Solving differential equation with two unknowns

[Muhammad Saqlain]

Hello Everyone
I am solving a differential equation (attached) of greenhouse energy balance on SIMULINK which has basically two unknowns (Tin and qg). One of them (qg) is model output and other (Tin) is also not know from any means. All 6 factors on right side of the equation are dependent on Tin. There is a operating set point for temperature given as 20 for day and 16 for night in the research paper. I do not know whether its initial condition for temperature or not. I am using integration technique to solve this differential equation but for that all other parameters should be known but unfortunately qg is also not known because it is the actual output of model. Can someone help me to solve this equation?
My simulink model is also attached.Plzzzz guide me

 

[HallsofIvy]

Do you have two "unknowns" that you need to solve for or are you saying that Tn is an unknown constant?

 

[Muhammad Saqlain]

Tin and qg both are unknown and I need to get both. As qg is the output of this model and all other terms including this qg are bounded with Tin so that is whY I am saying that there are two unknowns (Tin and qg)

 

[HallsofIvy]

What do you mean by "bounded with Tin"?

Combining all the other "q"s,
\(\displaystyle Q(t)= q_{solar}(t)+ q_{lamp}(t)- q_{con}(t)- q_{trans}(t)- q_l(t)- q_{vent}(t)\)
and \(\displaystyle A= \rho_a V_aC_a\)

We can write the equation as
\(\displaystyle A\frac{dT_{in}}{dt}= q_g(t)+ Q(t)\).

Separate variables
\(\displaystyle A dT= (q_g(t)+ Q(t))dt\)
and integrate:
\(\displaystyle AT= \int q_g(t)dt+ \int Q(t)dt\).

However, in general, you cannot solve for two unknowns with only one equation. We would need another equation that allows us to do the \(\displaystyle \int q_g(t)dt\) integration.