OCR Text |
Show - 8 - not large enough, and for To = 10 it is too large for effective radiative transfer. The effect of the opacity To on the thermal efficiency TJt of the heater is shown in Fig.5. The results reveal that there is an opacity for which the thermal efficiency is maximum, for the remaining parameters being constant and with hAe = 1X10s W /m3K. As expected from the results given in Fig.4, this occurs for To ~ 2. The efficiency is lower for relatively small opacities ( To = 1), because the optical thickness is not large enough. Radiation heat transfer is not sufficiently effective and accounts for a smaller fraction of the total heat transfer rate from the bed-gas system to the tube wall. At very large opacities ( To = 100) the porous bed is too opaque, and again radiative heat transfer to the tube is greatly reduced. The thermal efficiency of the heater is quite high, because the tube wall temperature used in the sample calculations was low. The operating conditions, location where heat is generated, and the volumetric heat transfer coefficient are expected to influence thermal efficiency of the heater. Effect of Convective Heat Transfer Between Gas and Solid The effect of parameter hAe on the temperature distribution in the gas and solid is shown in Fig. 6 and 7 for hAe = 1X10· and 1X107 W /m3K, respectively. Increase in the volumetric convection coefficient hAe decreases the temperature gradients in the gas, particularly in the lower part of the heater. The effect of hAe on the temperatures in the gas and solid are shown in Figs. 8 and g. Comparison of Figs. 3, 8 and 9 reveals that the temperature difference between the gas and solid is largest for hAe = 1 X 10· W /m3K and smallest for 1 X 107 W /m3K. It is also evident that decreasing hAe increases the maximum temperature of the gas and lowers that of the solid bed. For hAe = 1 X 108 W /m3K (Fig.9) ihe solid temperature is practically equal to the gas temperature, except in the immediate vicinity where the heat source is located. The effect of the parameter hAe on the thermal efficiency of the system is shown in Fig. 10. The results reveal that the thermal efficiency TJt increases with an increase in the value of hAe. For To = 2 the efficiency reaches 62% at hAe = 1X106 W /m3K. For values of hAe > 1X106 W /m3K the efficiency is a very weak function of the parameter hAe and approaches an asymptotic value. At hAe = 1X107 W /m3K the efficiency reaches values of 63.9 and 58.1% at opacities of To = 2 and To = 5, respectively. This is understandable because as hAe very large. The gas temperature is practically equal to the temperature of the solid bed (Fig.7). Effect of Single Scattering Albedo of Bed on Thermal Performance The effect of the single scattering albedo on convective-radiative heat transfer to the tube has also been examined, and the temperature distributions in the bed and gas and the local heat fluxes were found to be similar and will not be presented. Suffice it to mention that the thermal efficiencies were found to increase with the single scattering albedo w. For example, with To = 5 and hAe = 1X10sW /m3K, the efficiencies were found to be 49.8, 51.2, 56.5 and 47.8 per cent for albedos of 0.5, 0.8, 0.95 and 0.995, respectively. In fact, as w --+ 1 and the porous matrix becomes perfectly scattering the efficiency is expected to decrease. These results show that a highly scattering porous matrix may not be best for optimizing thermal performance of the system. |