problem4-44 - PROBLEM 4.44 KNOWN: Nodal temperatures from a...

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PROBLEM 4.44 KNOWN: Nodal temperatures from a steady-state, finite-difference analysis for a one-eighth symmetrical section of a square channel. FIND: (a) Beginning with properly defined control volumes, derive the finite-difference equations for nodes 2, 4 and 7, and determine T 2 , T 4 and T 7 , and (b) Heat transfer loss per unit length from the channel, . q SCHEMATIC: Node T( ° C) 1 430 3 394 6 492 8,9 600 ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) No internal volumetric generation, (4) Constant properties. ANALYSIS: (a) Define control volumes about the nodes 2, 4, and 7, taking advantage of symmetry where appropriate and performing energy balances, in out EE 0 = ±± , with Δ x = Δ y, Node 2 : abcd qqqq ′′′′ +++= 0 () 32 62 12 2 TT hxT T k y2 kx 0 xy x Δ − +Δ = ΔΔ Δ ( ) ( ) 21 3 6 T 0.5T 0.5T T h x k T 2 h x k ⎡⎤ =+ + + Δ + Δ ⎣⎦ ( ) [] 2 2 T 0.5 430 0.5 394 492 50W m K 0.01m 1W m K 300 K 2 0.50 + × ++ × + ⎢⎥ < 2 T 422K = Node 4 : abc qqq ′′′ ++= 0 ( ) 34 4 hx 2T T 0ky 2 0 x Δ− + + Δ Δ = ( ) 43 h x k T
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This note was uploaded on 12/07/2010 for the course MAE Heat Trans taught by Professor Lee,j.s. during the Spring '10 term at Seoul National.

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problem4-44 - PROBLEM 4.44 KNOWN: Nodal temperatures from a...

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