Transport Phenomena - short answer questions from AMIE exams (Summer 2018)

Answer the following in brief (10 x 2)

What are the factors on which diffusivity depends?

The rate of diffusion is affected by the concentration gradient, membrane permeability, temperature, and pressure.
Diffusion takes place as long as there is a difference between the concentrations of a substance across a barrier. However, diffusion stops, when the concentrations of the substance on either side of the barrier become equal.
The permeability of a membrane affects the rate of diffusion. Diffusion rate increases as membrane permeability increases.
Changes in temperature and pressure values also affect the diffusion of substances. Pressure plays an important role in the diffusion of gases as gases diffuse from a region of higher partial pressure to a region of lower partial pressure.

Creeping flow

Stokes flow also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. Re << 1. This is a typical situation in flows where the fluid velocities are very slow, and the viscosities are very large.

Flow past immersed bodies

Whenever a plate is held immersed at some angle with the direction of the flow of the liquid, it is subjected to some pressure. The component of this pressure, in the direction of the flow of the liquid, is known as drag and the component of this pressure at right angles to the direction of the flow of the liquid is known as lift.

According to Prandtl - the Blasius relation, the thickness of the boundary layer in laminar flow is

${\delta _{lam}} = \frac{{5x}}{{\sqrt {{R_{NX}}} }}$

and thickness of boundary layer in a turbulent flow,

${\delta _{tur}} = \frac{{0.377x}}{{{{({R_{NX}})}^{1.5}}}}$

where

x = Distance between the leading edge of the body and the section where the thickness of the boundary layer is required, and

Rnx = Reynold’s number at a distance x from the leading edge.

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).

Continuity equation

For a steady flow through a control volume with many inlets and outlets, the net mass flow must be zero.

AV = constant

Differentiate between turbulence 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.

The analogy between momentum and heat transfer

The Reynolds Analogy is popularly known to relate turbulent momentum and heat transfer. That is because in a turbulent flow (in a pipe or in a boundary layer) the transport of momentum and the transport of heat largely depend on the same turbulent eddies: the velocity and the temperature profiles have the same shape.

Reynolds's analogy gives the interrelationship between fluid friction and newton’s law of viscosity.

The Reynolds analogy is given by,

N_u/R_eP_r = S_t = C_f/2

where

Nu = Local Nusselt number, Re = Local Reynolds number, St = Local Stanton number, Pr = Prandtl number, Cf = Skin friction coefficient

Condensation over a flat vertical wall

Film condensation occurs when the temperature of a vertical, impermeable, and wettable wall next to a porous medium saturated with vapour falls below saturation temperature.

In addition to gravity-driven downward liquid flow, the liquid also infiltrates the vapour region due to capillary force. The latter will create a two-phase region between the liquid film and the vapour region, where both condensate and vapour are present.

Effect of pressure and temperature of mass diffusivity

Increasing pressure acts similar to decreasing temperature. Diffusivity or mass transfer coefficient enhances with temperature.

For gases, D is proportional to ${T^{1.5}}$

For liquids, D is proportional to T.

But, for gas diffusion, diffusivity decreases with pressure. So. increasing pressure increases the collision between molecules, which disrupts the flow for diffusion.

Increasing temperature increases the angular velocity of fluid molecules and reduces the time of diffusion.

For gases, D is inversely proportional to pressure.

Couette flow

In fluid dynamics, Couette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. The relative motion of the surfaces imposes shear stress on the fluid and induces flow.

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