Transport Phenomena — Summer 2024

Compare Scalar, Vector and Tensor.

Examine the following velocity fields for the zero divergence and Irrotational vector. (bold indicates vector)

u = byi + 0j+ 0k

v = bxi – bxj + 0k

w = byi + bxj + 0k

s = -byi + bxj + 0k

Estimate the thermal conductivity of following gas mixture at 1 atm and 293 Kfrom given data on the pure components at same pressure and temperature Mole Molecular µ ×107 k ×107 Species α fraction α α Weight (gm/cm.s) (cal/cm.s.K) x α CO 1 0.133 44.01 1462 3832 O 2 0.039 32 2031 6122 N 3 0.828 28.016 1754 6272

Oil has a kinematic viscosity of 2 × 10-4 m2/s and a density of 0.8 × 103 g/m3. If we want to have a falling film of thickness of 2.5 mm on a vertical wall, what should the mass rate of flow of the liquid be?

Find 𝝉·v (dot product) and 𝝉×v (cross product). τ is a tensor and v is vector

Derive the expression for max velocity, avg. velocity and mass flow rate for a flow through circular pipe system.

Aviscous fluid is in laminar flow in a slit formed by two parallel walls at a distance 2B apart. Make a differential momentum balance and obtain the expression for the distributions of momentum flux and velocity.1

Explain Newton’s Law of Viscosity

Give the significance of Total time derivative, Partial time derivative and Substantial time derivative with example.

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

State and explain the general shell momentum balance equation.

State the significance of three dimensionless numbers having thermal, momentum and molar diffusivity. (viz. Pr. Sc. and Le.)

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.

Explain Fourier’s Law of heat conduction

Compare thermal conductivity and thermal diffusivity with necessary equations

For heat conduction with electrical source, construct the expression of Max. Temperature, Avg. Temperature and heat outflow at surface of electric wire

Explain the molecular and convective and total heat flux

Explain the various boundary conditions used to solve heat transport problems.

Construct the expression of effectiveness of Cooling Fin

Explain Fick’s law of binary diffusion.

Explain Mass and Molar Fluxes, Convective Mass and Molar Fluxes.

Develop the mass flux equation for steady-state diffusion of Athrough stagnant Bwith the liquid vapor interface maintained at a fixed position.

Explain Temperature and Pressure dependence of diffusivities.

Explain Mass and Molar Concentrations, Mass Average and Molar Average Velocity.

Develop mass flux equation for diffusion Into a Falling Liquid Film (Gas Absorption, Forced Convection Mass Transfer)