function Latest_code
%%
for Pr = [1 2 3 4]
% Define constants

M = 0.5;
B = 0.5;
C = 0.2;
A = 0.1;
R = 0.1;
E = 0.1;
K = 0.5;
W = 0.1;
N = 0.1;
T = 0.3;
Q = 0.1;
N1 = 0.1;
N2 = 0.1;
S = 0.1;
d = 1;
m = 1;
E1 = 0.1;
Pe = 0.2;
S1 = 0.1;
M1 = 0.1;
O = 0.1;
% Defining initial guess
solinit = bvpinit(linspace(0, 2, 50), [1 0 0 0 1 1 1 1]);
% Solving the boundary value problem
sol = bvp4c(@bvpexam2, @bcexam2, solinit);
x = sol.x;
y = sol.y;
% Plotting of velocity
figure(2)
plot(x, y(4, :), ‘linewidth’, 1)
ylim([0 1])
xlim([0 9])
hold on
xlabel(‘eta’, ‘FontWeight’, ‘bold’, ‘FontSize’, 16)
ylabel(‘theta(eta)’, ‘FontWeight’, ‘bold’, ‘FontSize’, 16)
end
% System of first order ODEs
function yvector = bvpexam2(~, y)
yy1 = (1 / (1 + (1 / B))) * (2 * y(2) * y(2) – y(1) * y(3) + M * y(2) + K * y(2) – W * (y(4) – N * y(7) – R));
yy2 = -(1 / (((4 / 3) * R) + 1)) * (Pr * (y(1) * y(5) – y(2) * y(4) – T * y(2) + Q * y(4) + N1 * y(8) * y(5) + N2 * y(5) * y(5) + E * (1 + 1 / B) * y(3) * y(3) + (E * y(2) * y(2)) * (M + K)));
yy3 = -S * (y(1) * y(8) – y(2) * y(7) – C * y(2) – A * y(7) * ((1 + d * y(4)) ^ m) * exp(-E1 / (1 + d * y(4)))) – (N2 / N1) * y(6);
yy4 = (Pe * (y(9) * (y(10) + O) + y(11) * y(8))) – (S1 * ((y(11) – y(10)) * y(1))) + (S1 * M1 * y(2));
yvector = [ y(2); y(3); yy1; y(5); yy2; y(8); yy3 ; y(11); yy4 ];
end
% Residual of the boundary conditions
function residual = bcexam2(y0, yinf)
residual = [y0(1)- 1; y0(2) – 1; y0(4) – 1 +T ; y0(7)-1+C ; y0(10)-1+M1 ; yinf(2); yinf(4); yinf(7); yinf(10)];
end
endfunction Latest_code
%%
for Pr = [1 2 3 4]
% Define constants

M = 0.5;
B = 0.5;
C = 0.2;
A = 0.1;
R = 0.1;
E = 0.1;
K = 0.5;
W = 0.1;
N = 0.1;
T = 0.3;
Q = 0.1;
N1 = 0.1;
N2 = 0.1;
S = 0.1;
d = 1;
m = 1;
E1 = 0.1;
Pe = 0.2;
S1 = 0.1;
M1 = 0.1;
O = 0.1;
% Defining initial guess
solinit = bvpinit(linspace(0, 2, 50), [1 0 0 0 1 1 1 1]);
% Solving the boundary value problem
sol = bvp4c(@bvpexam2, @bcexam2, solinit);
x = sol.x;
y = sol.y;
% Plotting of velocity
figure(2)
plot(x, y(4, :), ‘linewidth’, 1)
ylim([0 1])
xlim([0 9])
hold on
xlabel(‘eta’, ‘FontWeight’, ‘bold’, ‘FontSize’, 16)
ylabel(‘theta(eta)’, ‘FontWeight’, ‘bold’, ‘FontSize’, 16)
end
% System of first order ODEs
function yvector = bvpexam2(~, y)
yy1 = (1 / (1 + (1 / B))) * (2 * y(2) * y(2) – y(1) * y(3) + M * y(2) + K * y(2) – W * (y(4) – N * y(7) – R));
yy2 = -(1 / (((4 / 3) * R) + 1)) * (Pr * (y(1) * y(5) – y(2) * y(4) – T * y(2) + Q * y(4) + N1 * y(8) * y(5) + N2 * y(5) * y(5) + E * (1 + 1 / B) * y(3) * y(3) + (E * y(2) * y(2)) * (M + K)));
yy3 = -S * (y(1) * y(8) – y(2) * y(7) – C * y(2) – A * y(7) * ((1 + d * y(4)) ^ m) * exp(-E1 / (1 + d * y(4)))) – (N2 / N1) * y(6);
yy4 = (Pe * (y(9) * (y(10) + O) + y(11) * y(8))) – (S1 * ((y(11) – y(10)) * y(1))) + (S1 * M1 * y(2));
yvector = [ y(2); y(3); yy1; y(5); yy2; y(8); yy3 ; y(11); yy4 ];
end
% Residual of the boundary conditions
function residual = bcexam2(y0, yinf)
residual = [y0(1)- 1; y0(2) – 1; y0(4) – 1 +T ; y0(7)-1+C ; y0(10)-1+M1 ; yinf(2); yinf(4); yinf(7); yinf(10)];
end
end function Latest_code
%%
for Pr = [1 2 3 4]
% Define constants

M = 0.5;
B = 0.5;
C = 0.2;
A = 0.1;
R = 0.1;
E = 0.1;
K = 0.5;
W = 0.1;
N = 0.1;
T = 0.3;
Q = 0.1;
N1 = 0.1;
N2 = 0.1;
S = 0.1;
d = 1;
m = 1;
E1 = 0.1;
Pe = 0.2;
S1 = 0.1;
M1 = 0.1;
O = 0.1;
% Defining initial guess
solinit = bvpinit(linspace(0, 2, 50), [1 0 0 0 1 1 1 1]);
% Solving the boundary value problem
sol = bvp4c(@bvpexam2, @bcexam2, solinit);
x = sol.x;
y = sol.y;
% Plotting of velocity
figure(2)
plot(x, y(4, :), ‘linewidth’, 1)
ylim([0 1])
xlim([0 9])
hold on
xlabel(‘eta’, ‘FontWeight’, ‘bold’, ‘FontSize’, 16)
ylabel(‘theta(eta)’, ‘FontWeight’, ‘bold’, ‘FontSize’, 16)
end
% System of first order ODEs
function yvector = bvpexam2(~, y)
yy1 = (1 / (1 + (1 / B))) * (2 * y(2) * y(2) – y(1) * y(3) + M * y(2) + K * y(2) – W * (y(4) – N * y(7) – R));
yy2 = -(1 / (((4 / 3) * R) + 1)) * (Pr * (y(1) * y(5) – y(2) * y(4) – T * y(2) + Q * y(4) + N1 * y(8) * y(5) + N2 * y(5) * y(5) + E * (1 + 1 / B) * y(3) * y(3) + (E * y(2) * y(2)) * (M + K)));
yy3 = -S * (y(1) * y(8) – y(2) * y(7) – C * y(2) – A * y(7) * ((1 + d * y(4)) ^ m) * exp(-E1 / (1 + d * y(4)))) – (N2 / N1) * y(6);
yy4 = (Pe * (y(9) * (y(10) + O) + y(11) * y(8))) – (S1 * ((y(11) – y(10)) * y(1))) + (S1 * M1 * y(2));
yvector = [ y(2); y(3); yy1; y(5); yy2; y(8); yy3 ; y(11); yy4 ];
end
% Residual of the boundary conditions
function residual = bcexam2(y0, yinf)
residual = [y0(1)- 1; y0(2) – 1; y0(4) – 1 +T ; y0(7)-1+C ; y0(10)-1+M1 ; yinf(2); yinf(4); yinf(7); yinf(10)];
end
end fluidmechanics MATLAB Answers — New Questions

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