Solving for a single unknown and plotting.

I need to plot the following equation where T is temperature and yd is a distance, as T vs y

(T-T_s)/(T_inf-T_s) = 1.5*yd/d_x-0.5*(yd/d_x)^3;

The entire code reads:

t0=0; tf=7;
Pr = 0.6;
y0=[0 0 0.332 0 0.332*Pr^(1/3)]'; 
[t,y]=ode45(@ydotcalc,[t0 tf],y0);
figure(1)
plot(t,y);grid on

U_inf = 1; %Free stream velocity
T_s = 300; %Surface temperature Celsius
T_inf = 27; %Ambient temperature
v = 30E-6; %m^2/s
x = 0.5; %distance (m)
Re_x = U_inf*x/v; %Reynolds
d_x = 5*x/sqrt(Re_x);

T = @(y) ((sqrt(U_inf*v*x)*y)-T_s)/(T_inf-T_s);
yd = [0.00 0.01 0.02 0.03 0.04 0.05]
(T-T_s)/(T_inf-T_s) = 1.5*yd/d_x-0.5*(yd/d_x)^3;
figure(2)
plot(T,yd);

function ydot = ydotcalc(t,y) 
Pr = 0.6;
ydot = zeros(5,1); 
ydot(1) = y(2);
ydot(2) = y(3);
ydot(3) = -0.5*y(1)*y(3);
ydot(4) = y(5);
ydot(5) = -0.5*Pr*y(1)*y(5);
end

How can I solve the equation and plot the results?

Thanks

[Star Strider]

See also: Plotting Temperature as a function of y from an ODE

Answer 1

[Star Strider]

Solving for ‘T’ is straightforward basic algebra:

yd = [0.00 0.01 0.02 0.03 0.04 0.05]
Tfcn = @(y) (1.5*y/d_x-0.5*(y/d_x).^3) * (T_inf-T_s) + T_s;

figure(2)
plot(Tfcn(yd),yd);
title ('y as a function of T')

figure(3)
plot(yd,Tfcn(yd));
title ('T as a function of y')

.