A hot fluid flowing through serpentine tube is enclosed in rectangular solid.Can temp. distribn be solved analytically and by commercial softwares? A fig is shown for clarity.
Gaurav, You are getting such a doubt perhaps because of relative inexperience. This is a rather straightforward analysis. When you have both conduction and convection, it is called a conjugate problem. In your case, there is no convection in the solid medium. This can be easily analyzed using commercial software packages by merely suppressing convection. For example, putting h = 0 will suppress convection. As the temperature of the fluid flowing through the coil will vary continuously (unless it is evaporating or condensing) you will need to simulate the entire serpentine coil.
In fact, more complicated cases such as a melting or freezing solid (heat storage or heat discharge in phase change materials, PCM) have been solved without any serious difficulty, so your case of pure conduction in the rectangular block is no big deal. Good luck.
Mr. Gaurav, ALL analytical solutions use simplifying assumptions, sometimes very drastic ones. You have a problem in 3-dimensional heat conduction in a rectangular block (rectangular co-ordinate system) as well as convection in the tubeside flow (cylindrical co-ordinate system). There is a conduction domain and a convection domain and the two need to be linked via suitable boundary conditions. While numerical methods can handle this, analytical methods cannot.
One simplification could be to assume cylindrical coordinates for the conduction region concentric with the pipe. Then the corners of the rectangle will give you trouble!
In your case, since there will be a continuous temperature drop from one tube to the next in the coil, you will need to make some simplifying assumptions here, viz., the heat flow from one tube does not affect heat flow from another tube. If the result of importance to you is the heat flow from each limb of the coil, you may get a reasonable answer by means of the (simplified) analytical method. But if the temperature distribution is your major concern, then take recourse only to numerical approach.
A collection of classical conduction solutions is given in the book "Conduction of Heat in Solids" by Carslaw and Jaeger. But you will not see a solution there for your case.
Ok, thankyou sir, I had somewhat the same idea in mind but thought that it will be very simplified with errors.Again, I didnt mentioned the fluid flowing in my case is steam, so i assume the above suggestions are suitable for these case.
Gaurav, then you can assume the tube wall temperature to be constant in the entire coil, can ignore simulation of convection in the tubes (i.e., you do not have to solve the Navier-Stokes equation and the energy equation and no modeling of the two-phase flow of steam-water). The problem simplifies to a 2-D conduction problem. You can take just one tube and the rectangular solid surrounding it. But since you will have some boundaries adiabatic and others discharging heat, you cannot use the analytical solutions existing in literature for 2-D shape factors. If this shape factor thing is unknown territory for you, look up
2-dimensional steady heat conduction in a standard Heat Transfer text book.
You still have not said what is the result of importance to you - temperature distribution or heat flow.
Sir, my primary concern is finding the tempearture distribution on the faces of rectangular block (faces parallel to the axis of tube ie. bigger faces shown in fig)
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