Two nested spherical tanks with the internal and outer diameters of the 100 cm by 104 cm and 114 cm by 118 cm is used to store hot water at 100 C. Both tanks are made of boron fiber epoxy with...


Two nested spherical tanks with the internal and outer<br>diameters of the 100 cm by 104 cm and 114 cm by 118 cm is<br>used to store hot water at 100 C. Both tanks are made of boron<br>fiber epoxy with different composite compositions. The<br>thermal conductivity of the inner tank is 1.5 W/m K while the<br>outer tank has a thermal conductivity of 0.5 W/m K. The gap<br>between the tanks is filled with air (use properties of air at<br>50°C). The tank is located in an open environment at 0'C. The<br>outer surface of the tank is white painted and heat transfer<br>between the outer surface of the tank and the surrounding is<br>by natural covection and radiation. The convection heat<br>transfer coefficient at the inner and the outer surface of the<br>pipe is h 20 W/m' K and h 10 W/m K. Determine;<br>a. the rate of heat loss from the tank<br>b. the inside, outside and intermediate surface temperatures.<br>Hint: Take the outer surface temperature as 3°C for radiation<br>calculations.<br>

Extracted text: Two nested spherical tanks with the internal and outer diameters of the 100 cm by 104 cm and 114 cm by 118 cm is used to store hot water at 100 C. Both tanks are made of boron fiber epoxy with different composite compositions. The thermal conductivity of the inner tank is 1.5 W/m K while the outer tank has a thermal conductivity of 0.5 W/m K. The gap between the tanks is filled with air (use properties of air at 50°C). The tank is located in an open environment at 0'C. The outer surface of the tank is white painted and heat transfer between the outer surface of the tank and the surrounding is by natural covection and radiation. The convection heat transfer coefficient at the inner and the outer surface of the pipe is h 20 W/m' K and h 10 W/m K. Determine; a. the rate of heat loss from the tank b. the inside, outside and intermediate surface temperatures. Hint: Take the outer surface temperature as 3°C for radiation calculations.
TABLE A-15<br>Properties of air at 1 atm pressure<br>Dynamic<br>Viscosity<br>µ, kg/m-s<br>Kinematic<br>Prandtl<br>Specific<br>Heat<br>Thermal<br>Thermal<br>Temp.<br>T, °C<br>Conductivity<br>k, W/m-K<br>Density<br>Diffusivity<br>Viscosity<br>v, m?/s<br>Number<br>P, kg/m³<br>Cp, J/kg-K<br>a, m?/s<br>Pr<br>-150<br>-100<br>8.636 x 10-6<br>1.189 x 10-5<br>2.866<br>983<br>0.01171<br>4.158 x 10-6<br>3.013 x 10-6<br>0.7246<br>8.036 x 10-6<br>1.252 x 10-5<br>1.356 x 10-5<br>1.465 x 10-5<br>1.578 x 10-5<br>1.696 x 10-5<br>2.038<br>966<br>0.01582<br>5.837 x 10-6<br>0.7263<br>0.01979<br>0.02057<br>-50<br>1.582<br>999<br>1.474 x 10-5<br>9.319 x 10-6<br>0.7440<br>1.527 x 10-5<br>1.579 x 10-5<br>1.630 x 10-5<br>1.680 x 10-5<br>1.729 x 10-5<br>1.754 x 10-5<br>1.778 x 10-5<br>1.802 x 10-5<br>1.825 x 10-5<br>1.849 x 10-5<br>1.872 x 10-5<br>-40<br>-30<br>1.514<br>1.451<br>1002<br>1004<br>1.008 x 10-5<br>1.087 x 10-5<br>0.7436<br>0.7425<br>0.7408<br>0.02134<br>0.02211<br>0.02288<br>-20<br>1.394<br>1005<br>1.169 x 10-5<br>-10<br>1.341<br>1006<br>1.252 x 10-5<br>0.7387<br>1.292<br>1006<br>0.02364<br>1.818 x 10-5<br>1.338 x 10-5<br>0.7362<br>1.880 x 10-5<br>1.944 x 10-5<br>2.009 x 10-5<br>2.074 x 10-5<br>2.141 x 10-5<br>2.208 x 10-5<br>1.269<br>1006<br>0.02401<br>1.382 x 10-5<br>0.7350<br>1.246<br>1.225<br>10<br>1006<br>0.02439<br>1.426 x 10-5<br>0.7336<br>15<br>1007<br>0.02476<br>1.470 x 10-5<br>0.7323<br>1007<br>1007<br>1007<br>1.516 x 10-5<br>1.562 x 10-5<br>1.608 x 10-5<br>1.655 x 10-5<br>20<br>1.204<br>0.02514<br>0.7309<br>25<br>1.184<br>0.02551<br>0.7296<br>30<br>1.164<br>0.02588<br>0.7282<br>35<br>1.145<br>1007<br>0.02625<br>2.277 x 10-5<br>1.895 x 10-5<br>0.7268<br>2.346 x 10-5<br>2.416 x 10-5<br>2.487 x 10-5<br>2.632 x 10-5<br>2.780 x 10-5<br>2.931 x 10-5<br>1.702 x 10-5<br>1.750 x 10-5<br>1.798 x 10-5<br>40<br>1.127<br>1007<br>0.02662<br>1.918 x 10-5<br>0.7255<br>1.109<br>0.02699<br>1.941 x 10-5<br>1.963 x 10-5<br>45<br>1007<br>1007<br>0.7241<br>50<br>1.092<br>0.02735<br>0.7228<br>0.02808<br>0.02881<br>2.008 x 10-5<br>2.052 x 10-5<br>2.096 x 10-5<br>1.896 x 10-5<br>1.995 x 10-5<br>2.097 x 10-5<br>2.201 x 10-5<br>60<br>1.059<br>1007<br>0.7202<br>1.028<br>0.9994<br>70<br>1007<br>0.7177<br>0.02953<br>0.7154<br>0.7132<br>80<br>1008<br>1008<br>3.086 x 10-5<br>3.243 x 10-5<br>3.565 x 10-5<br>2.139 x 10-5<br>2.181 x 10-5<br>2.264 x 10-5<br>2.345 x 10-5<br>90<br>0.9718<br>0.03024<br>100<br>0.9458<br>1009<br>0.03095<br>2.306 x 10-5<br>0.7111<br>120<br>0.7073<br>0.7041<br>0.8977<br>1011<br>0.03235<br>2.522 x 10-5<br>0.8542<br>0.8148<br>2.745 x 10-5<br>2.975 x 10-5<br>140<br>1013<br>0.03374<br>3.898 x 10-5<br>4.241 x 10-5<br>4.593 x 10-5<br>4.954 x 10-5<br>5.890 x 10-5<br>6.871 x 10-5<br>7.892 x 10-5<br>2.420 x 10-5<br>2.504 x 10-5<br>2.577 x 10-5<br>2.760 x 10-5<br>2.934 x 10-5<br>160<br>1016<br>0.03511<br>0.7014<br>180<br>0.7788<br>1019<br>1023<br>0.03646<br>3.212 x 10-5<br>0.6992<br>200<br>0.7459<br>0.03779<br>3.455 x 10-5<br>0.6974<br>0.6746<br>250<br>300<br>1033<br>0.04104<br>4.091 x 10-5<br>0.6946<br>4.765 x 10-5<br>5.475 x 10-5<br>0.6158<br>1044<br>0.04418<br>0.6935<br>3.101 x 10-5<br>3.261 x 10-5<br>3.415 x 10-5<br>3.563 x 10-5<br>3.846 x 10-5<br>350<br>0.5664<br>1056<br>0.04721<br>0.6937<br>6.219 x 10-5<br>6.997 x 10-5<br>7.806 x 10-5<br>9.515 x 10-5<br>8.951 x 10-5<br>1.004 x 10-4<br>1.117 x 10-4<br>1.352 x 10-4<br>1.598 x 10-4<br>1.855 x 10-4<br>2.122 x 10-4<br>2.398 x 10-4<br>3.908 x 10-4<br>5.664 x 10-4<br>0.6948<br>0.6965<br>400<br>0.5243<br>1069<br>0.05015<br>450<br>0.4880<br>1081<br>0.05298<br>500<br>0.4565<br>1093<br>0.05572<br>0.6986<br>600<br>0.4042<br>1115<br>0.06093<br>0.7037<br>4.111 x 10-5<br>4.362 x 10-5<br>700<br>0.3627<br>1135<br>0.06581<br>1.133 x 10-4<br>0.7092<br>1.326 x 10-4<br>1.529 x 10-4<br>800<br>0.3289<br>1153<br>0.07037<br>0.7149<br>900<br>0.3008<br>1169<br>0.07465<br>4.600 x 10-5<br>0.7206<br>1000<br>1500<br>4.826 x 10-5<br>5.817 x 10-5<br>6.630 x 10-5<br>0.2772<br>1184<br>0.07868<br>1.741 x 10-4<br>0.7260<br>0.09599<br>2.922 x 10-4<br>4.270 x 10-4<br>0.1990<br>1234<br>0.7478<br>2000<br>0.1553<br>1264<br>0.11113<br>0.7539<br>Note: For ideal gases, the properties C, k, µ, and Pr are independent of pressure. The properties p, v, and a at a pressure P (in atm) other than 1 atm are determined<br>by multiplying the values of p at the given temperature by Pand by dividing v and a by P.<br>

Extracted text: TABLE A-15 Properties of air at 1 atm pressure Dynamic Viscosity µ, kg/m-s Kinematic Prandtl Specific Heat Thermal Thermal Temp. T, °C Conductivity k, W/m-K Density Diffusivity Viscosity v, m?/s Number P, kg/m³ Cp, J/kg-K a, m?/s Pr -150 -100 8.636 x 10-6 1.189 x 10-5 2.866 983 0.01171 4.158 x 10-6 3.013 x 10-6 0.7246 8.036 x 10-6 1.252 x 10-5 1.356 x 10-5 1.465 x 10-5 1.578 x 10-5 1.696 x 10-5 2.038 966 0.01582 5.837 x 10-6 0.7263 0.01979 0.02057 -50 1.582 999 1.474 x 10-5 9.319 x 10-6 0.7440 1.527 x 10-5 1.579 x 10-5 1.630 x 10-5 1.680 x 10-5 1.729 x 10-5 1.754 x 10-5 1.778 x 10-5 1.802 x 10-5 1.825 x 10-5 1.849 x 10-5 1.872 x 10-5 -40 -30 1.514 1.451 1002 1004 1.008 x 10-5 1.087 x 10-5 0.7436 0.7425 0.7408 0.02134 0.02211 0.02288 -20 1.394 1005 1.169 x 10-5 -10 1.341 1006 1.252 x 10-5 0.7387 1.292 1006 0.02364 1.818 x 10-5 1.338 x 10-5 0.7362 1.880 x 10-5 1.944 x 10-5 2.009 x 10-5 2.074 x 10-5 2.141 x 10-5 2.208 x 10-5 1.269 1006 0.02401 1.382 x 10-5 0.7350 1.246 1.225 10 1006 0.02439 1.426 x 10-5 0.7336 15 1007 0.02476 1.470 x 10-5 0.7323 1007 1007 1007 1.516 x 10-5 1.562 x 10-5 1.608 x 10-5 1.655 x 10-5 20 1.204 0.02514 0.7309 25 1.184 0.02551 0.7296 30 1.164 0.02588 0.7282 35 1.145 1007 0.02625 2.277 x 10-5 1.895 x 10-5 0.7268 2.346 x 10-5 2.416 x 10-5 2.487 x 10-5 2.632 x 10-5 2.780 x 10-5 2.931 x 10-5 1.702 x 10-5 1.750 x 10-5 1.798 x 10-5 40 1.127 1007 0.02662 1.918 x 10-5 0.7255 1.109 0.02699 1.941 x 10-5 1.963 x 10-5 45 1007 1007 0.7241 50 1.092 0.02735 0.7228 0.02808 0.02881 2.008 x 10-5 2.052 x 10-5 2.096 x 10-5 1.896 x 10-5 1.995 x 10-5 2.097 x 10-5 2.201 x 10-5 60 1.059 1007 0.7202 1.028 0.9994 70 1007 0.7177 0.02953 0.7154 0.7132 80 1008 1008 3.086 x 10-5 3.243 x 10-5 3.565 x 10-5 2.139 x 10-5 2.181 x 10-5 2.264 x 10-5 2.345 x 10-5 90 0.9718 0.03024 100 0.9458 1009 0.03095 2.306 x 10-5 0.7111 120 0.7073 0.7041 0.8977 1011 0.03235 2.522 x 10-5 0.8542 0.8148 2.745 x 10-5 2.975 x 10-5 140 1013 0.03374 3.898 x 10-5 4.241 x 10-5 4.593 x 10-5 4.954 x 10-5 5.890 x 10-5 6.871 x 10-5 7.892 x 10-5 2.420 x 10-5 2.504 x 10-5 2.577 x 10-5 2.760 x 10-5 2.934 x 10-5 160 1016 0.03511 0.7014 180 0.7788 1019 1023 0.03646 3.212 x 10-5 0.6992 200 0.7459 0.03779 3.455 x 10-5 0.6974 0.6746 250 300 1033 0.04104 4.091 x 10-5 0.6946 4.765 x 10-5 5.475 x 10-5 0.6158 1044 0.04418 0.6935 3.101 x 10-5 3.261 x 10-5 3.415 x 10-5 3.563 x 10-5 3.846 x 10-5 350 0.5664 1056 0.04721 0.6937 6.219 x 10-5 6.997 x 10-5 7.806 x 10-5 9.515 x 10-5 8.951 x 10-5 1.004 x 10-4 1.117 x 10-4 1.352 x 10-4 1.598 x 10-4 1.855 x 10-4 2.122 x 10-4 2.398 x 10-4 3.908 x 10-4 5.664 x 10-4 0.6948 0.6965 400 0.5243 1069 0.05015 450 0.4880 1081 0.05298 500 0.4565 1093 0.05572 0.6986 600 0.4042 1115 0.06093 0.7037 4.111 x 10-5 4.362 x 10-5 700 0.3627 1135 0.06581 1.133 x 10-4 0.7092 1.326 x 10-4 1.529 x 10-4 800 0.3289 1153 0.07037 0.7149 900 0.3008 1169 0.07465 4.600 x 10-5 0.7206 1000 1500 4.826 x 10-5 5.817 x 10-5 6.630 x 10-5 0.2772 1184 0.07868 1.741 x 10-4 0.7260 0.09599 2.922 x 10-4 4.270 x 10-4 0.1990 1234 0.7478 2000 0.1553 1264 0.11113 0.7539 Note: For ideal gases, the properties C, k, µ, and Pr are independent of pressure. The properties p, v, and a at a pressure P (in atm) other than 1 atm are determined by multiplying the values of p at the given temperature by Pand by dividing v and a by P.
Jun 11, 2022
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