Please provide a full and detailed solution to the problem below. Thank you!

Considering an aluminum cylinder (k=240W/m K) which is 0.5 m long and 10 mm in diameter. No heat transfer in the radial direction is assumed. It is known that the temperature profile along the axial direction is: T = 12x 2 - 100x + 150 Note that the unit of x is meter and temperature is degree Celsius. Evaluate the heat transfer rate at x=0 m and x=0.5 m