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Cooling on a floor

Posted Jul 1, 2020, 11:40 a.m. EDT Heat Transfer Version 5.4 1 Reply

Sophie Truon
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Hi,

I modeled with Comsol the decrease in the temperature of a small cube whose initial temperature is Tc placed on the ground at constant temperature Ts.

Now, I would like to find my result by calculation without solving the heat equation. The situation is therefore as follows: a cube (L = 1 cm and kc = 1 W / mK) at the initial temperature Tc = 35 ° C is placed on the ground (semi-infinite plane and ks = 2 W / mK) which at a temperature of 20 ° C which is assumed to be constant. It is assumed that the sides of the cube in contact with the ambient air are insulated and that there is therefore no heat transfer by convection. There is only a transfer of heat by conduction between the side of the cube and the ground (the contact surface is 1 cm²). The cube is small enough to consider that the temperature field is uniform inside. In addition, we suppose the quasi-stationary regime.

Is there a general expression that gives the heat flow lost by the cube through the ground? Is a Newton's type relationship phi = cte (Tc - Ts) possible? If not exists a valid expression under conditions giving this flow ?

Thank you

1 Reply Last Post Jul 2, 2020, 3:33 p.m. EDT
Jeff Hiller COMSOL Employee

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Posted: 4 years ago Jul 2, 2020, 3:33 p.m. EDT
Updated: 4 years ago Jul 2, 2020, 3:35 p.m. EDT

Hello Sophie,

The challenge here is that if you make assumptions in your paper-and-pen model that are not in your COMSOL model, then that paper-and-pen model can't be used to verify the COMSOL solution.

With that caveat in mind, my first idea would be to start with a lumped model: if the conduction in the cube is fast enough, you can assume that the entire cube is at a single temperature and that reduces your problem to an ODE. If you can approximate the heat flux per unit area at the interface to be of the form , then you arrive at the conclusion that the temperature in the cube will follow an exponential decay, i.e. .

Best,

Jeff

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Jeff Hiller
Hello Sophie, The challenge here is that if you make assumptions in your paper-and-pen model that are not in your COMSOL model, then that paper-and-pen model can't be used to verify the COMSOL solution. With that caveat in mind, my first idea would be to start with a lumped model: if the conduction in the cube is fast enough, you can assume that the entire cube is at a single temperature and that reduces your problem to an ODE. If you can approximate the heat flux per unit area at the interface to be of the form c*(T_c-T_s), then you arrive at the conclusion that the temperature in the cube will follow an exponential decay, i.e. T_c(t)=(T_c(0)-T_s)*exp(-cte*S*t/mC_p) + T_s. Best, Jeff

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