A plane wall of thickness L=0.1 m and thermal conductivity 25 W/m.K, having uniform volumetric heat generation rate of q=0.3 MW/m³ is insulated on one side, while the other side is exposed to fluid at T = 92 °C. The convection heat transfer coefficient between the wall and this fluid is 500 W/m²K. Find the location and value of the maximum temperature within the wall. [Hint: with text equation16.43, evaluate integration constants C1 and C2 using dT/dx=0 at x=0 and T=T, at x=L. To obtain the value for T., perform an appropriate energy balance to show that T = T +(ġL/h)]. A brass rod (thermal conductivity k=133 W/mK) 100 mm long and 5 mm in diameter extends horizontally from a body at 200 °C and serves as a cooling fin. The rod is in an air environment with T = 20 °C and h=30 W/m²K. Choose results for the appropriate tip boundary condition and find the temperature of the rod at 25, 50 and 100 mm from the body. Determine the total fin heat transfer rate and the fin effectiveness. What is the percent error incurred for each of these five quantities if the simpler expressions for an infinite fin were used? VII. Unsteady heat conduction - Consider a cube of material of side 20 cm with two parallel faces exposed and the other four faces covered by perfect insulation. The entire cube, at a uniform temperature of 300 °C, is withdrawn from a furnace and quickly moved to room air at 25 °C with a convection heat transfer coefficient of 20 W/m²K. Using the lumped capacitance approximation, find the time taken for the cube to cool down to 50 °C, for each of the following cube materials: [i] pure copper [ii] plain carbon steel [iii] stainless steel AISI 316 and [iv] pyrex glass. Use the property values at 300 K from text Tables HT-1 and HT-2 for these materials.