problem4-46 - PROBLEM 4.46 KNOWN: Steady-state temperatures...

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PROBLEM 4.46 KNOWN: Steady-state temperatures at selected nodal points of the symmetrical section of a flow channel with uniform internal volumetric generation of heat. Inner and outer surfaces of channel xperience convection. e FIND: (a) Temperatures at nodes 1, 4, 7, and 9, (b) Heat rate per unit length (W/m) from the outer surface A to the adjacent fluid, (c) Heat rate per unit length (W/m) from the inner fluid to surface B, nd (d) Verify that results are consistent with an overall energy balance. a SCHEMATIC: A SSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties. ANALYSIS: (a) The nodal finite-difference equations are obtained from energy balances on control olumes about the nodes shown in the schematics below. v N ode 1 abcdg qqqqE ′′′′ ++++ = ± 0 () 31 21 TT 0k y / 2 k x / 2 0q x y / 4 0 xy ++Δ Δ = ΔΔ ± 2 12 3 T / 2 q x / 4 =+ + Δ ± k ° ( ) ( ) 63 6 2 1 T 95.47 117.3 C / 2 10 W / m 25 25 10 m / 4 10 W / m K 122.0 C ° + × × × = N ode 4 abcdef g qqqqqqE ′′′′′′ ++++++ = ± 0 ( ) 24 i, i 4 i k x/2 h y/2 T T h x/2 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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problem4-46 - PROBLEM 4.46 KNOWN: Steady-state temperatures...

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