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Calculate the rate of steady heat transfer from a 8 m-by-10 m roof of a building during a cold winter day. The roof temperature can be assumed to be constant at 12°C. The air temperature outside the building is -5°C. The sky temperature is -17°C. The solar irradiation at the location is 500 W/m². The convection coefficient can be assumed to be 8 W/m².°c. The emissivity of the roof is 0.75, and solar absorptivity is D.4. Neglect any conduction via the walls to the ground. 2173 W

Calculate the rate of steady heat transfer from a 8 m-by-10 m roof of a building during a cold winter day. The roof temperature can be assumed to be constant at 12°C. The air temperature outside the building is -5°C. The sky temperature is -17°C. The solar irradiation at the location is 500 W/m². The convection coefficient can be assumed to be 8 W/m².°c. The emissivity of the roof is 0.75, and solar absorptivity is D.4. Neglect any conduction via the walls to the ground. 2173 W

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Section: Chapter Questions
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Table 4 Properties of saturated water Temp. T, °C 0.01 5 10 15 20 25 Enthalpy Specific of Heat Density p, kg/m³ Thermal Conductivity k, W/m.K Vaporization Cp, J/kg.K hfg, kJ/kg Liquid Vapor Liquid Vapor 7.384 9.593 12.35 15.76 19.94 25.03 31.19 38.58 47.39 57.83 70.14 84.55 Liquid Vapor Liquid 0.6113 999.8 0.0048 2501 4217 1854 0.561 0.0171 1.792 x 10-3 0.8721 999.9 0.0068 2490 4205 1857 0.571 0.0173 1.519 x 10-3 1.2276 999.7 0.0094 2478 4194 1862 0.580 0.0176 1.307 x 10-3 1.7051 999.1 0.0128 2466 4185 1863 0.589 0.0179 1.138 x 10-3 2.339 998.0 0.0173 2454 4182 1867 0.598 0.0182 1.002 × 10-³ 3.169 997.0 0.0231 2442 4180 1870 0.607 0.0186 0.891 x 10-3 4.246 996.0 0.0304 2431 4178 1875 0.615 0.0189 0.798 x 10-3 5.628 994.0 0.0397 2419 4178 1880 0.623 0.0192 0.720 x 10-3 992.1 0.0512 2407 4179 1885 0.631 0.0196 0.653 x 10-3 990.1 0.0655 2395 4180 1892 0.637 0.0200 0.596 x 10-3 988.1 0.0831 2383 4181 1900 0.644 0.0204 0.547 x 10-3 985.2 0.1045 2371 4183 1908 0.649 0.0208 0.504 x 10-3 983.3 0.1304 2359 4185 1916 0.654 0.0212 0.467 x 10-3 980.4 0.1614 2346 4187 1926 0.659 0.0216 0.433 x 10-3 977.5 0.1983 2334 4190 1936 0.663 0.0221 0.404 x 10-3 974.7 0.2421 2321 4193 1948 0.667 0.0225 0.378 x 10- 971.8 0.2935 2309 4197 1962 0.670 0.0230 0.355 x 10-3 968.1 0.3536 2296 4201 1977 0.673 0.0235 0.333 x 10-3 965.3 0.4235 2283 4206 1993 0.675 0.0240 0.315 × 10-3 961.5 0.5045 2270 4212 2010 0.677 0.0246 0.297 x 10-3 957.9 0.5978 2257 0.679 0.0251 0.282 x 10-3 0.682 0.0262 0.255 × 10-3 2203 0.683 0.0275 0.232 x 10-3 2174 4263 2177 0.684 0.0288 0.213 x 10-3 2145 4286 2244 0.683 0.0301 0.197 x 10-3 2114 4311 2314 0.682 0.0316 0.183 x 10-3 2083 4340 2420 0.680 0.0331 0.170 x 10-3 2050 4370 2490 0.677 0.0347 0.160 x 10-3 2015 4410 2590 0.673 0.0364 0.150 x 10-3 1979 4460 2710 0.669 0.0382 0.142 x 10-3 1941 2840 0.663 0.0401 0.134 x 10-3 1859 4610 3110 0.650 0.0442 0.122 x 10-3 1767 4760 3520 0.632 0.0487 0.111 x 10-3 1663 4970 4070 0.609 0.0540 0.102 x 10-3 1544 5280 4835 0.581 0.0605 0.094 x 10-3 1405 5750 5980 0.548 0.0695 0.086 x 10-3 1239 6540 7900 0.509 0.0836 0.078 x 10-3 1028 8240 11,870 0.469 0.110 0.070 x 10-3 720 14,690 25,800 0.427 0.178 0.060 x 10-3 0 0.043 x 10-3 101.33 4217 2029 143.27 950.6 0.8263 2230 4229 2071 198.53 943.4 1.121 4244 2120 270.1 934.6 1.496 361.3 921.7 1.965 475.8 916.6 2.546 907.4 3.256 617.8 791.7 1,002.1 897.7 4.119 887.3 5.153 876.4 6.388 1,254.4 1,553.8 4500 864.3 7.852 840.3 11.60 813.7 16.73 783.7 23.69 750.8 33.15 713.8 46.15 667.1 64.57 610.5 92.62 528.3 144.0 317.0 317.0 Saturation Pressure Psat, kPa 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 220 2,318 240 3,344 260 4,688 280 6,412 300 8,581 320 11,274 340 14,586 360 18,651 374.14 22,090 Dynamic Viscosity μ, kg/m.s Vapor 0.922 x 10-5 0.934 x 10-5 0.946 x 10-5 0.959 x 10-5 0.973 x 10-5 0.987 x 10-5 1.001 x 10-5 1.016 × 10-5 1.031 x 10-5 1.046 x 10-5 1.062 x 10-5 1.077 x 10-5 1.093 x 10-5 1.110 x 10-5 1.126 x 10-5 1.142 x 10-5 1.159 x 10-5 1.176 x 10-5 1.193 x 10-5 1.210 x 10-5 1.227 x 10-5 1.261 x 10-5 1.296 x 10-5 1.330 x 10-5 1.365 x 10-5 1.399 x 10-5 1.434 x 10-5 1.468 x 10-5 1.502 x 10-5 1.537 x 10-5 1.571 x 10-5 1.641 x 10-5 1.712 x 10-5 1.788 x 10-5 1.870 x 10-5 1.965 x 10-5 2.084 x 10-5 2.255 x 10-5 2.571 x 10-5 4.313 x 10-5 Prandtl Number Pr Liquid Vapor 13.5 11.2 1.00 9.45 1.00 8.09 1.00 7.01 1.00 6.14 1.00 5.42 1.00 4.83 1.00 4.32 1.00 3.91 1.00 3.55 1.00 3.25 1.00 2.99 1.00 2.75 1.00 2.55 1.00 1.00 2.38 2.22 1.00 1.00 1.00 1.01 2.08 1.96 1.85 1.00 1.75 1.00 1.58 1.00 1.44 1.00 1.33 1.24 1.02 1.16 1.02 1.09 1.05 1.03 1.05 0.983 1.07 0.947 1.09 0.910 1.11 0.865 1.15 0.836 1.24 0.832 1.35 0.854 1.49 0.902 1.69 1.00 1.97 1.23 2.43 2.06 3.73 Volume Expansion Coefficient B, 1/K Liquid 1.00 -0.068 × 10-3 0.015 x 10-3 0.733 x 10-3 0.138 x 10-3 0.195 X 10-3 0.247 x 10-3 0.294 x 10-3 0.337 X 10-3 0.377 x 10-3 0.415 x 10-3 0.451 x 10-3 0.484 x 10-3 0.517 x 10-3 0.548 x 10-3 0.578 x 10-3 0.607 x 10-3 0.653 x 10-3 0.670 x 10-3 0.702 x 10-3 0.716 x 10-3 0.750 x 10-3 0.798 x 10-3 0.858 x 10-3 0.913 x 10-3 0.970 x 10-3 1.025 x 10-3 1.145 x 10-3 1.178 x 10-3 1.210 x 10-3 1.280 x 10-3 1.350 x 10-3 1.520 x 10-3 1.720 x 10-3 2.000 x 10-3 2.380 x 10-3 2.950 x 10-3 = Note 1: Kinematic viscosity v and thermal diffusivity a can be calculated from their definitions, v = μ/p and a = k/pcp v/Pr. The temperatures 0.01°C, 100°C, and 374.14°C are the triple-, boiling-, and critical-point temperatures of water, respectively. The properties listed above (except the vapor density) can be used at any pressure with negligible error except at temperatures near the critical-point value. Note 2: The unit kJ/kg-°C for specific heat is equivalent to kJ/kg.K. and the unit W/m.°C for thermal conductivity is equivalent to W/m.K.
Transcribed Image Text:Table 4 Properties of saturated water Temp. T, °C 0.01 5 10 15 20 25 Enthalpy Specific of Heat Density p, kg/m³ Thermal Conductivity k, W/m.K Vaporization Cp, J/kg.K hfg, kJ/kg Liquid Vapor Liquid Vapor 7.384 9.593 12.35 15.76 19.94 25.03 31.19 38.58 47.39 57.83 70.14 84.55 Liquid Vapor Liquid 0.6113 999.8 0.0048 2501 4217 1854 0.561 0.0171 1.792 x 10-3 0.8721 999.9 0.0068 2490 4205 1857 0.571 0.0173 1.519 x 10-3 1.2276 999.7 0.0094 2478 4194 1862 0.580 0.0176 1.307 x 10-3 1.7051 999.1 0.0128 2466 4185 1863 0.589 0.0179 1.138 x 10-3 2.339 998.0 0.0173 2454 4182 1867 0.598 0.0182 1.002 × 10-³ 3.169 997.0 0.0231 2442 4180 1870 0.607 0.0186 0.891 x 10-3 4.246 996.0 0.0304 2431 4178 1875 0.615 0.0189 0.798 x 10-3 5.628 994.0 0.0397 2419 4178 1880 0.623 0.0192 0.720 x 10-3 992.1 0.0512 2407 4179 1885 0.631 0.0196 0.653 x 10-3 990.1 0.0655 2395 4180 1892 0.637 0.0200 0.596 x 10-3 988.1 0.0831 2383 4181 1900 0.644 0.0204 0.547 x 10-3 985.2 0.1045 2371 4183 1908 0.649 0.0208 0.504 x 10-3 983.3 0.1304 2359 4185 1916 0.654 0.0212 0.467 x 10-3 980.4 0.1614 2346 4187 1926 0.659 0.0216 0.433 x 10-3 977.5 0.1983 2334 4190 1936 0.663 0.0221 0.404 x 10-3 974.7 0.2421 2321 4193 1948 0.667 0.0225 0.378 x 10- 971.8 0.2935 2309 4197 1962 0.670 0.0230 0.355 x 10-3 968.1 0.3536 2296 4201 1977 0.673 0.0235 0.333 x 10-3 965.3 0.4235 2283 4206 1993 0.675 0.0240 0.315 × 10-3 961.5 0.5045 2270 4212 2010 0.677 0.0246 0.297 x 10-3 957.9 0.5978 2257 0.679 0.0251 0.282 x 10-3 0.682 0.0262 0.255 × 10-3 2203 0.683 0.0275 0.232 x 10-3 2174 4263 2177 0.684 0.0288 0.213 x 10-3 2145 4286 2244 0.683 0.0301 0.197 x 10-3 2114 4311 2314 0.682 0.0316 0.183 x 10-3 2083 4340 2420 0.680 0.0331 0.170 x 10-3 2050 4370 2490 0.677 0.0347 0.160 x 10-3 2015 4410 2590 0.673 0.0364 0.150 x 10-3 1979 4460 2710 0.669 0.0382 0.142 x 10-3 1941 2840 0.663 0.0401 0.134 x 10-3 1859 4610 3110 0.650 0.0442 0.122 x 10-3 1767 4760 3520 0.632 0.0487 0.111 x 10-3 1663 4970 4070 0.609 0.0540 0.102 x 10-3 1544 5280 4835 0.581 0.0605 0.094 x 10-3 1405 5750 5980 0.548 0.0695 0.086 x 10-3 1239 6540 7900 0.509 0.0836 0.078 x 10-3 1028 8240 11,870 0.469 0.110 0.070 x 10-3 720 14,690 25,800 0.427 0.178 0.060 x 10-3 0 0.043 x 10-3 101.33 4217 2029 143.27 950.6 0.8263 2230 4229 2071 198.53 943.4 1.121 4244 2120 270.1 934.6 1.496 361.3 921.7 1.965 475.8 916.6 2.546 907.4 3.256 617.8 791.7 1,002.1 897.7 4.119 887.3 5.153 876.4 6.388 1,254.4 1,553.8 4500 864.3 7.852 840.3 11.60 813.7 16.73 783.7 23.69 750.8 33.15 713.8 46.15 667.1 64.57 610.5 92.62 528.3 144.0 317.0 317.0 Saturation Pressure Psat, kPa 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 220 2,318 240 3,344 260 4,688 280 6,412 300 8,581 320 11,274 340 14,586 360 18,651 374.14 22,090 Dynamic Viscosity μ, kg/m.s Vapor 0.922 x 10-5 0.934 x 10-5 0.946 x 10-5 0.959 x 10-5 0.973 x 10-5 0.987 x 10-5 1.001 x 10-5 1.016 × 10-5 1.031 x 10-5 1.046 x 10-5 1.062 x 10-5 1.077 x 10-5 1.093 x 10-5 1.110 x 10-5 1.126 x 10-5 1.142 x 10-5 1.159 x 10-5 1.176 x 10-5 1.193 x 10-5 1.210 x 10-5 1.227 x 10-5 1.261 x 10-5 1.296 x 10-5 1.330 x 10-5 1.365 x 10-5 1.399 x 10-5 1.434 x 10-5 1.468 x 10-5 1.502 x 10-5 1.537 x 10-5 1.571 x 10-5 1.641 x 10-5 1.712 x 10-5 1.788 x 10-5 1.870 x 10-5 1.965 x 10-5 2.084 x 10-5 2.255 x 10-5 2.571 x 10-5 4.313 x 10-5 Prandtl Number Pr Liquid Vapor 13.5 11.2 1.00 9.45 1.00 8.09 1.00 7.01 1.00 6.14 1.00 5.42 1.00 4.83 1.00 4.32 1.00 3.91 1.00 3.55 1.00 3.25 1.00 2.99 1.00 2.75 1.00 2.55 1.00 1.00 2.38 2.22 1.00 1.00 1.00 1.01 2.08 1.96 1.85 1.00 1.75 1.00 1.58 1.00 1.44 1.00 1.33 1.24 1.02 1.16 1.02 1.09 1.05 1.03 1.05 0.983 1.07 0.947 1.09 0.910 1.11 0.865 1.15 0.836 1.24 0.832 1.35 0.854 1.49 0.902 1.69 1.00 1.97 1.23 2.43 2.06 3.73 Volume Expansion Coefficient B, 1/K Liquid 1.00 -0.068 × 10-3 0.015 x 10-3 0.733 x 10-3 0.138 x 10-3 0.195 X 10-3 0.247 x 10-3 0.294 x 10-3 0.337 X 10-3 0.377 x 10-3 0.415 x 10-3 0.451 x 10-3 0.484 x 10-3 0.517 x 10-3 0.548 x 10-3 0.578 x 10-3 0.607 x 10-3 0.653 x 10-3 0.670 x 10-3 0.702 x 10-3 0.716 x 10-3 0.750 x 10-3 0.798 x 10-3 0.858 x 10-3 0.913 x 10-3 0.970 x 10-3 1.025 x 10-3 1.145 x 10-3 1.178 x 10-3 1.210 x 10-3 1.280 x 10-3 1.350 x 10-3 1.520 x 10-3 1.720 x 10-3 2.000 x 10-3 2.380 x 10-3 2.950 x 10-3 = Note 1: Kinematic viscosity v and thermal diffusivity a can be calculated from their definitions, v = μ/p and a = k/pcp v/Pr. The temperatures 0.01°C, 100°C, and 374.14°C are the triple-, boiling-, and critical-point temperatures of water, respectively. The properties listed above (except the vapor density) can be used at any pressure with negligible error except at temperatures near the critical-point value. Note 2: The unit kJ/kg-°C for specific heat is equivalent to kJ/kg.K. and the unit W/m.°C for thermal conductivity is equivalent to W/m.K.
Calculate the rate of steady heat transfer from a 8 m-by-10 m roof of a building during a cold winter day. The roof temperature can be assumed to be constant at 12°C. The air temperature outside the building is -5°C. The sky temperature is -17°C. The solar irradiation at the location is 500 W/m². The convection coefficient can be assumed to be 8 W/m².°c. The emissivity of the roof is 0.75, and solar absorptivity is 0.4. Neglect any conduction via the walls to the ground. 2173 W
Transcribed Image Text:Calculate the rate of steady heat transfer from a 8 m-by-10 m roof of a building during a cold winter day. The roof temperature can be assumed to be constant at 12°C. The air temperature outside the building is -5°C. The sky temperature is -17°C. The solar irradiation at the location is 500 W/m². The convection coefficient can be assumed to be 8 W/m².°c. The emissivity of the roof is 0.75, and solar absorptivity is 0.4. Neglect any conduction via the walls to the ground. 2173 W
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