Question

A furnace wall is to be built of 20-cm firebrick and building (structural) brick of same thickness. The thermal conductivities of fire brick and building brick are 1.6 and 0.7 W/m.K , respectively. The inner surface of the firebrick is at 980 °C, the outer surface of the structural brick is at 30 °C. The heat flux and the temperature of the brick interface are..

Answer 1

Answer:

q=2313.04$W/m^2$

T=690.86°C

Explanation:

Given that

Thickness t= 20 cm

Thermal conductivity of firebrick= 1.6 W/m.K

Thermal conductivity of structural brick= 0.7 W/m.K

Inner temperature of firebrick=980°C

Outer temperature of structural brick =30°C

We know that thermal resistance

$R=\dfrac{t}{KA}$

These are connect in series

$R=\left(\dfrac{t}{KA}\right)_{fire}+\left(\dfrac{t}{KA}\right)_{struc}$

$R=\dfrac{0.2}{1.6A}+\dfrac{0.2}{0.7A}\ K/W$

$R=\dfrac{23}{56A}\ K/W$

Heat transfer

$Q=\dfrac{\Delta T}{R}$

$Q=56A\times \dfrac{980-30}{23}\ W$

So heat flux

q=2313.04$W/m^2$

Lets temperature between interface is T

Now by equating heat in both bricks

$\dfrac{980-T}{\dfrac{0.2}{1.6A}}=\dfrac{T-30}{\dfrac{0.2}{0.7A}}$

So T=690.86°C