Heat transfer - PDE second order

[momo91]

Hello,

I am working with a heat transfer problem and have been looking for ways to solve the PDE, but I am really stuck. The energy equation boils down to;



In this case U and alfa can be treated as constant. Any advice for how I can solve this? Is a coordinate change necessary to solve it, if so any good material/video that I could look into?

Have a great evening
/M

The boundary conditions are as follows;
dT/dY = 0 at y=0, x=0
T = T_s at y=+- b (symmetric) where b is the distance from the centreline of the duct to the wall.

 

[Deleted member 4993]

Hello,

I am working with a heat transfer problem and have been looking for ways to solve the PDE, but I am really stuck. The energy equation boils down to;

View attachment 22358

In this case U and alfa can be treated as constant. Any advice for how I can solve this? Is a coordinate change necessary to solve it, if so any good material/video that I could look into?

Have a great evening
/M

The boundary conditions are as follows;
dT/dY = 0 at y=0, x=0
T = T_s at y=+- b (symmetric) where b is the distance from the centreline of the duct to the wall.

Please see the responses at:

Heat equation and help with BC

Hello I have heat equation: dT/dt=d^2T/dx^2 And: T(t,0)=T(t,l)=2 T(0,x)=0 What kind of type BC is that? And I don't know what should I do in separating variables process and then what to do with series (cos or sin?). Thank you very much, Piotr

www.freemathhelp.com

 

[momo91]

Is it possible to get guidence on where I can learn/see the explanation for the solution? Unfortunetly I do not have my multivariable calculus book anymore.