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Transport Phenomena Question Bank!

UNIT -I

TRANSPORT PHENOMENA BY MOLECULAR MOTION

PART A (2 MARK)

1.            What is the importance of Transport Phenomena?

2.            Explain the analogous nature of the different divisions of Transport Phenomena.

3.            What is substantial time derivative?

4.            What do you mean by reference frames?

5.            Compare Newton’s law of Viscosity with Hook’s law of elasticity

6.            What is the science of Rheology?

7.            What are the units of dynamic viscosity and kinematic viscosity?

8.            Define Newtonian Fluids.

9.            What is a pseudo plastic?

10.         What is Bingham plastics?

11.         Define Viscosity.

12.         What is meant by Thixotrophic fluid?

13.         What is the difference between dilatant and pseudoplastic fluids?

14.         Define non-Newtonian fluids.

15.         Explain Newton’s law of viscosity.

16.         What is slip velocity?

17.         State and explain power law of viscosity.

18.         List some models to characterize non-Newtonian fluids.

19.         What are boundary conditions?

20.         What is the velocity of fluid at the wall of a pipe?

21.         What is Oswald-de Waele model?

22.         Explain the Eyring model.

23.         What is Ellis model?

24.         How does the viscosity vary with temperature for liquids?

PART B

1. Write short notes on (a) Conservation Laws, (b) Continuous concept, (c) Field and reference frames, (d) Substantial Derivative, (e) Total derivative and (f) Boundary conditions.

2. What are the different methods of analysis adopted for experimental data? Differentiate between Differential and Integral analysis.

3. Develop the concept of Viscosity for the Newtonian Fluids and the corresponding rheological property terms for the Newtonian fluids.

4. Write Short Notes on: a) Newtonian Fluids, b) Bingham plastics, c) Oswald De-waele Model, d) The Ellis model, e) The Reiner-Philippof model.

5. Discuss the theories of of viscosity of gases and liquids in respect of effect of temperature and pressure.

6. Discuss the theories of of thermal conductivity of gases and liquids in respect of effect of temperature and pressure.

7. Discuss the theories of of diffusion of gases and liquids in respect of effect of temperature and pressure.

8. Compute the viscosity of CO₂ at 300 K and 1 atm pressure

    Given: e / R= 190 K; s  = 3.996 A^o  and W_m    = 1.286

9. Discuss in detail the various models explaining the non-newtonian behavior of fluids.

10. Discuss in detail about the laws of conservation of momentum, energy and mass for engineering flow systems.

11. Write briefly on the theory of viscosity of liquids

12. Describe the phenomenological equations for momentum, heat and mass transfer.

UNIT -II

ONE DIMENSIONAL TRANSPORT IN LAMINAR FLOW (SHELL BALANCE)

PART A (2 MARK)

(1) Define Lorenz number. What are its units?
(2) What is the co-efficient b for an ideal gas?
(3) Write the units of Viscosity and Thermal conductivity.
(4) What is the effect of temperature on thermal conductivity?
(5)What is meant by slip flow regime and Knudsen flow regime?
(6)Write down shell momentum balance equation.
(7) What is Hagen-Poisceulle Equation and when is it used?
(8)Define compressible and incompressible fluids?
(9) State the Newton’s second law of motion.
(10) Write the Hagen-Poiseuille equation.
(11) What is the proportion of Average velocity with the maximum velocity for flow of Newtonian fluids through circular ducts under laminar flow conditions?
(12) Define Reynolds number. What are its dimensions?
(13) What are the implied assumptions in the derivation of the Hagen-Poiseuille equation?
(14) What is hydraulic radius?
(15) Compare Fourier’s law with Newton’s law of viscosity.
(16) What is free convection?
(17) What is Forced convection?
(18) Define Nusselts number.
(19) State Dittus-Boeltier equation.
(20) A vessel at a higher temperature is insulated with two different insulating materials. The first layer has a higher thermal conductivity than the second. In which layer the temperature drop will be more?
(21) Define Prandtl number.
(22) What is Brinkman number?
(23) Write down Grashof number and indicate it as the ratio of forces.
(24) Define effectiveness of a fin.
(25) Differentiate between natural convection and forced convection.
(26) What are the dimensionless numbers that characterize free convection?
(27) Compare thermal resistances in series and the electrical resistances in series.
(28) What is the significance of Npr and Nsc ?
(29) Explain equimolar counter diffusion with an example
(30) Define mass average velocity.
(31) Give a comparative account of diffusion and heat transfer. (32) Define mass transfer coefficient.
(33) State Fick’s law of diffusion.
(34) Define molar average velocity.
(35) What is the effect of pressure on diffusivity?
(36) Define mass flux.
(37) What is diffusion?
(38) Define molar flux.
(39) What is the effect of temperature on diffusivity ?
(40) Define Sherwood number.
(41) What are the units of diffusivity?
(42) What are the units of mass transfer co-efficient.
(43) Write the dimensionless numbers significant for fluid flow processes.
(44) What purpose does wetted wall column serve?
(45) Write down the shell mass balance equation
(46) State the criteria for Boundary conditions in diffusion problems
(47) Compare and contrast homogenous and heterogeneous reactions.
(48) What is the relationship between friction factor and JH factor.
(49) Compare and contrast conduction and convection.

PART B

1. A fluid with constant viscosity and density flows along an inclined flat surface under the influence of gravity with no ripples. Derive the equations for momentum flux and velocity distribution.  Mention all your assumptions.

2. Two immiscible incompressible fluids are flowing in the z-direction in a horizontal thin slit of length ‘L’  and width W under the influence of a pressure gradient. The fluid rates are so adjusted that the slit is half filled with Fluid I (the more dense phase) and half filled with Fluid II (the less dense phase). Analyze  the system in terms of the distribution of velocity and momentum flux.

 Show how if the viscosities of both the liquids are same the results simplify to the parabolic velocity for laminar flow of pure fluid in a slit.

3. For flow of a viscous liquid in laminar flow in a slit formed by two parallel plates with a distance 2b apart. The wall length is ‘L’ and width “W” Make differential momentum balance and obtain the expression for the volumetric flow for the slit.

4. 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.

5. A non-Newtonian Fluid, described by Bingham Model.

          t  =t ₀   -  m₀ [dv_z / dr] if r > r₀     and     t = 0 if  t  £ t ₀

is flowing through a vertical tube as a result of a pressure gradient. The radius and length of the tube are ‘R’ & ‘L’ respect-tively. Obtain a relationship between the volumetric flow rate ‘Q’ and the pressure gradient by shell balance technique. Also show that for t ₀ = 0, the relationship reduces to Haegan-Poiseulle Eqn.

6. Derive the equation for the temperature distribution for heat conduction with a viscous heat source.

7. Derive an equation for heat transfer in a cooling rectangular fin.

8. An electric current passes through a wire of circular cross section with radius R and electrical conductivity K_e. The current density is I. Rate of heat production  per unit volume is S = [I² / K_e ] . Surface of the wire ia at a temperature T₀. Derive an equation to determine the radial temperature distribution.

9. Derive the equation for the rate of mass transfer in respect of ‘diffusion through a stagnant film’.

10. Derive the concentration profile in the gas film for diffusion with heterogeneous chemical reaction.

 11. Glycerine is flowing through a horizontal tube of 0.5 m long and 3 mm inside diameter. For a pressure drop of 3 atm., the flow rate is 0.0002 m³ / min. The density of glycerine is 1.26 g / cc. From the flow data find the viscosity of glycerine.

12. Determine the heat transfer per square meter of wall area for a furnace wall with inside gas at 1500 K. The furnace wall is composed of 0.108 m layer of fire clay brick and 0.7 cm thickness of mild steel at the outer surface. Heat transfer co-efficient h_i = 5,110 W/m²K  and h_o = 25 W/m²K respectively. Calculate the temperature at each surface and at the brick-steel interface.

13. An oil is acting as lubricant for a pair of cylindrical surfaces. The angular velocity of the outer cylinder is 7,900 rpm. Outer cylinder has a radius of 6 cm and the clearance between the cylinders is 0.02. What is the maximum temperature of the oil if both wall temperatures are at 160⁰C. The physical properties of the oil are m = 92.3 x 10^-3 N.s/m²;   r = 1200 Kg/m³ and k = 2.5 W/m⁰C

                    

14. A fluid is flowing through a circular tube of length ‘L’ and radius ‘R’. Viscosity and density are constant. The flow is laminar. Derive an equation for Hagen-Poiseuille. Indicate all the assumptions you have made.

15. Derivation of Flow through a circular tube under laminar conditions will lead to the Hagen Poiseuille equation. Page No. 42-46. Figure is to be drawn and the final expression for the volumetric flow rate  Q as:

                       Q = p [(P_o  - P_L ) R⁴/8 m L]

16. Develop an equation for heat conduction through composite cylindrical walls.

17. Derive the concentration distribution and molar flux distribution for diffusion with homogeneous chemical reaction.

18. Derive the differential equation for the absorption of a gas in a falling liquid film.

UNIT -III

EQUATIONS OF CHANGE AND THEIR APPLICATION

PART A (2 MARK)

(1) Explain partial time derivative. Enunciate with example
(2) Explain Total time derivative. Give example
(3) What is Navier-Stokes equation?
(4) Explain Stokes’ Law.
(5) Explain Euler’s Equation.
(6) Write the dimensionless numbers significant for fluid flow processes.
(7) Define friction factor.
(8) Define the terms isothermal and non-isothermal systems.
(9) What is drag coefficient?
(10) What purpose does wetted wall column serve?
(11) Write down the Equation of Continuity for binary mixture.
(12) Write Blake Kozney equation.
(13) What is the Laplacian operator?
(14) Write down the q-component of the Equation of motion in Cylindrical co-ordinates
(15) Write down the Equation of Continuity in rectangular and cylindrical co-ordinates.
(16) Write down the time smoothed equation of motion
(17) Write down the r-component of the Equation of motion in Cylindrical co-ordinates
(18) Write Blake Kozney equation.

PART B

(1)	Derive the equations of continuity for a binary mixture.
(2)	Derive the Navier – Stoke’s equation through shell momentum balances.

(3)	Derive the equation of Continuity from shell mass balances in three dimensional Cartesian co-ordinates
(4)	Determine the velocity distribution for the laminar flow of an incompressible fluid flowing through a cylindrical tube. The following equation is given for the z-component of the equation of motion:      0 = - (dP / dz) + m r d/d r [r (dVz / dr)]
(5)	Derive the Hagen–Poisueille equation by the application of Navier-Stoke’s equation.
(6)	Write Continuity equation, Navier-Stoke’s equation, Euler equation and explain their field of application.
(7)	A hollow steel sphere, 5 mm diameter with a mass of 0.05 g, is released in a column of liquid and attains a terminal velocity of 0.5 cm/sec. The liquid density is 0.9 g/cc. The local acceleration due to gravity is 981 cm/s2. The sphere is far enough from the container walls so that their effect may be neglected. (a) Compute the drag force; (b) Compute the drag co-efficient (c) Determine the viscosity of the liquid.
(8)	A fluid of constant density and viscosity is in a cylindrical container of radius R. The container is caused to rotate about its own axis at an angular velocity, W. The cylinder axis is vertical. Find the shape of the free surface when steady state is established. Given: r [vq2/ r] = (dP / dr) ; m(d / dr)[(1/r) (d / d r)(r vq)] = 0  &  [dP/dZ] = - r. g
(9)	Write Continuity equation, Navier-Stoke’s equation, Euler equation and explain their field of application.

UNIT -IV

TRANSPORT IN TURBULENT AND BOUNDARY LAYER FLOW

PART A (2 MARK)

(1)Write Blassius formula
(2) State Deissler’s empirical formula for the region near the wall.
(3) Define Prandtl mixing length.
(4) What is Von Karman’s Similarity hypothesis?
(5) What is a Boundary layer?
(6) State if the momentum boundary layer thickness is lower than the thermal boun- dary layer thickness.
(7) What is eddy viscosity?
(8) Define porosity.
(9) Define “Instantaneous Pressure” and “Time smoothed Pressure”.
(10) Write down the Burke-Plummer equation.
(11) Write down the Ergun’s equation.
(12) Define mass average velocity.
(13) What is Turbulence?
(14) What are the ranges of Reynolds number for flow over a flat plate.
(15) Write down the 1/7th power law.
(16) Write down the time smoothed equation of motion
(17) Write the expression for hydrodynamic boundary layer thickness for flow past a flat plate.
(18) Write down the expression for D=dT/d for the situation when D< 1
(19) Write down the expression for D=dC/d for the situation when D< 1

(20) Write the relationship between friction factor ‘ f ’ and  Reynolds number.

PART B

1.    Derive the logarithmic velocity distribution for turbulent flow. [For both near the wall and far away from wall].

2.    [a] Explain with a neat sketch, the velocity distribution for turbulent flow in tubes.

[b] Write down the equations for the three regions of turbulent flow.

3.    Explain The following :  (a) Reynolds stresses, (b) Eddy Viscosity, (c) Creeping flow  (d) Drag coefficient.

4.    What do you know about Boundary Layer theory? Illustrate with flow near a wall suddenly set in motion.

5.    Discuss the laminar and turbulent hydrodynamic, thermal and concentration boundary layer thicknesses.

6.    Obtain a description of the incompressible flow pattern near the leading edge of a flat plate immersed in a fluid stream.

7.    Write short notes on the following: (i) Boundary layer thickness; (ii) Displacement thickness; (iii) Momentum thickness and (iv) Energy thickness.

8.    Water is flowing through a long straight smooth pipe of 15 cm inside diameter at a temperature of 20⁰C. The pressure gradient along the length of the pipe is 50 mm Hg/kilometer. What is the volumetric rate of flow assuming the flow is turbulent.

9.    Write short notes on the following: (i) Boundary layer thickness; (ii) Displacement thickness; (iii) Momentum thickness and (iv) Energy thickness.

10. Explain in detail, the following: (a) Flow through packed bed & (b) Von Karman’s similarity hypothesis.

UNIT -V

ANALOGIES BETWEEN TRANSPORT PROCESSES

PART A (2 MARK)

(1) State the usefulness of analogy.

(2) Define JD  factor

(3) Write down the jD factor.

(4) Define jH factor.

(5) State Colburn analogy.

(6) State the Reynold’s analogy

(7)Define Soret coefficient s .

(8) What is Soret effect?

(9) Write down Schmidt number and compare with Prandtl number.

(10) Write down the expression for D=dC/d for the situation when D< 1

(11) Compare the temperature, pressure and composition dependence of mass diffusivity.thermal conductivity and viscosity.

PART B

(1)	Write what you know about Reynolds Analogy in detail.
(2)	Describe the Von Karman hypothesis in respect of analogy between the different transport operations.
(3)	Write an account of Colburn analogy
(4)	Write an essay about analogy that exists amongst the three transports- Momentum, Heat and Mass.
(5)	Write in detail about Prandtl Analogy.

(6)     Write Short notes on:

          (i) Reynolds analogy

          (ii) Prnndtl analogy

          (iii) Colburn analogy