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How to use FVM and FDM to solve Energy equation? |
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August 2, 2016, 03:18 |
How to use FVM and FDM to solve Energy equation?
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#1 |
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danny
Join Date: Jul 2016
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The case is flow into the two parallel plates (Top and Bottom).
The plate temperature is 500K (Fixed wall temperature). Flow into temperature is 300K (Ambient temperature is 300K). Assume: 1. Steady 2. Incompressible flow 3. Uniform flow 4. No heat source u = ( + ) = 1.225 kg / m^3 u = 2 m / s ( x component velocity ) v = 0 m / s ( y component velocity ) c = 1006.43 J / kg * K |
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August 3, 2016, 18:25 |
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#2 |
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Lane Carasik
Join Date: Aug 2014
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Quote:
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August 4, 2016, 02:10 |
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#3 | |
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danny
Join Date: Jul 2016
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Quote:
Assume: length = 0.001 m width = 0.001 m u = 2 m / s = 1.225 kg / m^3 k = 0.0242 W / m*K x = y = 0.001/2 = 0.0005 m Top and bottom are 300K. Flow into temperature is 100K (Ambient temperature is 100K). Temperature distribution: 300 300 300 300 100 86.7327 82.346 86.8175 100 90.4783 89.4623 96.7346 300 300 300 300 The temperature distribution is use MATLAB to solve. Code: u = 2; dx = 0.005; a = 0.0242/(1.225*1006.43); A = [2*u*dx-6*a a-u*dx 0 a 0 0;a-u*dx 2*u*dx-5*a a-u*dx 0 a 0;0 a-u*dx 2*u*dx-6*a 0 0 a;a 0 0 2*u*dx-6*a a-u*dx 0;0 a 0 a-u*dx 2*u*dx-5*a a-u*dx;0 0 0 0 2*a-u*dx 2*u*dx-6*a]; B = [100*u*dx-800*a;-600*a;100*u*dx-200*a;100*u*dx-800*a;-600*a;100*u*dx-800*a]; C = A\B C = 90.4783 89.4623 96.7346 86.7327 82.3460 86.8175 |
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