Your problem seems to be a very classical one : monodimensional heat transfer, which has been studied and solved n'y Fourier a long time ago. You'll have to prescribe a boundary condition on the right end of the rod in order to solve it. As far as i understand your configuration, it is maybe adiabatic at the right end side so du/dx(x=L,t)=0 (no heat flux at the end ?). Then you probably have to use a Fourier transformation of your mesured signal on the left end to get the one at the right, or derive an analytical solution and implement all this in simulink, which i've not done. Should be not so hard but maybe someone else already has the simulink corresponding process ...

Hello Jay Ginoya ,

The theoretical explanation you attached to your question says that the rod has a nonuniform temperature distribution along it length at t=0, that the sides of the rod are insulated, there is no heat source within the rod, and that the ends may be exposed. My question is to what are the ends exposed? In order to solve this problem you need both the initial conditions and the boundary conditions. It is not clear to me nor to Jean Collinet what the boundary conditions at x=0 and x=L are. Nothing is mentioned about the boundary condition at x=L, and you only mention something about heating and cooling at x=0. Can you be more expansive in your explanation? Does the book from which you have taken the excerpt provide anymore information about the boundary conditions further down on the page?

Regards,

Tom Cuff

Hi Jay Ginoya ,

I found the theoretical description at the following URL: https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf (see the attachment) and it does provide the boundary conditions further down on the page. Are these the same boundary conditions you are actually using?

Regards,

Tom Cuff

Hi Thomas Cuff

sorry for the late reply. yes i am using the same boundary condition as you have mentioned in the attachments.

thank you

Hello Jay Ginoya ,

Have you had any success configuring and solving this problem with Simulink? The reason I am asking is because that was your original question. Jean Collinet and I were, I believe, both unsure of the complete statement of the problem, which was why we were trying to get clarification from you. Now that I understand the complete statement of the problem, I am willing to try and help you, if you still need any help.

Regards,

Tom Cuff

Hello Thomas Cuff

yes, i have tried but i didn´t get any success. if you can help me that would be really great.

Thank you,

Jay

Hi Jay Ginoya ,

Please, tells us (in words or diagrams or both) how you have approached configuring the problem in Simulink, i.e., tell us which blocks you used and their connection(s) with one another. This way, we will not waste your time with configurations you have already tried.

Regards,

Tom

Hello Thomas Cuff

i am new to the simulink so, i didn´t know much about solving DE in simulnik or define boundaries in simulink but as a start i have used integrator to raise the temperature and then trying to make a loop but it wasn´t working.

Regards,

Jay

Hi Jay Ginoya and Jean Collinet ,

Jay, attached to this message you will find my first write-up on your problem and how to begin the solution in Simulink. Please, read it and comment on it. Be especially mindful that I have not made any algebra mistakes.

Jean, does this seem like a reasonable approach?

Regards,

Tom

Hi Thomas Cuff

Thank you very much for your support.

i have read your attachment and i think it is a correct approch for this model but i think in this case the BC_2: ``T(l,t) should not be 0 for t>0`` as the temperature of the other end of the rod is dependent on the temperature of the left side of the rod. still i am not sure for this.

i have attached an excel sheet which includes the temperature measurement data of the left side of the rod and right side of the rod with respect to time. all the measurement has been taken on each second. where, the temperature of the right side of the rod has to be identified by the temperature of the left side in Simulink. hope this attachmment will help to define the boundary conditions.

Regards,

Jay

Hello Jay Ginoya and Jean Collinet ,

Jay, I believe the issue is one of miscommunication. I believe the IC (Initial Condition) and the BC's (Boundary Conditions) for your experiment are substantially different than those given in the document by Hancock.

It appears that the IC might be that the rod is at a uniform, unspecified temperature, not some arbitrary function as envisioned by Hancock, although, a uniform temperature is still allowed by Hancock. With respect to the BC's, I believe the following is happening. At x=0, the rod temperature is being driven by a heat source, whose temperature is being monitored, and at the x=l end, the rod is basically insulated except for the presence of a thermocouple, thermistor, or some other kind of temperature measuring device. How well the x=l end is insulated will depended on how much heat leaks out of the rod to the thermocouple or whatever you are using.

Can you send us a photograph of your experimental setup along with a detailed description? Since we are not in your laboratory, it is hard for us to visualize your apparatus. Remember, we are not looking over your shoulder.

I apologize for not realizing earlier that Hancock's problem was not the one you were trying to solve; it just had the same geometry. In my defense, you did message us two days ago that your BC's were the same as given in Hancock's document.

Regards,

Tom

Hi Thomas Cuff ,

i think somwwhere it´s my fault that i could not describe my exact experimental setup situation, IC and BC.

can you share me your mail id or any other contact detail so, that i can send you my experimental setup and stuff.

Regards,

Jay

Sorry for my late replying.

we see here how important the boundary and initial conditions are in order to solve any thermal problem. Still I suppose you can use the Simulink approach proposed by Thomas but you'll have to modify the left and right extreme blocks to fit your boundary conditions (temperature source on the left and dT/dx=0 on the right end). This should do the job at the end. Otherwise you can follow the same approach as previously described searching T(x,t)=f(x)g(t), but this time with other boundary constains. doing this between two of your measurement times t0 and t1 leads to solution in c*ch(a(x-l))exp(b(t-t0)) when T(x=0) is growing or c*cos(a(x-l))exp(b(t-t0)) when T is falling. This could justify trying to get T(x=l, t=t1)=T(x=0,t=t1)/T(x=0,t=t0)*T(x=l,t=t0). This seems to work with your data at least for the rising phase and also in the falling phase if restarted after t=680 (see attached file, obviously T(x) cannot be in ch(x-l) nor cos(x-l) during the slope change and the solution in f(x)g(t) cannot describe the change from rising to falling T but it seems to work during the other phases). I also tried in excel to implement a macro solving explicitly the equation (implicit method would be better) with these BC and it seems to work more or less in the increasing temperature regime, but then there is some discrepancy in the decreasing part. Is the right side cooled at one moment ?

Hope it helps, even if I'm not a specialist of Simulink...

Best regards

Jean

Hello Jean Collinet

thank you very much for your help. i am sorry but i don´t understand what do you mean by right side cooled at one moment?

Best regards,

Jay

Sorry i just wondered if the boundaries should change between the different phases (from adiabatic on the right side to another imposed flux for instance). Anyway only you can fix that knowing the materials used and the real conditions.

Regards

Hi Jay Ginoya and Jean Collinet ,

I have corrected and expanded my write-up. Please, let me know what you think.

Regards,

Tom