$2021/2022$ FALL SEMESTER

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ME $343-$ HEAT TRANSFER MIDTERM EXAM

ne$-$dimensional, steady$-$state conduction with uniform internal energy generation occurs in a plane wall with a thickness of $60$ mm and constant thermal conductivity of $4\frac{W}{m}K.$ The surface at $x=0$ has a temperature of $110C$ and experiences convection with a fluid for which $T={24}^{\text{'}}C$ and $h=12\frac{W}{m^2}K.$ The surfaceat $x=1$ is well insulated. If the properties of the wall are known as $=1600k\frac{g}{m^3}$ and $c_p=4000\frac{\text{I}}{k}g$ K;

Sketch the scheme and write the boundary conditions. $($All parameters and boundary conditions must be written properly$)(30$ pts$)$

Applying an overall energy balance to the wall, calculate the volumetric energy generation rate $(4)(20$ pts$)$

Simplify the Heat Equation for given conditions and find the temperature distribution as a function of $x.(30$ pts