Energy balance of stirred tank

Hello everyone!

I want to solve this equation in order to plot the theoretical temperature profile T:

I know the value of mass (10000), specific heat (2000), U (120), area (25) and the profile of T_w during time.

The experimental values of temperature T are known:

Thanks in advance!

Answer 1

[Torsten]

syms rho cp V u A Tw T0 T(t) Tw(t)
eqn = rho*cp*V*diff(T,t) == u*A*(Tw-T);
cond = T(0)==T0;
T = dsolve(eqn,cond)

T = 

[Alan Stevens]

Note that this is only applicable if Tw is constant, but Nicola stated she knows the profile of Tw through time, suggesting Tw varies with time.

[Nicola De Noni]

@Alan Stevens got the point! The temperature Tw is not constant and I know its profile through the time.

[Torsten]

@Nicola De Noni

I updated the symbolic computation for Tw being time-dependent. See also Sam Chak's answer.

I remember we had this question several times now. I think you should accept that the model you use for T is not adequate for the measurements of T you have.

Consider again the experimental conditions and see whether they make the deviations between model and measurements plausible.

[Sam Chak]

Hi @Nicola De Noni

The theoretical solution for the Temperature profile subject to

, and

where

is given by:

[Nicola De Noni]

Thanks @Sam Chak and @Torsten! You're very kind.

Answer 2

[Alan Stevens]

Try

doc ode45