Its been assumed that the surfaces TL and TR of the same constant temperature.
Tmax = TL/R + (qdoto*L2)/(8*k)
q = ΔT/R
Rconvection = 1/hA
The Attempt at a Solution
The problem I am having with this question is conceptualising which dimensions to use (I have no solutions to this question but I am trying to see what is realistic or not).
For part a, I have done the following:
Assuming - L = 0.01m, h = 0.25m and w (depth into page) = unit length of 1.
TL/R = Tsurface = 200°C - ((0.8*106)*(0.01)2)/(8*1) = 190°C
From a thermal network, I know that the temperature difference between the plate and the convective fluid is:
ΔT = Tsurface - Tfluid = 190°C - 90°C = 100°C
Here is my problem, assuming that my associations for the geometry are correct, the convective area (for the thermal resistance equation) should be:
A = p*L + 2*(h*w), where p = perimeter.
Hence, A = 2*(0.25 + 1)*0.01 +2*(0.025*1) = 0.525 m2
And the heat generated, q = V*qdoto = (0.01*0.25*1)*(0.8*106) = 2,000 W
Hence, from the thermal resistance equation qo = ΔT/R = ΔT/(1/hA) ⇒ h = qo / (ΔT*A). h = (2000)/(100*0.525) = 38.1 W/m2K
This seems reasonable for a fluid such as oil, but begs the question whether assuming a unit length into the page is the correct thing to do in this case (where only two dimensions are given)?
Any help would be appreciated!