Solving for Flux. Basic Calculus question.

[kdhutchi]

Homework Statement

Basic Question. My book describes the rate of heat transfer per unit of system area as $\dot{Q}$=$\int$$\dot{q}$dA.

The Attempt at a Solution

I'm trying to solve for the flux. I've already discovered that the correct answer question is just the derivative of $\dot{Q}$ with respect to area, but this goes against other things I've read. I thought taking the derivative of an integral with respect to the same variable as the integration yields zero. For example, if I was integrating something with respect to area, and I take the derivative of the integral with respect to area, then the whole thing cancels out. Isn't this true? How would I solve for the flux in this case?

 

[gneill]

When you integrate, the entire "argument" of the integration is the differential element of the desired function. The integration just sums them up. So for example,
$$F(x) = \int f(x) dx$$
then the differential element for F(x) is f(x)dx. That is to say, dF = f(x)dx.

Rearranging, you find dF/dx = f(x).

So in your case $d\dot{Q} = \dot{q}dA$ and $\frac{d\dot{Q}}{dA} = \dot{q}$

 

[kdhutchi]

I think I understand what you are saying. The part where you mention dF=f(x)dx comes from just taking a derivative from both sides, correct? So dividing by dx will produce the dF/dx=f(x) I sought earlier correct?

 

[gneill]

Right.

 

[kdhutchi]

Thank you for your help Gneill!