(Solved): heat transfer 2. [25 pts] Consider a 50cm-thick wall with.a thermal conductivity of 25W/mK, ...

2. [25 pts] Consider a $50-\mathrm{cm}$-thick wall with.a thermal conductivity of $25\mathrm{W}/\mathrm{m}\cdot \mathrm{K}$, exposed to a constant heat flux of $q_0$ at $x=0$. The outside surface $(x=L)$ temperature is $T_{\mathrm{L}}=225^{\circ }\mathrm{C}$ and is exposed to surrounding air temperature at $25^{\circ }\mathrm{C}$ with average convection heat transfer coefficient of $15\mathrm{W}/{\mathrm{m}}^2\mathrm{K}$, and emissivity of 0.70 . (a) Starting from the heat equation and applying boundary conditions, show that the temperature in the wall can be expressed as: $T(x)=\left({\dot{g}}_0/k\right)(L-x)+T_L$. (b) Find wall heat flux, $q_0$ : (c) Determine the temperature of the left surface of the wall at $T(x=0)$. (d) Calculate the heat flux on the surface at $x=L$ due to convection. (e) Calculate the heat flux on the surface at $x=L$ due to radiation.