seawater desalination in a direct contact heat exchanger

Lastly, the volumetric heat transfer coefficient ( U v )was calculated fromUa m&swhfgU v = =VeVe⋅ LMTDor,(31)m& swhfg = U vVe⋅ LMTD(32)2a being the effective heat transfer surface area ( m )and U ≅ hc. The fact ( U ≅ hc) is due to the twofactors: First is the absence of the heat transferresistance of the heat transmitting material and secondis the negligible heat transfer resistance of the dispersedphase compared to the combustion products (Kreith andBoehm, 1988). Logarithmic mean temperaturedifference ( LMTD ) was defined as( Tcp− Tsw)− ( Tp− Tsw)LMTD =(33)Tcp− TswlnTp− TswIn using LMTD , the products were assumed to exit theevaporator as superheated at T p = 375KWater vapor (10 -3 kg/s)9080706050403020100WV, Tcp = 1197 K (Propane-Air)TWV, Tcp = 1197 KWV, Tcp = 1263 K (Hydrogen-Air)TWV, Tcp = 1263 KWV, Tcp = 423 K (Hydrogen-Air)TWV, Tcp = 423 K0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Hydrogen or Propane mass flow rate (10 -3 kg/s)Figure 5. Water vapor mass flow rate with fuels mass flowrate (equal mass flow rate).We present local model resultsm& wv , m & t , wv , A e , t e ,Δ x e , and V e in Figs. (5)- (16). In Figs. (5) and (6),m& wv and m & t , wv increase with m& H 2 or m& C3H8due tothe total enthalpy carried away by the combustionproducts, or m& cp . The effect of void fraction ( ε d ) onthe cross- section area of the evaporator is shown in Fig.(7). ε d values were less than 0.1% for the Propane-aircombustion ( T cp = 1197K), Hydrogen-air combustion( T cp = 1263K), and Hydrogen-air combustion( T cp = 1263K, equal mole flow rate) and less than0.01% for the Hydrogen-air combustion ( T cp = 423K).These results indicate that indeed the dispersed phaseoccupies only a small fraction of the total evaporatorvolume.In Figs. (8)-(11),values was nearly the same forΔ xewas seen to decrease with h c ; t eT cp = 1197KandT cp = 1263K which substantially differed forT cp = 423K (See Fig. 12). As h c increased, V e wasseen to decrease. This was shown in Figs. (13)-(16).Results in Figs. (8)- (16) were included for uniform(constant) h c values. In the course of evaporation, h cchanges were reported for a bubble column design(Kendoush, 2004) and the references therein.Water vapor (10 -3 kg/s)4.543.532.521.510.50WV, Tcp = 1263 K (Hydrogen-Air)TWV, Tcp = 1263 K0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Hydrogen mass flow rate (10 -3 kg/s)Figure 6. Water vapor mass flow rate with fuel mass flow rate(equal mole flow rate).Ae (m 2 )7.06.05.04.03.02.01.00.0Propane-Air (Tcp = 1197 K)Hydrogen-Air (Tcp = 1263 K)Hydrogen-Air (Tcp = 423 K)Hydrogen-Air (Tcp = 1263 K) Eq Mole0 0.5 1 1.5 2 2.5 3 3.5Hydrogen or Propane mass flow rate (10 -3 kg/s)Figure 7. Evaporator cross-section area versus fuels massflow rate.Larger values for m& wv in Figs. (2) and (3) versus Figs.(5) and (6) was due to the properties of the combustionproducts evaluated at T cp (global model) versus T m(local model). Heat of vaporization ( h fg ) valuesdirectly plugged into the local model resulted in smallvalues for m& wv6