I would like to know about the heat transfer equation for atmospheric air to endless thickness i.e. ground surface. For example, the Atmospheric temperature is 25 degrees C, and the ground temperature is 11 degrees C. In this case, what would be the equation of heat transfer from atmospheric air to the ground? Is it only the free convection or it is the combination of convection and conduction? If it is the combination of convection and conduction, then what would be the thickness for conduction heat transfer.
I would like to apply this equation in a coal mining tunnel where the air temperature is 25 degree C, but surrounding rock of infinite thickness temperature is 11 degree C. So, what would be the heat transfer equation from the air to the rock? I have attached a picture for your better understanding.
Thanks in advance.
If there's no direct contact then we call it convection, not conduction, even if the fluid (air) is not flowing rapidly. The convection may be mostly of the "natural" type as compared to "forced" convection. A reasonable estimate for the convective heat transfer coefficient, h, should be easy to obtain from the literature for similar conditions where people and machines interact with spaces, buildings, tunnels, etc. So what do you hope to learn from this exercise? I would imagine the actual conditions would significantly depend on other things, such as: wind blowing through the tunnel, fans placed to provide ventilation, cars rolling on tracks, drilling equipment, etc. Some gold mines in South Africa use chilled water to operate hammer drills and then run the water through something like a cooling tower to cool the air in this case because it's so hot humans can't work otherwise. They accomplish two things with one stream of water.
Hi, air has relatively lower thermal conductivity and so that the conduction is mostly not relevant. In air, the heat transfer is carried out due to convection. In the solid materials like rocks etc. you have to consider only conduction. The best way to solve that is to simplify it. If the surface temperature of the rock will be constant without any effect of the warm air, I would consider that the air heat transfer can not change the boundary conditions and in this case, the rock can only cooling air. (What is happened exactly in the rock is not relevant for the heat air calculation.) As was suggested in previous answer, find the theory for the natural convection and you can estimate the heat transfer from the rock to air. No exact value, only estimated results, because to determine exactly the heat convection coefficient is in fact impossible. To complex problem.
Exact analytical soultion of this, or maybe similar thermal problem can be found here:
H.S. Carslaw and J.C.Jaeger "Conduction of Heat in Solids" 2nd edition, Oxford at Clarendon Press, 1959, paragraph 12.4.II pp.305-306
Derivative of the solution over x at x=0, times thermal conductivity, will give you formula for heat flux versus time.
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