Quiz 2

Front 1

What is the main heat exchange process involved in convective heat transfer?

Back 1

The main heat exchange process in heat convection is between a moving fluid and a
surface, when the two are at different temperatures.

Front 2

State and explain Newton’s law of cooling

Back 2

Newton’s law of cooling: qw = h ( Tw - Tf)
Where qw the rate of heat exchange between a surface and a fluid per unit area
h the coefficient of wall heat flux
Tw the wall temperature
Tf the fluid temperature

Front 3

In Newton’s law of cooling how is the fluid temperature defined?

Back 3

In External flows Tf is the fluid free stream temperature Tinfinity.

In Internal flows Tf is the fluid bulk temperature over the cross-section of the passage.

Front 4

What is the mathematical expression for the rate of heat transfer per unit area qW from a surface to a fluid and why?

Back 4

The law of heat conduction, qw = - k ( deltaT / deltaY )w, because at the wall the fluid velocity falls to zero and only heat conduction is present.

Front 5

How does the fluid motion influence the rate of heat exchange between a fluid and a
solid surface qW?

Back 5

The motion of the fluid away from the wall does however influence qw by controlling the
temperature distribution within the fluid and thus the temperature gradient at the wall,
( deltaT / deltaY )w .

Front 6

Present two dimensionless forms of the wall heat flux coefficient?

Back 6

The Nusselt number, Nu, defined as ( h L / k ).

The Stanton number, St, is used instead of the Nusselt number, defined as:
St = ( h / Ro U c )

Front 7

What other dimensionless groups are involved in forced heat convection analysis?

Back 7

Re = (Ro U L / Mu) which represents the ratio between the inertial and viscous forces
within the fluid.
Pr =(Mu c / k) which can also be written as ( V / alpha ), where alpha is the thermal diffusivity (k / Ro c)
Nu = ƒ ( Re, Pr )

Front 8

Which physical laws are used to derive the differential heat convection equation?

Back 8

he law of Heat Conduction, qx=-kDeltaT/Deltax

The law of convective transport of thermal energy, qx=RoUCp

The energy balance

Front 9

In the differential equation for heat convection across a turbulent boundary layer, what
is the time-averaged term Rovt called (where v and t are the fluctuating velocity normal
to the wall and the fluctuating temperature respectively) and what physical process
does it represent?

Back 9

Represents the transfer of thermal energy in a direction normal to the wall, due to the mixing of turbulent eddies.

Front 10

What is the definition of the thickness of a thermal boundary layer, deltaT?

Back 10

The thermal boundary layer thickness, deltaT
, is defined as the distance at which (T-T w)
=0.99 (Tinfinity-Tw).

Front 11

For laminar flow over a heated plate, explain how the thickness the thermal boundary
layer, DeltaT is related to that of the velocity boundary layer Delta.

Back 11

For Fluids where Pr = 1 DeltaT =Delta
For Fluids where Pr > 1 DeltaT < Delta
For Fluids where Pr < 1 DeltaT > Delta

Front 12

For turbulent flow over a heated plate, explain how the thermal boundary layer, is related to that of the velocity boundary layer.

Back 12

The overall thickness of the thermal boundary layer is similar to that of the velocity boundary layer, because they are both determined by the mixing effect of the turbulent eddies.
The main difference is in the thickness of the wall-sublayers across which, in relation to viscous diffusion in the case of velocity and heat conduction in the case of temperature, momentum and heat transfer due to turbulence mixing are negligible.
For fluids with Pr>1 the conduction sub-layer is thinner than the viscous sub-layer, while for fluids with Pr<1 the conduction sub-layer extends beyond the viscous sub-layer

Front 13

Provide the definition of the enthalpy thickness, , and state what it represents.

Back 13

*

Represents the amount of thermal energy added to the fluid by the wall.

Front 14

State how the boundary layer momentum integral equation is derived and also what assumptions are involved in the version shown on the right.

*

Back 14

The enthalpy integral equation is derived by integrating the boundary layer form of the heat convection equation across the boundary layer.

*

The above form is derived by assuming constant free stream velocity and temperature and also constant wall temperature.

Front 15

What is the definition of a fully developed thermal field in internal flows?

Back 15

A thermal field in an internal flow is said to have reached fully developed conditions when the wall heat flux coefficient, h, does not change in the flow direction x. dh/dx=0

Front 16

Sketch the variation of the wall and fluid bulk temperature with the flow direction in a
straight pipe heated:
a) Under uniform wall heat flux conditions.
b) Under uniform wall temperature conditions.

Back 16

*

Front 17

For fully-developed laminar flow in a passage heated under uniform wall heat flux boundary conditions, assuming the velocity variation across it is already known, outline the main steps involved in the calculation of the Nusselt number.

Back 17

Step 1: Use the known expression for the velocity variation to eliminated the local velocity from the fully developed form of the heat convection equation for uniform wall heat flux heating.
Step 2 Integrate the heat convection equation over the cross section sing appropriate boundary

conditions. To obtain an equation for the temperature variation across the passsage.u
Step 3
Use the energy balance to replace the bulk temperature gradient in the equation of the
temperature variation obtained in Step 2, with the wall heat flux rate.
Step 4.
Using the known velocity and temperature variations over the cross section, integrate to
obtain an expression for the difference between the wall and the fluid bulk temperature ,in terms
of the wall heat flux rate, fluid bulk velocity and physical properties, which will result in an
expression for the wall heat flux coefficient and Nusselt number.