Transport Phenomena - short answer questions from AMIE exams (Summer 2019)

Answer the following in brief (10 x 2)

What are the factors on which viscosity depends?

The viscosity of the liquid increases if the density of the liquid increases. 
We know that the density of the liquid decreases as the temperature increases and hence viscosity also decreases.
So we can say that the viscosity of liquid depends on both density and temperature both. 

Differentiate between free and wall turbulence.

Turbulence can be generated in two ways: (1) by friction forces at solid walls (or surfaces) 
and (2) by the flow of fluid layers with different velocities past the other. These two types 
of turbulence are, respectively, known as wall turbulence and free turbulence.

What is ‘The Von Karman analogy?

Von Karman extended Prandtl’s analogy by separating the flow field into three distinct layers: a viscous sublayer, a buffer layer, and a turbulent core. In the buffer layer, molecular and eddy diffusivities are assumed to be of the same order of magnitude.

St = \frac{h}{{\rho {C_p}{v_m}}} = \frac{f}{2}\left( {\frac{1}{{1 + 5\sqrt {f/2} \{ (\Pr  - 1) + \ln [(5\Pr  + 1)/6]}}} \right)

The physical significance of Prandtl and Schmidt numbers

Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes.

In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers. When Pr is small, it means that the heat diffuses quickly compared to the velocity (momentum).

Equation of motion.

Similarly in other directions.

Explain Newton’s law of viscosity and Fourier’s law of conduction.

Newton’s law of viscosity defines the relationship between the shear stress and shear rate of a fluid subjected to mechanical stress. The ratio of shear stress to shear rate is a constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity. Newtonian fluids obey Newton’s law of viscosity. The viscosity is independent of the shear rate.

Non-Newtonian fluids do not follow Newton’s law and, thus, their viscosity (ratio of shear stress to shear rate) is not constant and is dependent on the shear rate.

{\tau _{yx}} =  - \mu \left( {\frac{{d{V_x}}}{{dy}}} \right)

Fourier’s law states that the negative gradient of temperature and the time rate of heat transfer is proportional to the area at right angles of that gradient through which the heat flows.

q =  - k\nabla T

Boiling curve

The boiling curve is a graph of heat flux versus wall superheat, the difference between the wall temperature and the saturation temperature (or boiling point). The curve is often drawn with log scales to accommodate the rather large range of variables.


Effect of pressure and temperature of thermal conductivity

For all liquids, the coefficient of thermal conductivity increases with increasing pressure. 

The thermal conductivity of liquids decreases with increasing temperature as the liquid expands and the molecules move apart. While in solids, the thermal conductivity decreases at higher temperatures due to the anharmonic scattering which is inversely proportional to the temperature changes.

Universal distribution laws of Newtonian fluids

{v^ + } = \frac{1}{K}\ln {y^ + } + {C_2}
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