Consider a steel pipe (AISI 1010) that has an internal diameter of 1 m and a wall with 40mm thickness. The pipe is strongly insulated on the outside and, before the start of the flow, the walls of the pipe are at a uniform temperature of -20 C. With the start of flow, hot oil at 60C is pumped through the pipe, creating a conduit surface convective that corresponds to h= 500 W/m² K at the surface of the pipe.

a) Draw the temperature profiles along the thickness of the pipe, at 2 min, 3 min, 5 min, 6 min. min, 9 min, and 12 min, use the approximate equation for unsteady heat conduction on a flat wall, with n=1.

b) Determine the heat flux to the pipe from the oil at t = 2, 3, 5, 9, and 12 min.