- #1

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- 10

## Homework Statement

Its been assumed that the surfaces T

_{L}and T

_{R}of the same constant temperature.

## Homework Equations

T

_{max}= T

_{L/R}+ (q

^{dot}

_{o}*L

^{2})/(8*k)

q = ΔT/R

R

_{convection}= 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.

T

_{L/R}= T

_{surface}= 200°C - ((0.8*10

^{6})*(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 = T

_{surface}- T

_{fluid}= 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 m

^{2}

And the heat generated, q = V*q

^{dot}

_{o}= (0.01*0.25*1)*(0.8*10

^{6}) = 2,000 W

Hence, from the thermal resistance equation q

_{o}= ΔT/R = ΔT/(1/hA) ⇒ h = q

_{o}/ (ΔT*A). h = (2000)/(100*0.525) = 38.1 W/m

^{2}K

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!

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