A Thermal resistance network is defined for analysis by creating a model. How to solve the system of equations? Kindly advice
Solving a thermal resistance network is very similar to a pipe network, in fact, that's the way I solve pipe networks, such as fire protection sprinkler systems and water distribution systems for evaporative cooling towers. What you want is mathematically called a "contraction", that is, an operation that won't figuratively "blow up" or "run away"" when you put it inside a loop and successively substitute the current results over and over again. This works with resistance networks just like electrical resistors in series and parallel, where you're trying to find the current through each branch. For your thermal resistance network, the heat transfer is the current and R=1/UA is the resistance. Voltage is temperature. Kirchhoff's laws apply here as well. The first law of thermodynamics is the same thing as all the currents entering and leaving a node sum to zero and the temperatures (voltages) at a point are all the same.
Thank you Dr.Dudley J Benton . I have managed to formulate the thermal resistance network with regard to the system under consideration. However I would like to understand the methods of solving the system of equations as certain parameters are unknown. Are there any specific material that can help me accomplish the results by iteration?
The unknown parameters are usually function of temperature. You can assume values first and make a run which will give other temperatures than those assumed. According to the new values you can build up a logical change of chosen values and proceed by iterations. In general such procedures are converging.
Thank you Nick Hamburger . That makes sense. However, Can you please provide me a reference material or literature on solving the equations? Or the method to be considered for evaluating the results.
If equations are linear they build a system which can be solved either with determinants or with matricial computing. The procedures are in all books about mathematics for linear systems.
Thank you again Nick Hamburger for guiding me. I am new to such an approach and I'm glad to hear from you. What if the equation also consists of non-linear equations?
Then you can try to linearise them in a first approach.
It depends on the relative weight of nonlinearity if your "linearised" result will be near or far from the true result.
Look in books on algebraic system solutions and you will find how to solve the systems. It is for you better if you do this by your own you will enlarge your horizon and profit later of it.
Thank you so much for your guidance and I have duly noted all the pointers. Nick Hamburger .
Nick Hamburger What do you think about considering Tri-diagonal matrix algorithm(TDMA) for solving a system of equations? And further iterating the solution till convergence? Which are the other methods that we can consider? Looking forward to hearing from you.
I think that for you it would be better to try at least 2 approaches since then you will be able to compare for the future which one is more appropriated for the job.
If you have values then look at the solution with matrix inversion and product.
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