Dear Robert,

The last question is to how I can plot the surface temperature [ u(0,t) ] versus t.

I tried the value command but not successful.

Thanks in advance.

Mo

Dear Robert,

Another issue just came to my mind:

What is there is a constant in the equation:

u[t]=r[i]u[xx] + 1000

where 1000 is for instance a heat source. what would the mapped equation look like? will 1000 be affected?

Thanks again,

Mo

Dear Robert,

Thanks a lot for the example. I am really impressed. Through this mapping, the flux conservation at the interfaces are perfectly satisfied.

Do you think I can apply the same strategy to a more complex equation such as:

u[t]=r[i]u[xx]+exp(x)+(30-u)+A.u^2

where

u[t] is diff((x,t),t)

u[x,x] is diff((x,t),x,x)

u is u(x,t)

A is another piecewise function that specifies some constants depending on the domain.

Best regards,

Mo

Dear Robert,

Thanks a lot for the example. I am really impressed. Through this mapping, the flux conservation at the interfaces are perfectly satisfied.

Do you think I can apply the same strategy to a more complex equation such as:

u[t]=r[i]u[xx]+exp(x)+(30-u)+A.u^2

where

u[t] is diff((x,t),t)

u[x,x] is diff((x,t),x,x)

u is u(x,t)

A is another piecewise function that specifies some constants depending on the domain. 

Best regards,

Mo

Dear Robert,

Thanks a lot for your answer.

I have implemented your instructions and introduced a new variable X=x/k. But then I cannot define the PDE and I receive an error (Please refer to the attachment).

Maybe the way I define X is wrong.

Would you please guide me how to define the new variable (X) and relate it correctly to the PDE, BC and the piecewise function in Maple?

I do appreciate your help.

Best regards,

Mo

multilayer-NEW.mw

multilayer-NEW.pdf

Dear Mr. Israel,

Thanks for your response.

I have attached another worksheet in which the thermal conductivity of the layers changes largely from one domain to the other.

There should be a change in the temperature gradient between 0.3<x<0.4 and 0.15<x<0.3 because the thermal conductivity of these two domains are hugely different. But maple did not capture this phenomenon.

What would be the solution for this?

Thanks,

Mo

multilayer-conductio.mw

multilayer-conductio.pdf