Write a script to determine the change in temperature of the liquid over a 200 minute time period using the following equation: T(i+1)=T(i​)+K*(Delta​_t)*(F-T(i​))

The start Temperature of a liquid is 50 and is placed into a fridge of temperatue 5. (F=5)

Have to calculate each value of T(i+1) from the value of ܶT(i) from the previous time step over a space of 200 minutes where the time in dived into time steps each of duration delta_t. Must be computed using a 'For' loop. Also K = 0.045

I cant seem to get the time incrments correct as i always get negative values for my temperature which doesnt make any sense realistically.

clear all

clc

F=5

K=0.045

for x=200:-20:0

T=50:-5:5

T_final=T+K*x*(F-T)

end

plot(x,T_final)

[Kyle]

Any help would be much appreciated as i feel i have exhausted my knowledge

Answer 1

[William Rose]

@Kyle,

The change in temperature in each time step is proportional to the difference bwteeen the current temp and the fridge temp (Tf=5, constant):

deltaT = K*(T-Tf)*deltat

where deltaT is the change in temp (it changes with each time step) and deltat is the time step size (constant). I have assumed that K is a "rate of decay" constant, with units of 1/time.

You get negative values because you assume the temperature just declines at a constant rate, instead of assuming that it decays at a rate proportional to the difference between current tmp and fridge temp.

You can put that idea into a Matlab script.

By the way, this problem also has an analytical solution, involving an exponential function:

T(t)=(Tinit-Tf)*exp(-Kt) + Tf

If you plug in t=0 and t=infinity, you see that T(0)=Tinit=50 and T(infinity)=Tf=5, which makes sense.

[Kyle]

Okay makes senes thanks.

[William Rose]

@Kyle, you're welcome and good luck.