OCR Text |
Show - 7 - In the sample calculations presented, the thermophysical properties are assumed to be constant and buoyancy effects are neglected; therefore, the momentum equations are uncoupled rrom the energy equation. The thermal efficiency or the system is defined as TIt = ~x/(2L'~Y'1' Lllic) (16) The heat extracted rrom the system at the surrace or the duct is given by Q.x = ~ J [4><q,i + (l-4»q",i + t/>q.,i ]ds · 1 . j-l 0 (17) where <lg and <Is are the heat fluxes due to heat conduction in the gas and solid, respectively, <Ir is the net radiative heat flux, and s is the coordinate (x or y) along the surrace or the duct. Since the fluxes on the sides or the square duct are different, appropriate lengths or the duct are used to obtain the total heat extraction rate rrom the system by the working fluid circulated through the tube. Effect or Opacity The effect or opacity (optical dimension) was examined by performing calculations with To ranging rrom 1 to 100. Figure 2a and 2b show the isotherms in the gas and solid, respectively, ror an opacity or 5.0. The results ror an opacity or 10 are very similar and are thererore not given. As expected, the highest gas temperature is at the location where the heat is released. In general, the temperature distributions ror the opacities differing by an order or magnitude are similar. The isotherms shown in Fig.2 ror . To = 5.0 reveal that the temperature gradients are largest at the vertical side walls and at the bottom or the duct, and are smallest at the top or the duct. This means that the average convective heat flux at the side wall and bottom are larger than at the top. Examination or Fig.3 reveals that in the vicinity or the location where the heat is released the gas and solid temperatures differ greatly (by as much as 700 K). This suggests that a use or an equilibrium model, where the gas and solid temperatures are assumed to be the same would be inappropriate. Calculations have shown that the temperature distributions ror To = 5 and To = 100 are very close. This suggests that increasing the opacity To beyond 5 has little effect on the temperature. In the region past the tube, the gas temperature is very close to the solid temperature. Note that near the bottom or the bed, the temperature or the solid is higher than that or the gas ( air). This is due to the ract that the solid was heated by radiation and the air-gas mixture was assumed to enter the heater at a temperature of 300 K. Decrease in the opacity increases the maximum gas temperature and the gas temperature leaving the heater. A comparison or the convective and radiative fluxes around the tube is shown in Fig.4. The inset in the figure illustrates the coordinate (x or y) around the square channel. As expected, the convective heat flux is much larger on the rorward than the backward side or the duct. Furthermore, the radiative flux is considerably smaller than the convective flux on the bottom or the tube, but the two fluxes are or the same order or magnitude on the side and on the top or the channel. The results show that both the convective and the radiative fluxes are not sensitive to the opacity or the porous matrix To. As expected, the local radiative flux is highest ror To = 2. For To = 1 the opacity is |