# Question:Finding Skin friction using Theta method

## Question:Finding Skin friction using Theta method

Maple

Hello,

I solve a partial differential equation using the THETA METHOD on Maple17, but what is also of essence is the skin friction and Nusselt Number which are {diff(u(x, t), x)} at x = 0 and {diff(T(x, t), x)} at x = 0 respectively. How can I achieve the two using the THETA METHOD? This is the PDE in it full flesh.

PDE := {diff(phi(x, t), t) = (diff(phi(x, t), x, x))/S__c, diff(u(x, t), t) = diff(u(x, t), x, x)-M^2*(u(x, t)+m*w(x, t))/(m^2+1)-u(x, t)/`&varkappa;`-2*Omega^2*w(x, t), diff(w(x, t), t) = diff(w(x, t), x, x)+M^2*(m*u(x, t)-w(x, t))/(m^2+1)-w(x, t)/`&varkappa;`+2*Omega^2*u(x, t), diff(theta(x, t), t) = lambda*(diff(theta(x, t), x, x))/P__r+D__r*(diff(phi(x, t), x, x))}

With conditions: BC := {phi(0, t) = 1, phi(12, t) = 0, phi(x, 0) = 0, u(0, t) = t, u(12, t) = 0, u(x, 0) = 0, w(0, t) = 0, w(12, t) = 0, w(x, 0) = 0, theta(0, t) = 1, theta(12, t) = 0, theta(x, 0) = 0}

Where the parameter like P_r, S_c  e.t.c are constants to assign value to.

Thanks.

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