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

Answer the following in brief (10 x 2)

State Bernoulli theorem.

The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant.

$p + (p{v^2}/2) + \rho gh = cons\tan t$

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.

What is Reynold’s analogy?

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

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.

Differentiate between free turbulence and 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 Prandtl Mixing Length?

The mixing length is the distance that a fluid parcel will keep its original characteristics before dispersing them into the surrounding fluid. Here, the bar on the left side of the figure is the mixing length.

According to Prandtl, the mixing length l, is the distance between two layers in the transverse direction such that lumps of fluid particles from one layer could reach the other layer and the particles are mixed in the other layer in such a way that the momentum of the particles in the direction of x is same.

The relation between shear stress and mixing length is given by

$\tau = \rho {l^2}{\left( {\frac{{du}}{{dy}}} \right)^2}$

State the similarities and differences between NewtonV law of viscosity and Fourier’s law of heat 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.

$q = - k\nabla T$

The physical significance of Schmidt and Grashof's number

Grashof number, Gr, as the ratio between the buoyancy force and the viscous force:

$Gr = \frac{{{l^3}{\rho ^2}\beta \Delta T}}{{{\mu ^2}}}$

It can be written as

$Gr = (\rho {l^3}\beta \Delta T)\left( {\frac{{\rho {v^2}{l^2}}}{{{{(\mu vl)}^2}}}} \right)$

= bupyant force x (inertia force/visous force²)

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.

Write the Sieder Tate equation for convective heat transfer.

Sieder- Tate modified the Dittus Boelter equation and accounted for the viscosity fluctuation with temperature when the temperature difference between the surface and the fluid is substantial.

$\frac{{hD}}{k} = 0.023{\left( {\frac{{Du\rho }}{\mu }} \right)^{0.8}}\left( {\frac{{{C_p}\mu }}{k}} \right){\left( {\frac{\mu }{{{\mu _w}}}} \right)^{0.14}}$

The Sieder-Tate equation is valid for ${N_{{{\rm Re}\nolimits} }} > 10,000;0.7 < {N_{\Pr }} < 700$ .

Continuity equation

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

AV = constant

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