We only know the entering temperature to the heat exchanger (T_in=0), it doesn't change with time, and also we have an analytical relation (see attached schematic).
According to schematic, there will significant asymmetry between heat flow to diving and rising arms of exchanger. Horizontal temperature gradient in ground will develop. I doubt analytics of this problem exist. Please use FEM software like Thermal Desktop (or any free alternative) to calculate actual temperature distribution and heat fluxes.
thank you Nizhnik,
please refer to :
"Evaluation of heat exchange rate of GHE in geothermal heat pump systems" ,Renewable Energy 01/2009; 34(12):2898-2904. DOI:10.1016/j.renene.2009.04.009
this paper investigated heat transfer per unit length of borehole and outlet temperature of vertical heat exchanger ,but i didn't understand that fluid entering temperature to VGHX is constant or no?
please note that analytical solutions like "infinite line source" , "infinite cylindrical source" assume that heat transfer per unite length of borehole is constant .
please after reading the paper, discuss the method and results used in the paper.
thank you
The paper is junk. The experimenters did not run experiment long enough (~50 years for 70m pipe) to get steady-state heat flux. Instead they ran 0.2 years and reported incredibly large flux of 40W/m. You may notice flux dropping with time on Fig. 2
Also, outlet temperature is too high for shallow holes, indicating hydrothermal activity in area. With flow of warm water underground, all thermal resistance calculations will be incorrect.
i solved this problem.m-file is attached.
i used analytical solution of infinite line source for simplicity.first, i guessed heat flux,q, and outlet temperature of fluid,T_out, then i solved nonlinear equation with Fsolve command in matlab. note that we have 2 unknown and 2 equation. i compared the results with a paper result that solved this problem with fluent software.if you have trouble with m-file ask it here.
cannot say anything about output of your program because you write too matlab-specific.
program inconvertible to scilab i use.
but your fun() looks like 1-D FEM implementation.
more reliable is to use proven FEM software - especially fo such common problem like heat diffusion
I didn't use numerical method like finite element ,i only used analytical solution for solving the problem,you can use one of the analytical solution like :"infinite line source" ," finite line source " or "infinite cylindrical source".
Numerical solutions are more reliable as you mentioned, but they are very time consuming.and if we want to compute outlet temperature from more than one borehole(one heat exchanger) it will be very time consuming computation. Whereas with analytical solutions, computation time decreases up to seconds with errors that we can neglect them.
I didn't use scilab,if i could convert m-file to scilab file i put it here.
Article Efficient Computation of Heat Flux Signals Ensuring Reproduc...
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