I Change of variables for this derivative in a heat transfer equation

[rudy]

TL;DR Summary

How to perform change of variables for an equation in my textbook. I cannot reproduce their result.

Hello-

In the attached screenshot from my textbook, I am trying to understand how they get from equation 6.5 to 6.5a. I have attached my attempt to solve it, but I am stuck evaluating the left side. I do not see how to get their result.

Relevant information:
k, T_w, T_inf, h and L are all constants.
T (no subscript) and y are the only variables.

Any suggestions are appreciated. If it helps this equation is for heat transfer from a wall to the atmosphere. The idea is that at y = 0 (or on the surface of a plate) the heat transfer by conduction and the heat transfer by convection are equal. This part I understand, I just don't understand their steps.

Thanks for any help,

-rudy

 

[BvU]

Hi,

With $\displaystyle {\partial (y/L)\over \partial y}= 1/L$ your (6) is their (6a) !

 

[rudy]

Oh snap, thanks BvU. I thought it might be something obvious.