The BC you describe is not very clear. Uniform heating meaning Th is constant? Liear heating meaning Th is linear? what about Tc? Is Th specified all along the left inclined surface or just the area marked in red?

The geometry should still be a straight inclined line started from (0, 0) with inclination angle of phi. What you see in the left probably results from the window you show in the plotting. It is possible that you asked the graphic tool to show the results that outside your physical domain.

Hi Shiuh-Hwa, Thanks for the response. T_h & T_c indicates that the left and right inclined walls are respectively maintained uniform hot and cold temperatures. In this case, I am getting correct plots. But, when I specify a non-uniform temperature (e.g. a linear temperature, T=1-Y), the isotherms are not within the boundary. I could not understand where I am going wrong...

The actual problem is when the temperature is uniform along the inclined boundary, the plots are good, but for non-uniform or adiabatic conditions (dt/dx=0), I am not getting correct plots.

I think, there won't be any issues with the remapping, as I am correct results for uniform heating. I appreciate your interest and kind response.

Hi Sankar,

I guess the linear temperature is specify on the left incline surface. The lower and upper surfaces remain adiabatic. The right incline surface is uniform. Correct me if I am wrong. If your left surface temperature is a linear function, then you should never have an isotherm on it. If you intend to plot it, let's say T=1, and your graphic tool allow you so, then your isotherm T=1 will surely be outside your physical domain.

What I mean is it's just an illusion. All you need to do is getting rid of it.

To check if the current figure is correct, you can overlap your isotherm figure with real physical boundary, and dictate the wall temperature data from the intersection of wall and isotherm, then you can see if the temperature is linearly distributed.

Here is how graphic tools do:

There are data of Ts on (xs, ys). You want to use some sort of contour commands to plot isotherms in a rectangle window enclosed within (Xmin, Ymin), (Xmax, Ymin), (Xmax, Ymax), (Xmin, Ymax). Your physical domain is within the window. For those isotherms in the physical domain, they are obtain by interpolating from the existing neighboring data of Ts from (xs, ys). Since that you also allow graphic tool to draw the isotherms outside of the physical domain, it extrapolate isotherms using the data within the physical domain.

Two ways to resolve this. (1) Use your computational, which is rectangle, to generate isotherms, then transform the coordinate of isotherms to physical domain, then draw those lines of isotherms. (2) Try to erase the lines outside of your physical domain.