I used finite-volume method to calculate heat maps for underground shelter/building - ceiling is on the ground level.
The strange is that why on the walls denisty of heat transfer is about 12 W/m2 but on substructed foundation it is about 6 W/m2. High of building is 2,4 m, longitude of the shelter is 36 m.
In first 3 attachments are heat maps after 1 day, 120 days and 330 days.
In 4th and 5th attachement is figure of density of heat transfer in time (days) - blue line. f.png - substructed foundation, s.png - walls
Anyone can explain me the cause of this (for me) curiosity?
Thank you Vitalii for your excellent answer and the very useful attachment. I have been observing the remarkable answers you have been giving consistently. This is what is needed but is rather rare on RG! On behalf of the readers of RG, I convey our gratitude.
Radoslaw, the words in Polish gave me some trouble! I hope that I have understood your problem correctly. On that basis, I have provided a graphic answer that hopefully complements Vitalii's mathematical answer. I have attached a crudely hand-drawn flux plot to indicate the paths of heat flow. It shows that the path length varies and therefore the heat flow too will vary. The sketch is for a steady-state two-dimensional case, but it might be enough to explain the idea.
If you were to look at the local fluxes, it might show a steady decline, as the path length increases. As per your plots, the shelter is at a higher temperature and the ambient at a lower temperature. The temperature gradients are higher at the top, steadily declining as you proceed to the top corner and down along the depth. This is consistent with my sketch. If you plotted heat flux instead of temperature, I believe the results will corroborate my statements above.
@Ariadne, Thank you for the attached books. Although it does not give a direct answer to the question of Radoslaw, it gives a lot of valuable information. Regards.
Dear Radosław Sierociuk
I think...
The heat fluxes in the walls and partly in the foundations are linked to the aboveground conditions (Especially in spaces in low depth). To have a right understanding and judgment of the heat fluxes, knowing the configuration of your simulation (initial temperature, boundary conditions, materials of both wall and foundation, climate, temperature and humidity profile of soil in depth, etc.) is required. What can be found from figures are the constant temperature conditions, inside the space (air-conditioned space), at aboveground climate conditions, and in soil temperature profile through the year (A steady state in the interior and exterior climatic conditions such as high latitude climate conditions). In this case, the provided sketch by professor Raghavan as a general answer could be your answer; otherwise, different results will be achieved during the year.
Regards
Alipour
Mr. Alipour is absolutely correct. For cyclic variations of the ambient temperature, it would be impossible to give a simple, graphic answer that brings out the principle involved. That is why I covered my seat with the words "for a steady-state two-dimensional case, but it might be enough to explain the idea" :-)
Dear professor Raghavan
Your answer is useful and it explains the idea very well.
My original order was how relying on simulation results and judgment on them. Because, the simulation conditions and assumptions are determining factors of results.
Best Regards
Alipour
I am so glad for your answers! That are realy helpful informataions. I hope I am understading this problem now.
I have to add that material of foundation and walls are the same - 50 cm reinforced concrete. Dr Wasilczuk (Military Univeristy of Technology) proofed in his work that aproximately soil and reinforced concrete have similar qualities for heat flow. Inital temperature iniside the shelter is 20 oC.
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