Transport Phenomena — Summer 2022

Discuss the significance of momentum, thermal and mass diffusivities.

Find which of the following velocity fields v(x,y,z) are irrotational? a. v = by, v = 0, v = 0 x y z b. v = bx, v = 0, v = 0 x y z c. v = by, v = bx, v = 0 x y z d. v = -by, v = bx, v = 0 x y z

Compare Newton’s Law of viscosity with Fourier’s Law of heat conduction and Fick’s of mass diffusion for their analogies.

Define thermal diffusivity and Prandtl number.

Discuss about temperature and pressure dependency of thermal conductivity.

Derive equation of motion from momentum balance and modify it to the Navier-Stoke’s equation.

Derive Continuity equation and prove that for incompressible fluids divergence of velocity vector is zero i.e. ∇.v = 0

What are commonly used boundary conditions of shell momentum balance?

Explain the molecular momentum flux and write the components of the molecular momentum flux tensor.

A Newtonian fluid is flowing in laminar flow through a narrow slit formed by two parallel plates a distance 2B apart (as shown in fig.) where B << Wso that end effects can be neglected. Obtain the shear stress and velocity profile for the flow.

Discuss the general trends of viscosity with temperature and pressure for ordinary fluids.

Glycerine at 26.5 0C is flowing through a horizontal tube 1 ft long and with 0.1 in. inside diameter. For a pressure drop of 40 psi, the volume flow rate1 is 0.00398 ft3/min. The density of glycerine at 26.5oC is 1.261 g/cm3. From the flow data, find the viscosity of glycerine in centipoises and in Pa.s.

Aliquid is slowly flowing down an inclined flat plate of length Land width W. Find Velocity distribution as a function of the fluid film thickness. Also find maximum and average velocity. Neglect end effects.

Define the molecular and convective and total heat flux.

Acopper wire has a radius of 2 mm and a length of 5 m. For what voltage drop would the temperature rise at the wire axis be 10oC, if the surface temperature of wire is 20oC? For copper, Lorentz No. k/(k T ) is 2.23 x 10-8 volt2 /K2 e 0

Consider an electric wire of circular cross section with radius Rand electrical conductivity k ohm-1 cm-1. Through this wire there is an e electric current with current density Iamp/cm2. The transmission of an electric current is an irreversible process, and some electrical energy is converted into heat (thermal energy). The rate of heat production per unit volume is given by the expression S = I2/k . The surface of the wire is e e maintained at temperature T . Find the radial temperature distribution o within the wire.

State the fundamental law that governs the convictive heat transfer.

An oil is acting as a lubricant for a pair of concentric cylindrical surfaces. The outer cylinder rotates leading to the viscous heat dissipation given by equation T −T 𝜇v2x 1 x x x o b = (1− )+ T −T 2k bT −Tb b b o b o What is the temperature at the center (x = b/2) in the annulus? Both wall temperatures are known to be 70 oC. Data: Angular velocity = 7908 rpm Radius of The outer cylinder = 5.06 cm Clearance between the cylinders = 0.027 cm. Viscosity = 92.3 cp Density = 1.22 g/cm3 Thermal conductivity = 2.303 W/moC

Define Mass and Molar Concentrations, Mass Average and Molar Average Velocities, Molecular Mass and Molar Fluxes

Explain temperature and pressure dependency of diffusivity.

Show that for equimolar counter diffusion DAB = DBA OR2

Define and explain binary Diffusivity.

Shortly explain the theory of diffusion in gases at low density.

Derive equation of molar flux for steady state diffusion of one gaseous component through stagnant non diffusing second component.