hw06soln - 1. A flue passing hot exhaust gases has a square...

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1. A flue passing hot exhaust gases has a square cross section, 300 mm to a side. The walls are constructed of refractory brick 150 mm thick with a thermal conductivity of 0.85 W/m•K. Use a grid spacing of 75 mm. The outer wall is held at 25°C while the inner wall is held at 350°C. (a) From a finite control volume, derive the finite-difference equation for a two- dimensional steady interior point without energy generation. Clearly sketch the control volume, labelling the nodes and the heat transfer rates. (b) Determine the steady-state temperature distribution. (a) st out gen in E E E E = - + 0 E E out in = - (m, n) (m, n-1) (m-1, n) (m+1, n) (m, n+1) L x y 0 q q q q ) 1 n , m ( ) n , m ( ) n , 1 m ( ) n , m ( ) n , m ( ) 1 n , m ( ) n , m ( ) n , 1 m ( = - - + + + - - 0 y Δ T T xL Δ k x Δ T T yL Δ k y Δ T T xL Δ k x Δ T T yL Δ k n , m 1 n , m n , m n , 1 m 1 n , m n , m n , 1 m n , m = - + - + - - - - + + - - 0 T T T T T T T T n , m 1 n , m n , m n , 1 m 1
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hw06soln - 1. A flue passing hot exhaust gases has a square...

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