1. The wall of the unshielded combustion chamber of the steam boiler is made of foam-fireclay (rho =950kg/m^3) with a thickness of delta _(1)=300 mm and a layer of tripoli brick with a thickness of delta _(2)=150mm The layers are tightly adjacent to each other. The temperature on the inner surface of the combustion chamber is t_(s1)=600^circ C and on the outer surface is t_(s3)=10^circ C Calculate the heat flux and temperature in the place of contact between the layers.

To solve this problem, we need to use the concept of heat conduction and the thermal conductivity of the materials involved. The thermal conductivity of tripoli brick is given as $k_{2}=0.8W/mK$, and the thermal conductivity of foam-fireclay is $k_{1}=0.07W/mK$.<br /><br />First, let's calculate the heat flux using the formula for heat conduction:<br /><br />$q=\frac{k_{1} \cdot \delta_{1}}{\delta_{1}+\delta_{2}} \cdot \frac{t_{s1}-t_{s3}}{\delta_{1}+\delta_{2}}$<br /><br />Substituting the given values, we get:<br /><br />$q=\frac{0.07 \cdot 0.3}{0.3+0.15} \cdot \frac{600-10}{0.3+0.15}$<br /><br />Simplifying the equation, we find:<br /><br />$q=0.07 \cdot 0.3 \cdot \frac{590}{0.45}$<br /><br />$q=0.07 \cdot 0.3 \cdot 1313.33$<br /><br />$q=28.33W/m^{2}$<br /><br />Now, let's calculate the temperature at the place of contact between the layers using the formula for heat conduction:<br /><br />$t_{c}=t_{s1}-\frac{q}{k_{1}}$<br /><br />Substituting the given values, we get:<br /><br />$t_{c}=600-\frac{28.33}{0.07}$<br /><br />Simplifying the equation, we find:<br /><br />$t_{c}=600-406$<br /><br />$t_{c}=194^{\circ }C$<br /><br />Therefore, the heat flux at the place of contact between the layers is $28.33W/m^{2}$, and the temperature at the place of contact is $194^{\circ }C$.