Problem 1 A one-dimensional plane wall of thickness 2L=100 mm experiences a uniform thermal energy generation = 1000 W/m and is convectively cooled at x = 50 mm by an ambient fluid characterized by T = 20C. The steady- state temperature distribution measured within the wall can be approximated as: T(x)=a(-x)+b, where a=10C/m and Th b=30C. 1- Develop an expression for the thermal conductivity k of the wall material, and calculate it numerically. 2L Th 2- Develop and expression for the convection heat transfer coefficient h, and calculate it numerically. Problem 2 The steady-state temperature distribution in a semi-transparent material (thermal conductivity: k; thickness: L) exposed to laser irradiation is of the form: T(x)= +Bx+C, ka [solution: h=5 W/m-K] laser irradiation T(x) where A,a,B,C are known constants. For this situation, radiation absorption in the material is manifested by a distributed heat generation term, (x). semi-transparent medium 1- Obtain expressions for the conduction heat fluxes at the front and rear surfaces 2- Derive an expression for e(x) 3- Derive an expression for the rate gabs at which radiation is absorbed in the entire material, per unit surface area. Express your result in terms of the known constants for the temperature distribution, the thermal conductivity of the material, and its thickness. [solution: gabs = (1-e)] a