The local and average Nusselt number in a square cavity

I am in the process of programming the local & average Nusselt number in a left vertical wall but my Matlab script gives me inappropriate values and it doesn't change with changing of Rayleigh number!!

The problem is: how to calculate and impliment the local Nusselt number in a vertical left wall of a cavity. The expressions of the local nusselt: $$-\dfrac{\partial T}{\partial x}|_{x=0}$$

My script: using finite difference approximation with 5 points-Forward scheme ( j=1 to m+1 and i=1 )

for j=1:m+1
Nu_loc(j) = -(-25*T(1,j)+48*T(1+1,j)-36*T(1+2,j)+16*T(1+3,j)-3*T(1+4,j))/(12*hx);
end

• The Nusselt number is a dimensionless number, but your formula has units $K/m$. It can't be right. Commented Mar 23, 2022 at 16:43
• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Commented Mar 23, 2022 at 20:20
• @WolfgangBangerth in this case T and x are both dimensionless parameters Commented Mar 23, 2022 at 23:45
• OK, but I still don't understand what the question is. You are computing the derivative with a finite difference stencil that looks correct to me. What is it you want to ask? Your post has no question mark. Commented Mar 24, 2022 at 21:46
• Mr. @WolfgangBangerth my question: are the formulation and the implimentation above right or need to try another ones? Commented Mar 25, 2022 at 10:34