Question

# Problem 3: A 1D plane wall has a thermal conductivity k=2 W/m-K and a thickness 2*L=20 mm, where Lis the half-thickness of the wall. It also has uniform volumetric heat generation ġ, as well as convection on both of its outer surfaces (x = ±L) where the free stream temperature is 30°C on both sides, but the convection coefficients are different. The steady-state temperature distribution in the wall is T(x) =-200000x2 + 1200x + 200, with T in units of degrees C and x in units of meters, and the coordinate origin (x = 0) is at the midplane of the walI. (a) Plot the temperature distribution using a graphing program (Excel, or Matlab), attach it to your solution, and answer these questions: i) is the temperature in the wall symmetric around not, what could be ca using it to be non-symmetric? iii) Can you guess which side has the higher convection coefficient? Why do you think that?= 0? ii) If (b) What is the volumetric rate of heat generation ġ in the wall? HINT: you should use the Heat Diffusion Equation (HDE) for this part. \text { (c) At what } x \text {-location in the wall is the heat flux } q_{x}^{\prime \prime}(x)=0 ? \text { Ans } 3 \mathrm{~mm}  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5