hw07soln

# hw07soln - One end of a stainless steel(AISI 316 rod of...

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Unformatted text preview: One end of a stainless steel (AISI 316) rod of diameter 10 mm and length 0.16 m is inserted into a fixture maintained at 200C. The rod, covered with an insulating sleeve, reaches a uniform temperature throughout its length. When the sleeve is removed, the rod is subjected to ambient air at 25C such that the convective heat transfer coefficient is 30 W/m 2 K. Assume one-dimensional heat transfer with constant properties (thermal conductivity 14.8 W/mK and thermal diffusivity 3.63e-6 m 2 /s). Using the explicit finite-difference technique with a spatial increment of 0.016 m, estimate the time required for the tip of the rod to reach 100C. Derive the equations from a control volume, clearly labeling nodes and heat transfer rates. Provide a copy of the code used to solve this problem. Clearly indicate the method used to solve the equations such as Fortran code, Excel spreadsheet, etc. Plot the temperature T(x,t) versus position along the rod x at this time. Assumptions: (1) One-dimensional transient conduction in rod, (2) uniform h along roda at end, (3) Negligible radiation exchange between rod and surroundings, (4) Constant properties. Analysis: (a) Choosing x=0.016 m, the finite-difference equations for the interior and end nodes are obtained. T =200 L = 0.16 m D = 10 mm T = 25 h = 30 W/m 2 K L/2 L 200 T(x, t), x T(x,0) T(x,t) T(x, ) 1 x m-1 m+1 m 9 10 T m-1 T m+1 T m q a q b q c x T 9 T...
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hw07soln - One end of a stainless steel(AISI 316 rod of...

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