane and vapor properties. The experimentally determined value of C was equivalent to the value reported in literature (C= 8.5E-7 kg/m2.s.Pa). 4. Effect of feed temperature on permeate flux Permeate flux is largely dependent on fee temperature. Fluxes of pure water and aqueous NaCl solution is represented in Fig. 6. Elevation of feed temperature leads to a rise in permeate flux as a consequence of rise in vapor pressure of gas-liquid interface on liquid feed side, which causes a simultaneous increase in the driving force of mass transfer. 5. Effect of feed flow rate on permeate flux At a constant temperature the mass flux is dependent on feed flow rate as depicted in Fig. 7 showing the flux time curve at four feed flow rate at a constant temperature of 40?C. The mass flux rate is directly proportional to feed flow rate since a rise in feed flow rate causes a rise in turbulence, reduction of heat transfer resistance in the boundary layers and consequential rise in mass transfer rates. Moreover, the increase of feed boundary heat transfer coefficientwith Reynolds number lead to further rise membrane surface temperatureand temperature polarization coefficients as depicted in Fiq.8. As a result of higher feed surface temperatureand lower permeate surface temperaturesc leads to larger driving force resulting in elevated mass flux. Table 1 lists the examples of heat transfer coefficients. 6. Effect of feed concentration on permeate flux Feed concentrations are another major determinants of permeate flux rates, with higher concentrations leading to lower permeate flux rates as shown in Fig. 8. Vapor pressure is suspected to be the chief determinant of these changes. Decline in permeate flux rate has also been reported with time, the decrease being further accelerated by increasing feed concentrations. Concentrations of aqueous NaCl solution were seen to affect the temperature polarization and concentration polarization thus influencing heat and mass transfer and the thickness of boundary layer. A lowering of vapor pressure as a consequence of rise in concentration of aqueous NaCl solution leads to decline in the driving force across the membrane, thereby causing a lowering of permeate flux. 7. Heat Transfer Analysis: On the basis of Fig. 9 the values of temperature polarization coefficients can be deduced to lie within the range of 0.86-0.93. These values are indicative of the suitability of the system design and also portray the fact that mass transfer across the membrane is a major determinant of the process. Rise in temperature polarization coefficients (TPC) as a consequence of increased feed flow rate is due to lowering of heat transfer resistance within the boundary layer. This leads to an elevation of TPC, which results in increased driving force for mass transfer across the membrane. However TPC lowers with rise in feed temperature as depicted in Fig. 9, and there is a fall in mass flux. However, there is a simultaneous rise in heat flux invading the thermal boundary layer leading to exaggeration of temperature gradient as can be derived from Eqs (4) and (8). Table 2 provides the calculations leading to determination of heat transfer components. Heat flux rises with feed temperatures and falls with feed concentration, which concurs with the above discussion. At a constant heat transfer coefficient for the permeate stream, the system heat transfer is determined by heat transfer across the membrane. The resistance across the membrane is approximately 27-46 times larger than that for the feed stream. The loss of conduction across the membrane was 60-85%, which further rose with an increase in feed concentration, but fell with rise in feed temperatures. 8. Conclusion The temperature polarization coefficient has been demonstrated to rise with feed flow rate and fall with an increase in feed temperature. Values as high as 0.86-0.94 were obtained for temperature polarization coefficient, indicating the efficiency of system with respect to heat transfer. The system heat transfer, on the other hand is determined by the heat transfer across the membrane with its resistance for heat transfer being approximately 27-46 times greater than that for the feed stream. Read More