problem4-61 - PROBLEM 4.61 KNOWN Long bar with trapezoidal...

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PROBLEM 4.61 KNOWN: Long bar with trapezoidal shape, uniform temperatures on two surfaces, and two insulated urfaces. s FIND: Heat transfer rate per unit length using finite-difference method with space increment of 0mm. 1 SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant roperties. p ANALYSIS: The heat rate can be found after the temperature distribution has been determined. Using the nodal network shown above with Δ x = 10mm, nine finite-difference equations must be written. Nodes 1-4 and 6-8 are interior nodes and their finite-difference equations can be written irectly from Eq. 4.29. For these nodes d (1) m,n+1 m,n-1 m+1,n m-1,n m,n T T T T 4T 0 m 1 4, 6 8. + + + = = For nodes 5 and 9 located on the diagonal, insulated boundary, the appropriate finite-difference equation follows from an energy balance on the control volume shown above (upper-right corner of schematic), in out a b E E q q = + = ± ± 0 ( ) ( ) m-1,n m,n m,n-1 m,n T T T T k y 1 k x 1 0 x y Δ ⋅ + Δ ⋅ = Δ Δ .
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