HEAT TRANSFER REVIEW QUESTIONS

- What is the difference between diffusion and radiation heat transfer ?

Diffusion heat transfer is due to random molecular motion. Neighboring molecules move randomly and transfer energy between one another - however there is __no bulk motion__. Radiation heat transfer, on the other hand, is the transport of heat energy by electromagnetic waves. All bodies emit thermal radiation. In particular, notice that unlike diffusion, radiation heat transfer does not require a medium and is thus the only mode of heat transfer in space. The time scale for radiative heat transfer is much smaller than diffusive heat transfer.

- How is natural convection different from forced convection ?

In __natural convection__, the movement of the fluid is due entirely to density gradients within the fluid (e.g. hot air rises over cold air). There is no external device or phenomenon which causes fluid motion. In __forced convection__, the fluid is forced to flow by an external factor - e.g. wind in the atmosphere, a fan blowing air, water being pumped through a pipe. Typically heat transfer under forced convection conditions is higher than natural convection for the same fluid.

- Define a black surface

A black surface is defined by three criteria:

- it absorbs all radiation that is incident on it
- it emits the maximum energy possible for a given temperature and wavelength of radiation (according to Planck's law)
- the radiation emitted by a blackbody is not directional (it is a diffuse emitter)

A black surface is the perfect emitter and absorber of radiation. It is an idealized concept (no surface is exactly a black surface), and the characteristics of real surfaces are compared to that of an ideal black surface.

- What is the range of values for the emissivity of a surface ?

The emissivity e ranges between 0 and 1.

- What are the conditions to be satisfied for the application of a thermal circuit ?

The problem must be a steady state, one-dimensional heat transfer problem.

- Will the thermal resistance of a rectangular slab be increased or decreased if:

- the thermal conductivity is increased ?
- the cross sectional area is increased ?
- the thickness of the slab is increased ?

- resistance will decrease
- resistance will decrease
- resistance will increase

- State the condition which must be satisfied to treat the temperature distribution in a fin as one-dimensional.

When ht/k <<1 where h is the convective heat transfer coefficient, t is the thickness of the fin and k is the thermal conductivity of the fin, one can consider that the temperature gradient in the thickness direction is very small and the analysis can be considered as one-dimensional.

- Define and state the physical interpretation of the Biot number.

The Biot number is given by:

Bi = hL/k

where

h = convective heat transfer coefficient,

k = thermal conductivity

L = characteristic length.

It is a ratio of the temperature drop in the solid material and the temperature dropthe solid and the fluid. So when the Bi <<1 , most of the temperature drop is in the fluid and the solid may be considered isothermal

- What is a lumped system ?

A lumped system is one in which the dependence of temperature on position (spatial dependence) is disregarded. That is, temperature is modeled as a function of time __only__ .

- When can the unsteady temperature in a spatial body be considered uniform ?

When the Biot number is small (Bi << 0.1).

- What is the Fourier number ?
- What is internal energy generation ? Give examples where internal energy generation occurs.
- Both the Nusselt number and the Biot number have the same form. What are the differences between them in terms of the variables employed and their physical significance ?
- What is the effect of the Prandtl number of a fluid on the relative thicknesses of velocity and temperature boundary layers when the fluid flow is parallel to a flat plate ?

The Fourier number is defined as:

Fo = at/L^{2}

where

a = thermal diffusivity,

t = time

L = characterisitic length

The Fourier number is a __dimensionless__ measure of time used in transient conduction problems.

Internal energy generation is the generation of heat within a body by a chemical, electrical or nuclear process. Examples are the heating of a nuclear fuel rod (due to fission within the rod), the heating of electrical wires (due to the conversion of electrical to heat energy), microwave heating and the generation of heat within the Earth. The heat generated in each case is being converted from some other form of energy.

13. What do you understand by stability criterion for the solution of transient problems ?

When solving transient problems using finite-difference methods, it is possible that the solution undergoes numerically induced oscillations and becomes unstable i.e. the temperature values diverge. The stability criterion is a restriction on the values of Dt and Dx which ensures that the solution remains stable and converges. The criterion is usually expressed as a function of Fourier's number. For example, for an interior node in a two dimensional system the stability criterion is :

Fo < 1/4 or

aDt/(Dx)^{2} < 1/4

Both the Biot number and the Nusselt number are of the form (hL/k). However, for the Biot number, the thermal conductivity k used is that for the solid; for calculating Nusselt number the k value as that of the __fluid__. The Biot number is a measure of the ratio of the temnperature drop in the solid material and the temperature drop between the solid and the fluid. The Nusselt number is a dimensionless version of the temperature gradient at the surface between the fluid and the solid, and it thus provides a measure of the convection occurring from the surface.

For laminar flow, the ratio of the boundary layer thickness d to that of the thermal boundary layer, dt, is given by:

d/dt µ
Pr^{n}

The higher the Prandtl number, the larger is the ratio.

16. Two fluids, with different properties, flow with equal free stream velocities parallel to a flat plate. What property of the fluid determines whether the velocity boundary layer of one is thicker than the other ?

The thickness of the boundary layer depends on the __Reynolds number__:

17. What do you understand by the terms fully developed velocity and temperature profile regions in internal flow ?

In the fully developed region, the cross-sectional velocity/temperature profile is of a constant shape at any axial location. Thus the profile has ceased to change. Also there is no radial component of velocity i.e. every particle of fluid is flowing purely in the axial direction.

18. Do you expect the convective heat transfer coefficient in the thermally developing region to be higher or lower than the convective heat transfer coefficient in the fully developed temperature profile region ? Support your answer with qualitative logic.

We should expect that the convective heat transfer coefficient is higher in the thermally developing region. Near the tube entrance, the thickness of the boundary layer is very small, and the temperature gradients at the surface will be high, implying high rates of convective heat transfer. As the flow develops, the thickness of the boundary layer increases and the temperature gradients decreases, decreasing h. In the fully developed region, the temperature gradients are constant and h is also a constant.

19. Explain why the temperature boundary layer grows much more rapidly than the velocity boundary layer in liquid metals.

Liquid metals are characterised by very low Prandtl numbers since their thermal conductivity is high, hence the heat diffusion is much faster than momentum diffusion.

20. You are told that in a particulat case of fluid flow over a flat plate the temperature boundary layer thickness is much smaller than the velocity boundary layer thickness. What can you conclude about the nature of the fluid ?

You can conclude that the fluid is a high Prandtl number fluid e.g.oil.

21. What is a gray surface ?

A gray surface is defined as one for which the emissivity (e) and the absorptivity (a) are __independent of wavelength__ (l).

22. What is a diffuse surface ?

A diffuse surface is defined as one for which the emissivity (e) and the absorptivity (a) are __independent of direction__ (q).

23. Define a view factor.

A view factor is defined in the context of two surfaces A and B. It is defined as the fraction of radiation leaving A which is incident directly on surface B. A view factor must be defined in terms of surface A to surface B (F_{AB}).

24. If a surface emits 200 W at a temperature of T, how much energy will it emit at a temperature of 2T ?

Since E µ
T^{4}, a 2-fold increase of temperature brings a (2^{4}) = 16-fold increase in energy. Thus the surface will emit (16)(200) = 3200 W.

25. You might have observed early morning frost on a clear day even when the minimum air temperature during the night was above 0° C. On a clear day, the effective sky temperature can be as low as -45° C. Explain how such frost formulation takes place.

The frost is created because of radiative losses to the sky

26. A greenhouse has an enclosure that has a high transmissivity at short wavelengths and a very low transmissivity (almost opaque) for high wavelengths. Why does a greenhouse get warmer than the surrounding air during clear days ? Will it have a similar effect during clear nights ?

Solar radiation is skewed towards shorter wavelengths. On a clear day the glass of the greenhouse admits a large proportion of the incident radiation. Inside the greenhouse, the various surfaces (plants etc.) reflect the radiation; but the reflected radiation is spectrally different, having more of a high wavelength contribution. Thus the reflected radiation is not transmitted well by the glass, and is reflected back into the greenhouse. The interior heats up due to this 'trapped' radiation. The same effect will not be seen on a clear night, since there is no solar radiation.

27. Define overall heat transfer coefficient.

The overall heat transfer coefficient is defined in terms of the total thermal resistance between two fluids. If there are a number of thermal resistances between the two fluids, the overall heat transfer coefficient is given by:

U = 1/SR

28. Your friend asserts that, in a heat exchanger, it is impossible for the exit temperature of the cold fluid to be greater than the exit temperature of the hot fluid when both fluids are single phase fluids. What is your response ?

The statement is true for a parallel flow heat exchanger. However, in a counterflow heat exchanger the outlet temperature of the cold fluid can in fact exceed the outlet temperature of the hot fluid.