A heating cable is embedded in a concrete slab to melt snow on a 5-m × 5-m surface area. The heating cable is heated electrically with joule heating. The concrete has a thermal conductivity of 1.4 W/m•K, and the layer between the slab surface and the heater surface is 50 mm. When the surface is covered with snow, the heat generated from the heating cable can melt snow at a rate of 0.1 kg/s. According to the National Electrical Code (NFPA 70), the power density (heat flux) for embedded snow-melting equipment should not exceed 1300 W/m2. Under the given conditions, does the concrete slab with the embedded heating cable operate in compliance with the NFPA 70 code? Also, to minimize thermal stress in the concrete, the temperature difference between the heater surface (T1) and the slab

Question

surface (T2) should not exceed 21°C (2015 ASHRAE Handbook—HVAC Applications, Chap. 51). Do the current operating conditions allow T1 ? T2 ? 21°C?







What will be an ideal response?

Answer 1

A 5 m × 5 m concrete slab with embedded heating cable melts snow at a rate of 0.1 kg/s. The power density (heat flux) for the embedded heater is to be determined whether it is in compliance with the NFPA 70 code. Also, the temperature difference between the heater surface and the slab surface is to be determined whether it exceeds 21°C, as recommended in the ASHRAE Handbook to minimize thermal stress.

Assumptions1 Steady operating conditions. 2 Slab surface and heater surface temperatures are uniform. 3 Heat transfer through the concrete layer is one-dimensional. 3 Properties of the concrete are constant. 4 The heater heats the surface uniformly.

Properties The thermal conductivity of concrete is given as 1.4 W/m•K. The latent heat of fusion for water is 333.7 kJ/kg (Table A-2).



AnalysisThe heat rate required for melting snow at 0.1 kg/s is



For a surface area of 5 m × 5 m, the power density (heat flux) is

To determine the temperature difference between the heater surface(T1) and the slab surface(T2), we use the Fourier law of conduction:



DiscussionThe power density for the embedded heating cable in the concrete slab slightly exceeds the limit set by the National Electrical Code® (NFPA 70) of 1300 W/m2. The temperature difference between the heater surface and the slab surface is about 27°C higher than the recommended value by the 2015 ASHRAE Handbook—HVAC Applications, Chapter 51.