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A long solid bar (k = 28 W/m·K and α = 12 × 10−6 m2/s) of...

A long solid bar (k = 28 W/m·K and α = 12 × 10−6 m2/s) of square cross section is initially at a uniform temperature of 32°C. The cross section of the bar is 20 cm × 20 cm in size, and heat is generated in it uniformly at a rate of ??̇ = 8 × 105 ??⁄??2. All four sides of the bar are subjected to convection to the ambient air at T∞ = 30 °C with a heat transfer coefficient of h = 45 W/m2·K. Using the explicit finite difference method with a mesh size of Δx = Δy = 10 cm, the centerline temperature after 20 minutes is desired. (a) Obtain the finite-difference nodal equations required to solve this problem and (b) Determine the upper limit of the time step that can be used to ensure numerical stability of the explicit finite-difference solution.
Do not solve fo the temperatures. Only construct the nodal equations and determine the limit on ∆t.

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genius_generous answered 3 years ago
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