Question

The wall of an industrial furnace is constructed from 0.15-m-thick, fireclay brick having a thermal conductivity of LZ W/m.K. Measurements made during steady state operation reveal temperatures of 1400 and 1150 K at the inner and outer sur- faces, respectively. What is the rate of Teat loss through a wall that is 0.5 m by 1.2 m on a side?

Answer 1

Answer:

The rate of heat loss through the wall is 1700 watts.

Explanation:

The complete statement of the problem is:

The wall of an industrial furnace is constructed from 0.15-m-thick, fireclay brick having a thermal conductivity of 1.7 W/m·K. Measurements made during steady state operation reveal temperatures of 1400 and 1150 K at the inner and outer sur- faces, respectively. What is the rate of heat loss through a wall that is 0.5 m by 1.2 m on a side?

Given that wall of the industrial furnace is under steady conditions of heat transfer and whose configuration is a flat element, we use the equation of conductive heat transfer rate ($\dot Q$), measured in watts:

$\dot Q = \frac{k\cdot w\cdot h}{l}\cdot (T_{i}-T_{o})$

Where:

$k$ - Thermal conductivity, measured in watts per meter-Kelvin.

$w$ - Width of the wall, measured in meters.

$h$ - Height of the wall, measured in meters.

$l$ - Thickness of the wall, measured in meters.

$T_{i}$ - Inner surface temperature, measured in Kelvin.

$T_{o}$ - Outer surface temperature, measured in Kelvin.

If we know that $k = 1.7 \,\frac{W}{m\cdot K}$, $w = 1.2\,m$, $h = 0.5\,m$, $l = 0.15\,m$, $T_{i} = 1400\,K$ and $T_{o} = 1150\,K$, the steady state heat transfer is:

$\dot Q = \left[\frac{\left(1.7\,\frac{W}{m\cdot K} \right)\cdot (1.2\,m)\cdot (0.5\,m)}{0.15\,m} \right]\cdot (1400\,K-1150\,K)$

$\dot Q = 1700\,W$

The rate of heat loss through the wall is 1700 watts.