How do I solve a single for temperature with one PDE containing dT/dx and dT/dt?

I have a single differential equation. I am trying to solve a heat transfer problem. The equation relates the temperature of the near surroundings of a panel (T), and the front and backside temperature of a panel (Tf and Tr). This leaves me with 3 variables and 3 unknowns. I can somewhat relate the two together, like Tfront will be facing a heat source and so will definitely be higher than T rear at any point in time. But thats about it. Any help is appreciated.

EDIT

After going through the equations again, i've noticed that the two temperature terms can be combined with a dx to make a dT/dx. So now I have a single differential equation with one dT/dt term and a dT/dx term. How do I solve this now? I don't know what syntax I should use for the ode45 script, since I have a parameter with respect to another variable.

9730*dT/dt=(.1*(1-(((-2.26376*(10^-4))*T^2)+((6.9035*(10^-2))*T)+26.1855203))... cosd(24.5)(1006.5)+(5.672*10^(-8))*.9*T^4)+dT/dx

[Torsten]

Posting the equation for T might help.

[Alessandro Maria Laspina]

Posted.

Answer 1

[Star Strider]

If you need to estimate the other parameter, see Optimizing a Simulation or Ordinary Differential Equation (link).

[Alessandro Maria Laspina]

I actually have an ode with one dT/dt term and one dT/dx term. Is it solvable?

Answer 2

[Torsten]

This is a partial differential equation for T.

If [a;b] is the x-interval on which you want to solve the equation and a=x1<x2<...<xn=b is a spatial grid, you can discretize dT/dx in x=xi as (T(i+1))-T(i))/(x(i+1)-x(i)) for 1<=i<n.

The resulting system of ordinary differential equations for the temperatures in the grid points then reads

9730*dT(i)/dt=(.1*(1-(((-2.26376*(10^-4))*T(i)^2)+((6.9035*(10^-2))*T(i))+26.1855203))...
    * cosd(24.5)*(1006.5)+(5.672*10^(-8))*.9*T(i)^4)+(T(i+1))-T(i))/(x(i+1)-x(i))

for 1<=i<n.

and a specified temperature T(n) at x=xn.

You can use ODE15S to solve.

Look up "method of lines" for more details.

Best wishes

Torsten.

[Alessandro Maria Laspina]

I tried to implement this in matlab but I have issues with the syntax. I've followed the page for ode15s but I still am a little clueless. Could you refer me to an example?

[Torsten]

https://de.mathworks.com/matlabcentral/answers/371313-error-in-solving-system-of-two-reaction-diffusion-equations

Best wishes

Torsten.

[Alessandro Maria Laspina]

I have already followed the cfs format. I do not have a second order term in my equation and I believe it was the reason for the errors I was receiving. Ill post the error up in a bit.