Steady State Conduction with solutions

Pagina 1

0.1 Correlations and Tables CORRELA TIONS f 0.790 ln Re 1.64 2 f 64 Re Nu 2 0.44Re0.5 0.066Re0.667 Pr 0.4 Nu 0.0376Re0.8 871 Pr 1 3 Nu x 0.332Re0.5 x Pr 1 3 Nu x 0.0296Re0.8 x Pr 1 3 Nu 0.60 0.387Ra1 6 1 0.559 Pr 9 16 8 27 2 Nu 3.66 0.0668GzL 1 0.04Gz2 3 L Nu 0.023Re0.8Pr n cooling : Tw Tb n 0.3 heating : Tw Tb n 0.4 Nu CRan Ra 109 C 0.59 n 1 4 Ra 109 C 0.10 n 1 3 Nu CRemPr 1 3 Cm Re 4 101;4 103 0.683 0 .466 Re 4 103;4 104 0.193 0 .618 Re 4 104;4 105 0.027 0 .805 Nu CRam Cm Ra 102; 104 0.850 0 .188 Ra 104; 107 0.480 0 .250 Ra 107; 1012 0.125 0 .333 One-term approximation RF o y ✓ T z, t T Ti T ✓m Tm t T Ti T Plane thickness Fo ↵t R2 y z R ✓ C exp 2Fo cos y ✓ C exp 2Fo sin Cylinder radius Fo ↵t R2 y z R ✓ C exp 2Fo J0 y ✓ C exp 2Fo 2J1 Sphere radius Fo ↵t R2 y z R ✓ C exp 2Fo sin y y ✓m 3C 3 exp 2Fo sin cos Coe cients used in the one-term approximation Bi 0.2 0.4 0.6 0.8 1 2 4 6 8 10 50 Plane 0.433 0.593 0.705 0.791 0.860 1.078 1.265 1.349 1.398 1.429 1.539 1.571 wall C 1.031 1.058 1.081 1.102 1.119 1.179 1.229 1.248 1.257 1.262 1.273 1.273 Cylinder 0.617 0.851 1.019 1.149 1.256 1.600 1.908 2.050 2.128 2.179 2.355 2.405 C 1.048 1.093 1.135 1.173 1.207 1.339 1.470 1.526 1.552 1.568 1.600 1.602 Sphere 0.759 1.053 1.265 1.432 1.572 2.030 2.456 2.652 2.766 2.836 3.076 3.142 C 1.059 1.116 1.171 1.224 1.274 1.480 1.720 1.833 1.892 1.925 1.996 2.000 Blackbody radiation function T µm K 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 50000 F0 [-] 0.067 0.273 0.481 0.634 0.738 0.808 0.856 0.890 0.914 0.985 0.995 0.999 Bessel functions x 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 J0 x 1.000 0.990 0.960 0.912 0.846 0.765 0.671 0.567 0.455 0.340 0.224 0.110 0.003 J1 x 0.000 0.100 0.196 0.287 0.369 0.440 0.498 0.542 0.570 0.582 0.577 0.556 0.520 1 0.2 1D-Steady…