Chemistry: Afurnace consists of a 100 cm thick brick wall chamber in which gaseous material is combusted. the air surrounding the furnace chamber is at ambient temperature (25°c) and circulates due to natural convection with a value of the convection coefficient at 15 w/(m2.k). assuming a thermal conductivity of 1 w/(m.k) for brick wall, which can be assumed a blackbody, calculate the of the furnace wall if the outer wall inner temperature of the furnace wall if the oute temperature reaches 80°c at steady-state.

Afurnace consists of a 100 cm thick brick wall chamber

kenzierosa

04.01.2022

Explanation:

The heat transferred through conduction = heat transfer through radiation + heat transfer through convection

It is given that thermal conductivity of wall is 1 W/(m.K)

Boltzmann constant ( $\sigma_{e}$ ) = $5.68 \times 10^{-8} W/T^{4} m^{2}$

Formula to calculate the inner temperature of the furnace is as follows.

kA(T - 80) = $\sigma_{e} \times A \times (80 + 273)^{4} - (25 + 273)^{4} + hA(80 - 25)$

It is known that for black body emissitivity = 1

Now putting the given values into the above formula as follows.

kA(T - 80) = $\sigma_{e} \times A \times (80 + 273)^{4} - (25 + 273)^{4} + hA(80 - 25)$

$1 \times A(T - 80)$ = A ( $\sigma_{e} \times (80 + 273)^{4} - (25 + 273)^{4} + h(80 - 25)$ )

T - 80 = $5.68 \times 10^{-8} \times [(353)^{4} - (298)^{4}] + 1 \times 55$

T = $1338.25^{o}C$

Thus, we can conclude that the inner temperature of the furnace wall is $1338.25^{o}C$ .

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