Problem 3.1





Moving plate sets fluid in motion in the x-direction.
Since plates are infinite the flow field does not vary in the axial direction x.
The effect of pressure gradient is negligible.
The fluid is incompressible (constant density).
Use Cartesian coordinates.
Problem 3.2

Moving plate sets fluid in motion in the x-direction.

Since plates are infinite the flow field does not vary in the axial direction x.

The effect of pressure gradient must be included.

The fluid is incompressible.

Using Fourier’s law, Temperature distribution gives surface heat flux of the moving
plate.

Use Cartesian coordinates.
Problem 3.3

Moving plate sets fluid in motion in the x-direction.

Since plates are infinite the flow field does not vary in the axial direction x.

The fluid is incompressible (constant density).

Use Cartesian coordinates.
Problem 3.4

Moving plates set fluid in motion in the positive and negative x-direction.

Since plates are infinite the flow field does not vary in the axial direction x.

The fluid is incompressible (constant density).

The fluid is stationary at the center plane y = 0.

Symmetry dictates that no heat is conducted through the center plane.

Use Cartesian coordinates.
Problem 3.5

Fluid motion is driven by axial pressure drop.

For a very long tube the flow field does not vary in the axial direction z.

The fluid is incompressible (constant density).

Heat is generated due to viscous dissipation. It is removed from the fluid by convection at
the surface.

The Nusselt number is a dimensionless heat transfer coefficient.

To determine surface heat flux and heat transfer coefficient requires the determination of
temperature distribution.

Temperature distribution depends on the velocity distribution.

Use cylindrical coordinates.
Problem 3.6

Fluid motion is driven by axial pressure drop.

For a very long tube the flow field does not vary in the axial direction z.

The fluid is incompressible (constant density).

Use cylindrical coordinates.
Problem 3.7

Fluid motion is driven by axial motion of the rod. Thus motion is not due to pressure
gradient.

For a very long tube the flow field does not vary in the axial direction z.

The fluid is incompressible (constant density).

Heat is generated due to viscous dissipation. It is removed from the fluid by conduction at
the surface.

The Nusselt number is a dimensionless heat transfer coefficient.

To determine the heat transfer coefficient require the determination of temperature
distribution.

Temperature distribution depends on the velocity distribution.

Use cylindrical coordinates.
Problem 3.8

Fluid motion is driven by gravity.

No velocity and temperature variation in the axial direction.

The fluid is incompressible (constant density).

Heat is generated due to viscous dissipation.

Temperature distribution depends on the velocity distribution.

Use Cartesian coordinates.
Problem 3.9

Fluid motion is driven by gravity.

No velocity and temperature variation in the axial direction.

The fluid is incompressible (constant density).

Heat is generated due to viscous dissipation.

Temperature distribution depends on the velocity distribution.

the inclined surface is at specified temperature and the free surface exchanges heat by
convection with the ambient.

Use Cartesian coordinates.
Problem 6.10

This is an internal forced convection problem.

The channel has a rectangular cross section.

Surface temperature is uniform.

The Reynolds and Peclet numbers should be checked to establish if the flow is laminar or
turbulent and if entrance effects can be neglected.

Channel length is unknown.

The fluid is air.
Problem 3.11

Fluid motion is driven by shaft rotation

The housing is stationary.

Axial variation in velocity and temperature are negligible for a very long shaft.

Velocity and temperature do not vary with angular position.

The fluid is incompressible (constant density).

Heat generated by viscous dissipation is removed from the oil at the housing.

No heat is conducted through the shaft.

The maximum temperature occurs at the shaft.

Heat flux at the housing is determined from temperature distribution and Fourier’s law of
conduction.

Use cylindrical coordinates.
Problem 3.12

Fluid motion is driven by sleeve rotation

The shaft is stationary.

Axial variation in velocity and temperature are negligible for a very long shaft.

Velocity and temperature do not vary with angular position.

The fluid is incompressible (constant density).

Heat generated by viscous dissipation is removed from the oil at the housing.

No heat is conducted through the shaft.
 The maximum temperature occurs at the shaft. (ix) Use cylindrical coordinates.
Problem 3.13

Fluid motion is driven by shaft rotation

Axial variation in velocity and temperature are negligible for a very long shaft.

Velocity, pressure and temperature do not vary with angular position.

The fluid is incompressible (constant density).

Heat generated by viscous dissipation is conducted radially.

The determination of surface temperature and heat flux requires the determination of
temperature distribution in the rotating fluid.

Use cylindrical coordinates.
Problem 3.14

Axial pressure gradient sets fluid in motion.

The fluid is incompressible.

The flow field is determined by solving the continuity and Navier-Stokes equations.

Energy equation gives the temperature distribution.

Fourier’s law and temperature distribution give surface heat flux.

Axial variation of temperature is neglected.