Consider a fluid (of constant density ρ) in-compressible, laminar flow in a tube of circular cross section inclined at an angle β to the vertical. End effects may be neglected because the tube length L is relatively very large compared to the tube radius R. The fluid flows under influence of both a pressure difference Δp and gravity.

a) Determine expressions for the steady-state shear stress distribution and the velocity distribution profile for a Newtonian fluid (of constant viscosity μ ).

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.