problem4S.3 - PROBLEM 4S.3 KNOWN Structural member with...

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PROBLEM 4S.3 KNOWN: Structural member with known thermal conductivity subjected to a temperature difference. FIND: (a) Temperature at a prescribed point P, (b) Heat transfer per unit length of the strut, (c) Sketch the 25, 50 and 75 ° C isotherms, and (d) Same analysis on the shape but with adiabatic-isothermal oundary conditions reversed. b SCHEMATIC: ASSUMPTIONS: (1) Two-dimensional conduction, (2) Steady-state conditions, (3) Constant properties. ANALYSIS: (a) When constructing the flux plot, note that the line of symmetry which passes through the point P is an isotherm as shown above. It follows that ( ) ( ) ( ) 1 2 T P T T 2 100 0 C 2 50 C = + = + = D D . < (b) The flux plot on the symmetrical section is now constructed to obtain the shape factor from which the eat rate is determined. That is, from Equation 4S.6 and 4S.7, h ( ) 1 2 q kS T T and S M N = = A . (1,2) F rom the plot of the symmetrical section, o S 4.2 4 1.05 = = A A . For the full section of the strut, o M M 4.2 = = but N = 2N o = 8. Hence, o S S 2 0.53 = = A and with q q ′ = A , giving ( ) q 75W m K 0.53 100 0 C 3975W m = × = D A .
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