Answer:
The right wall surface temperature and heat flux through the wall is 35.5°C and 202.3W/m²
Explanation:
Thickness of the wall is L= 20cm = 0.2m
Thermal conductivity of the wall is K = 2.79 W/m·K
Temperature at the left side surface is T₁ = 50°C
Temperature of the air is T = 22°C
Convection heat transfer coefficient is h = 15 W/m2·K
Heat conduction process through wall is equal to the heat convection process so
[tex]Q_{conduction} = Q_{convection}[/tex]
Expression for the heat conduction process is
[tex]Q_{conduction} = \frac{K(T_1 - T)}{L}[/tex]
Expression for the heat convection process is
[tex]Q_{convection} = h(T_2 - T)[/tex]
Substitute the expressions of conduction and convection in equation above
[tex]Q_{conduction} = Q_{convection}[/tex]
[tex]\frac{K(T_1 - T_2)}{L} = h(T_2 - T)[/tex]
Substitute the values in above equation
[tex]\frac{2.79(50- T_2)}{0.2} = 15(T_2 - 22)\\\\T_2 = 35.5^\circC[/tex]
Now heat flux through the wall can be calculated as
[tex]q_{flux} = Q_{conduction} \\\\q_{flux} = \frac{K(T_1 - T_2)}{L}\\\\q_{flux} = \frac{2.79(50 - 35.5)}{0.2}\\\\q_{flux} = 202.3W/m^2[/tex]
Thus, the right wall surface temperature and heat flux through the wall is 35.5°C and 202.3W/m²
