problem4-70 - PROBLEM 4.70 KNOWN: Straight fin of uniform...

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PROBLEM 4.70 K NOWN: Straight fin of uniform cross section with insulated end. FIND: (a) Temperature distribution using finite-difference method and validity of assuming one- dimensional heat transfer, (b) Fin heat transfer rate and comparison with analytical solution, Eq. 3.76, (c) ffect of convection coefficient on fin temperature distribution and heat rate. E SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction in fin, (3) Constant roperties, (4) Uniform film coefficient. p ANALYSIS: (a) From the analysis of Problem 4.43, the finite-difference equations for the nodal arrangement can be directly written. For the nodal spacing Δ x = 4 mm, there will be 12 nodes. With A >> w representing the distance normal to the page, ( ) 2 22 2 3 3 c hP h 2 h 2 500W m K 2 x x x 4 10 mm 0.0533 kA k w kw 50W m K 6 10 m ⋅⋅ × ⋅Δ Δ = Δ = × = ⋅×× A A Node 1: or -2.053T () 2 100 T 0.0533 30 2 0.0533 T 0 ++ ×− + = 1 1 + T 2 = -101.6 Node n: or n1 n T T 1.60 2.0533T 0 +− = n T 2.053T T 1.60 += Node 12: 11 12 T 0.0533 2 30 0.0533 2 1 T 0 + = or 11 12 T 1.0267T 0.800 =− Using matrix notation, Eq. 4.48, where [A] [T] = [C], the A-matrix is tridiagonal and only the non-zero
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problem4-70 - PROBLEM 4.70 KNOWN: Straight fin of uniform...

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