1) Fluid X is flowing in a circular pipe with a constant velocity v (m/s). The fluid is cooled by a jacket kept at constant temperature, Tj. Fluid velocity is plug shaped, in other words uniform at radial positions. Assume that temperature is uniform in radial positions because of turbulent flow conditions; p and Cp of the fluid are constants. The inlet temperature (at z=0) is constant and uniform at T. (T.>T;). Assume that thermal conduction of heat along the z axis is small relative to convection. Heat transfer film coefficient is h. Cooling Az jacket, Tj v, To, p, Cp z=0 a) Perform an unsteady state energy balance using shell balance technique and obtain a PDE model. State the boundary and initial conditions. Do not solve