2. (13 pts) A long cylinder of certain material with a diameter of 3 inch is initially at a uniform temperature of

80 °F. The cylinder is then placed in a medium at 1000 °F with an associated convective heat-transfer

coefficient of 5 Btu/(hr ft²-F). Material properties of the cylinder: the thermal conductivity

213 Btu/(hr ft "F), density 555 lbm/ft, and the specific heat capacity 0.092 Btu/(lbm-F). Can we

assume that the temperature gradient within the cylinder is quite small leading to an approximately uniform

temperature? Provide your reasoning.