Plug flow in a circular tube with constant wall temperature (asymptotic solution for large z ). Please refer to the figure on the following page when solving this problem. A fluid is flowing axially in a circular tube of radius R (see figure below). Before the fluid arrives at the plane z=0, it is at a uniform temperature T0. For >0, the tube wall is maintained at a constant temperature Tw. Assume that the velocity vz of the fluid is uniform over the tube cross-section; i.e., plug flow. (i) Neglecting axial conduction and viscous dissipation, determine the temperature distribution T(r,) of the fluid for >>. (ii) Use the expression for T(r,z) to find an expression for the radial averaged temperature, Tb. (iii) Consider the dimensionless temperature given by: =Tb(z)TwT(r,z)Tw Show that for large values of z, is only a function of r and is independent of z. (iv) Derive and expression for the Nusselt number for large z. Plug flow in a circular tube with constant wall temperature (asymptotic solution for large z ). Please refer to the figure on the following page when solving this problem. A fluid is flowing axially in a circular tube of radius R (see figure below). Before the fluid arrives at the plane z=0, it is at a uniform temperature T0. For >0, the tube wall is maintained at a constant temperature Tw. Assume that the velocity vz of the fluid is uniform over the tube cross-section; i.e., plug flow. (i) Neglecting axial conduction and viscous dissipation, determine the temperature distribution T(r,) of the fluid for >>. (ii) Use the expression for T(r,z) to find an expression for the radial averaged temperature, Tb. (iii) Consider the dimensionless temperature given by: =Tb(z)TwT(r,z)Tw Show that for large values of z, is only a function of r and is independent of z. (iv) Derive and expression for the Nusselt number for large z