Nu and Sh value should be non-zero

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

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I want some non-zero value of Nu and Sh but '0' is coming (which is wrong). Please correct me where I am wrong.

[Walter Roberson]

 kf = 0.613;

You did not round that value correctly, it should be 0.612.

Or perhaps it was some other of your "magic numbers" that you assumed that we would immediately recognize even without telling us what kind of problem you are dealing with, and with only four comments in the entire code and without showing us the mathematical form of the equations.

As outside observers, in such a situation, we have to assume that the code is perfectly right and that it is your interpretation of the results that is the difficulty. To us, the code defines the problem to be solved. If not, if there is some problem being implemented, then we need to be given the documentation of what that problem is in order to compare the problem to the implementation.

[MINATI PATRA]

@ Dear Walter Roberson

Thanks for your concern

I corrected myself, it was in B.C.

But still my last conversation with you was unsolved. If you have time to rearrange the FULL CODE following:

https://in.mathworks.com/matlabcentral/answers/607426-generalization-needed-in-dsolve-code?s_tid=mlc_ans_email_view#comment_1082988