How to solve a function with one independent variables with different values so that i can make a plot?

Hello, first of all, thanks for help me.

I want to solve an equation: theta= 1- exp(b^2)*erfc(b) solving for b, where theta= (T_surf-Tini)/(T_fluid-Tini). The T_surf is the independent variables with 10 different variable. I want to solve the equation and the output result for b should be in matrix form, so that i can plot "b" against "T_surf".

Further, b=(h*sqrt(a*t))/k solving for h, where t is the changing variables which are corresponding to T_surf mentioned above; that this T_surf1 is corresponding to t_1, T_surf2 is corresponding t_2, and etc.

So at the end, I would be able to plot "t vs. h".

But i do not know where my code went wrong, could you help me with this issue?? Thanks!!

PS: he attached picture is my code.

[Richard Marveldoss]

According to the code attached solving for b using beta=solve(eqn,b) doesn't give a solution. Is this something that is intentional for your problem. The below code doesn't produce a solution for beta.

Tsurf=[190;129;110]
s=length(Tsurf);
Tini=200*ones(1,s)
Tfluid=40*ones(1,s);
k=3;a=2;
t=[3,6,9];
theta=[(Tsurf-Tini)/(Tfluid-Tini)]
Thetat=theta';
syms b;
eqn= 1-exp(b^2)*erfc(b)==theta;
beta=solve(eqn,b)

Answer 1

[Walter Roberson]

You have

theta=[(Tsurf-Tini)/(Tfluid-Tini)]

which is an array matrix-divided by an array, which is like (Tsurf-Tini) * pinv(Tfluid-Tini) . Are you sure that is what you want and not

theta = (Tsurf-Tini) ./ (Tfluid-Tini)

?

Either way your theta is going to be a vector of length 3. You then have

eqn= 1-exp(b^2)*erfc(b)==theta

which says that one fixed b has exactly the same relationship to three different numeric values. The only way that can happen is if the three different numeric values are identical.

Your Tsurf is 3 x 1. Your Tini is is 1 x 3. Tsurf - Tini, 3 x 1 minus 1 x 3, would be a prohibited operation in all versions prior to R2016b; starting in R2016b it gives a 3 x 3 result, equivalent to bsxfun(@minus, Tsurf, Tini) . Are you sure you want that?