function main
x = linspace(0,1,101); t = x; m = 0; sol = pdepe(m,@pde,@ic,@bc,x,t,[]);
U = sol(:,:,1); T = sol(:,:,2); C = sol(:,:,3);
xq = x; xq(1:end - 1) = xq(1:end - 1) + diff(xq)./2;
[u,dudx] = pdeval(m,x, A1*U(2,:,1),xq); Sk = dudx(1); %% Derivative of U at x = 0
[v,dvdx] = pdeval(m,x, - A7*T(2,:,1),xq); Nu = dvdx(1); %% Derivative of T at x = 0 (with negative)
[w,dwdx] = pdeval(m,x, - C(2,:,1),xq); Sh = dwdx(1); %% Derivative of C at x = 0 (with negative)
disp([Sk Nu Sh])
function [c,f,s] = pde(x,t,u,dudx)
Re = 1; p = 0.01; L0 = 1; L = 0.1; eps = 1; w = 0.2; M = 1; Kp = 0.5;
Gr = 0.5; Gc = 0.5; Pe = 1; N = 2; Sr = 0.5; Le = 1; G = 1; Pr = 01;
rhos = 19300; cps = 129; ks = 301; betaTs = 42*10 ^(-6); betaCs = 1.25*10^(-5); sigmas = 4.11*10^6;
rhof = 997.1; cpf = 4179; kf = 0.613; betaTf = 21*10^(-5); betaCf = 298*10^(-5); sigmaf = 0.05;
a = 13.5; b = 904.4; n = 3/0.62; sigma = sigmas/sigmaf; % n = 4.8387;
A1 = 1 - p + p * (rhos/rhof); A2 = 1 + a*p + b*p^2; A3 = (1 + (3*p*(sigma-1)/((sigma+2)-p*(sigma-1))))/A1;
A4 = 1 - p + p * ((rhos*betaTs)/(rhof*betaTf)); A5 = 1 - p + p * ((rhos*betaCs)/(rhof*betaCf));
A6 = 1 - p + p * ((rhos*cps)/(rhof*cpf)); A7 = (ks + (n-1)*kf + (n-1)*p*(kf-ks))/(ks + (n-1)*kf - p*(kf-ks));
c = [Re*A1; Pe*A6; Re;]; f = [A2.*dudx(1); A7.*dudx(2); (1/(Le*Pr)).*dudx(3) + Sr*dudx(2)];
s = [L0 + L*eps*abs(exp(i*w*t)) + A4*Gr*u(2) + A5*Gc*u(3) - (A3*M^2 + (A2/Kp))* u(1); N^2*u(2); - G*u(3)];
end
function u0 = ic(x)
u0 = [0; 0; 0];
end
function [pL,qL,pR,qR] = bc(xL,uL,xR,uR,t)
pL = [uL(1); uL(2); uL(3)]; qL = [0; 0; 0]; pR = [uR(1); uR(2)-1; uR(3)-1]; qR = [0; 0; 0];
end
end
%%%%%%%%
I want some non-zero value of Nu and Sh but '0' is coming (which is wrong). Please correct me where I am wrong.
