Question

list the assumptions (if appropriate), provide a sketch (if appropriate)

A thin flat plate of length L-120 mm, thickness t=4 mm, width W=30 mm, and thermal conductivity k-20 W/m-K is thermally joined to heat sinks at different temperatures, where T(x 0) = To-100°C and T(x = L) Ti-35°C. The top surface of the plate is subjected to uniform heat flux q"-20 kW/m2, and the bottom surface of the plate is subjected to uniform convection with a convection coefficient of h-50 W/m2-K and freestream temperature Too-25°C. (a) Derive the differential equation that describes the steady-state temperature T(x) in the plate. You MUST include appropriate boundary conditions with your differential equation. You DO NOT need to solve the differential equation to find T(x). (b) Sketch what T(x) might look like for two cases: 1) specified q", and 2) q"-0. Clearly show the differences between the two cases on your sketch q" TL To h, T

Answer 1

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(b) 300 250 200 50 oo 5 0 30 20 60 80 70 50 40 distan ce mm) the mid pout at Occur Maximum temp does not shigih tacoardls the x- but the values and Auiting 6o)= Sinhx) sinh(AL inh(Az) Sinh 22 (-1-1)in (1-e) CS Scanned with CamScanner TEmp (c) C

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(i) h 200 Wm2K (ii) The value torohich (o) O Cth h= 200 Wm2 K condition o is - 4927 m2 Rea last Cunve The the twhich temp radint Cs Scanned with CamScanner