$(2)$ Consider a plane wall of $L=25cm$ thickness and conductivity of $5\frac{W}{m}K.$ The wall is

experiencing a uniform volumetric heat generation rate of $10$ kW per cubic meter. The wall is

separating two flow environments as shown in the figure. The flow on the left has an undisturbed

temperature of $10C$ providing a convection coefficient of $20\frac{W}{m^2}K,$ while the one on the right

has an undisturbed temperature of $20C$ providing a convection coefficient of $40\frac{W}{m^2}K.$ The

right surface of the wall also looks at a large enclosure $($surrounding surface$)$ that is in thermal

equilibrium with the fluid away from the wall surface. Take the wall surface emissivity as $0\mathrm{.}9.$

a$)$ By help of the approach taken for the first problem, obtain suitable set of equations for

determining the wall surface temperatures including the radiation effects.

b$)$ What are the values of the wall surface temperatures? Use a root finding technique if

necessary.

$T_{,2}=50C$

$h_2=10\frac{W}{m^2}K$

$T_{,1}=10C$

$h_1=20\frac{W}{m^2}K$

$L=0\mathrm{.}25m$