Heat is being conducted radially through a cylindrical pipe. The temperature at a radius r is T(r). In Cartesian co-ordinates,
show that
Thank you so much, but I dont understand what the first expression is and how you got it?
your saying ?
How comes?
Also for , you took the partial derivative of r with respect to x, from the equation ?
so you get this expression ;
but how does that equal the expression; ?
thank you.
All I'm doing is substituting the equation into the expression so you can see that T is a composite function of x and y, and therefore the partial of T with respect to x can be calculated using a chain rule.Thank you so much, but I dont understand what the first expression is and how you got it?
your saying ?
How comes?
Also for , you took the partial derivative of r with respect to x, from the equation ?
so you get this expression ;
but how does that equal the expression; ?
thank you.
The derivative of a function like is .
You have to apply the chain rule to find the partial of r with respect to x.
Remember that so just substitute that into the partial derivative for r with respect to x, and you get