8HP - Transport Phenomena - October 2000
Part A (20 x 2 = 40 Marks)
- Define Newton's law of viscoity.
- What is meant by non-Netwtonian fluids?
- Give the ranges of Reynolds number for laminar flow and turbulent flow.
- What is teh shear stress at the centre of the pipe?
- State the Newton's second law of motion.
- Define Fourier's law of heat conduction.
- Write on 'Shell-energy balance'.
- Show that the 'Grashof number' is dimensionless.
- Explain the term free convection and forced convection.
- Define the terms isothermal and non-isothermal systems.
- How is thermal diffusivity defined? What are its units?
- Compare Fick's law of diffusion with Newton's law of viscosity.
- Define Stoke's law.
- What are the units of mass transfer coefficient?
- Define the term diffusion controlled chemical reaction.
- Define Fick's second law of diffusion.
- What is meant by Reynold's stress?
- Give equations for mass transfer rate for counter diffusion.
- Write the momentum balance for equations of motion.
- Define effectiveness of a fin.
Part B (5 x 12 = 60 Marks)
- (a) Derive the momentum flux and velocity distribution equations for a fluid flowing through an annulus of inner radius KR, outer radius R and length L. The density of the fluid is constant and the flow is steady and laminar.
(b) A fluid with constant viscosity and density flow along an inclined flat surface under the influence of gravity with no ripplings. Derive the equations for momentum flux and velocity distribution. The film thickness is measured away from the wall (that is, x = 0 at the wall, x = d at the edge of the film). Write all your assumptions.
- (a) Derive the Navier-Stoke's equation.
(b) A fluid of constant density and viscosity is in a cylindrical container of radius R. The container is rotated about its own axis at an angular velocity of W. The cylinder axis is vertical. Fine the shape of the free surface when steady state is reached.
- (a) (i) Discuss about the velocity distribution in turbulent flow. (4)
(ii) Derive semi-empirical expression for Reynold's stress. (8)
(b) Derive the Ergun equation.
- (a) Develop an equation for heat conduction through composite cylindrical walls.
(b) An oil is acting as a lubricant for a pair of cylindrical surfaces. The angular velocity of the outer cylinder is 7900 rpm. Outer cylinder has a radius of 6 cm and the clearance between the cylinders is 0.02 cm. What is the maximum temperature of the oil if both wall temperatures are at 160oC? The physical properties of oil are m = 92.3 x 10-3 N.s/m2; r = 1200 kg/m3 and k = 2.5 W/m.oC.
- (a) Derive the equation for the rate of mass transfers in 'diffusion through a stagnant gas film'.
(b) Derive the concentration profile in the gas film for diffusion with heterogeneous chemical reaction.