Snow Melting Concrete Slab Heating Cable Temperature Profile

What is the required thickness of the concrete slab to maintain the specified temperature difference?

Considering the data provided, how can we formulate the temperature profile in the concrete slab?

Answer:

By applying the Fourier's law of heat conduction and plugging in the given values, we ascertain that the required thickness of the concrete slab is 29 mm to maintain the required temperature difference.

To determine the required thickness of the concrete slab to maintain the specified temperature difference, we utilize Fourier's Law of heat conduction. This law relates the heat flux, thermal conductivity, temperature difference, and the thickness of the material.

Firstly, we have the heat flux (q) of 1200 W/m2, the thermal conductivity (k) of the concrete as 1.4 W/m⋅K, and the temperature difference (T1 - T2) not exceeding 25°C. By substituting these values into the formula and rearranging for the thickness (L), we find that L = -1.4 * 25 / 1200, which gives L = -0.029 m or -29 mm.

The negative sign indicates the direction of heat flow, but since thickness cannot be negative, we consider the absolute value. Therefore, the thickness of the concrete slab required is 29 mm to maintain the specified temperature difference between the heater surface and the slab surface.

For formulating the temperature profile in the concrete slab, we utilize the principles of heat conduction to understand how heat moves through the material. This analysis ensures that the concrete slab will distribute heat uniformly and efficiently to melt snow without experiencing excessive thermal stress.