A Solving a differential equation with two unknowns

[Muhammad Saqlain]

TL;DR Summary

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 the 6 factors on right side of the equation are dependent on Tin.

One thing that is given in paper (attached) is a operating set point for temperature which is given as 20 for day and 16 for night but I do not know whether its initial condition for temperature or not. Can anyone please guide me that what kind of equation is it and how can I solve it with these two (qg and Tin) unknowns. My main output is qg but all other parameters are dependent on Tin so first I have to find Tin by any means from this equation.
Please help me if you can

 

[BvU]

Hello @Muhammad Saqlain ,

One thing that is given in paper

What paper ? Can't you provide a pdf or a link ? If you want to keep us in the dark, you have succeeded. A normal paper has a list of vaiables and their meaning.

$T_{in}$ is probably the input for the model, so you need to find that somewhere.

 

[Muhammad Saqlain]

Hello @Muhammad Saqlain ,

What paper ? Can't you provide a pdf or a link ? If you want to keep us in the dark, you have succeeded. A normal paper has a list of vaiables and their meaning.

$T_{in}$ is probably the input for the model, so you need to find that somewhere.

Thank you for your reply sir. Sure I can share pdf file of that paper in which this model is discussed. Actually Tin is input of model but I have to calculate it through this equation otherwise there is no mean to know this.

 

[willem2]

You solve this with a computer. You just run the model with some plausible Tin, and after a few days the initial value should make no difference. The hotter it is, the more energy will be lost. . You can easily test this of course, by running it twice with different intitial temperatures.
Note that many of the q_i also involve metereological data, such as hourly sunshine and temperature data. You'll have to get those from climate statistics, and run your model many times to get average energy costs and crop yields.
Much of the details of the q's seem to be in "Appendix A. Supplementary Material" that I can't access.

 

[BvU]

Don't have access to ref 33 in your pdf (Chen model), but here I find $T$ is to be optimized depending on crop requirements to maximize crop yield (3.3) in combination with an energy optimization (3.2). Quite a challenge. They have some nice results predicting energy consumption and also mention a number of parameters -- perhaps useful for you too.

 

[Muhammad Saqlain]

You solve this with a computer. You just run the model with some plausible Tin, and after a few days the initial value should make no difference. The hotter it is, the more energy will be lost. . You can easily test this of course, by running it twice with different intitial temperatures.
Note that many of the q_i also involve metereological data, such as hourly sunshine and temperature data. You'll have to get those from climate statistics, and run your model many times to get average energy costs and crop yields.
Much of the details of the q's seem to be in "Appendix A. Supplementary Material" that I can't access.

Thank you for your reply but here problem lies in calculating qg. We can get Tin by integration but for that we need qg at input as is shown in my model (attached). So now my problem is how can I get qg?

 

[Muhammad Saqlain]

Don't have access to ref 33 in your pdf (Chen model), but here I find $T$ is to be optimized depending on crop requirements to maximize crop yield (3.3) in combination with an energy optimization (3.2). Quite a challenge. They have some nice results predicting energy consumption and also mention a number of parameters -- perhaps useful for you too.

Thanks for your feedback sir. Here problem lies in qg, we can optimized Tin if we know qg which is a input for integration of Tin