problem4-03 - PROBLEM 4.3 KNOWN: Temperature distribution...

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PROBLEM 4.3 K NOWN: Temperature distribution in the two-dimensional rectangular plate of Problem 4.2. FIND: Expression for the heat rate per unit thickness from the lower surface (0 x 2, 0) and result ased on first five non-zero terms of the infinite series. b SCHEMATIC: A SSUMPTIONS: (1) Two-dimensional, steady-state conduction, (2) Constant properties. A NALYSIS: The heat rate per unit thickness from the plate along the lower surface is () x2 out y 2 1 y0 x0 T qd q x , 0 k d x k T T yy ∂∂ == = = = = ′′ =− = ∫∫ d x θ (1) w here from the solution to Problem 4.2, n1 1 21 11 s i n h n y L TT 2 nx sin TT n Ls i n h n W L π ππ + = −+ ⎛⎞ ≡= ⎜⎟ ⎝⎠ . (2) E valuate the gradient of θ from Eq. (2) and substitute into Eq. (1) to obtain out 2 1 n L c o s h n y L 2n x qk T T s i n d nL s i n h n W L x + = = = = 2 out 2 1 n T T c o s ns i n h n W L L + = = x out 2 1 T T 1 c o s n i n h n L + = <
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problem4-03 - PROBLEM 4.3 KNOWN: Temperature distribution...

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