A concrete slab is 10.0 cm thick and has an area of 6.00 m2. Electric heating coils are installed under the slab to melt the ice on the surface in the winter months. What minimum power must be supplied to the coils to maintain a temperature difference of 21.0°C between the bottom of the slab and its surface? Assume all the energy transferred is through the slab, and the thermal conductivity of the concrete is 1.3 J/s · m · °C.

Question
Asked Oct 20, 2019

A concrete slab is 10.0 cm thick and has an area of 6.00 m2. Electric heating coils are installed under the slab to melt the ice on the surface in the winter months. What minimum power must be supplied to the coils to maintain a temperature difference of 21.0°C between the bottom of the slab and its surface? Assume all the energy transferred is through the slab, and the thermal conductivity of the concrete is 1.3 J/s · m · °C.  

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Expert Answer

Step 1

Given,

А - бm?
аT 3D 21°С
dх %3D10cт%30. 1m
- 21°C
k 1.3J/(sec)(m)°C
° C
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А - бm? аT 3D 21°С dх %3D10cт%30. 1m - 21°C k 1.3J/(sec)(m)°C ° C

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Step 2

Power through a given slab due to heat conduction is given as,

Р-kА
dx
|H
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Р-kА dx |H

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Step 3

By substituting gi...

ат
Р -kА
dx
21
P (1.3)(6)
0.1
Р-1638W
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ат Р -kА dx 21 P (1.3)(6) 0.1 Р-1638W

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Heat Transfer

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