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1
Q

What’s the difference between fin efficiency and fin effectiveness? (3 marks)

A

The fin efficiency is the ratio between the actual heat transfer from the fin and the ideal heat transfer from the fin if the entire fin were at its base temperature.

The fin effectiveness is the ratio between the heat transfer rate from the fin base of area A_b and the heat transfer rate from the surface of area A_b

2
Q

State Wien’s displacement law and explain its physical significance. (2 marks)

A

The wavelength at which the peak occurs for a specified temperature is given by:
(λT)_maxpower = 2897.8μmK
Their product between this wavelength and the corresponding temperature is a constant

3
Q

Give the mathematical formula for the surface resistance due to radiation and explain its physical meaning (2 marks)

A

R = (1-ε)/Aε
This is the resistance due to the fact that the surface is not a blackbody, but instead gray and so the maximum possible emissive power is not emitted. The emissivity is smaller than 1 in this case

4
Q

When the linear system resulting from the finite-difference discretization of the heat transfer conduction equation is of small order, which is more likely to be used, a direct or iterative method? Clearly explain why. (2 marks)

A

Direct method. The resulting matrix is small, so it can easily be inverted. There is no need to iterate (like Gauss-Siedell) to find the solution

5
Q

Define Kirchhoff’s Law and explain the diagram that shows this (2 marks)

A

The emissivity and the absorptivity of a surface at a given temperature and wavelength are equal.

Small body inside an enclosure. Small body has A_s, ε, and α inside. Squiggly arrow pointing to small body labelled G, and squiggly arrow coming out of the small body labelled E_emit. T pointing to small body, T pointing to inside surface of enclosure

6
Q

What’s the mathematical relationship that links absorptivity, reflectivity, and transmissivity? (2 marks)

A

α + ρ + τ = 1

7
Q

Discuss the two main methods to study heat exchangers: the log-mean temperature
method and the effectiveness-NTU method. (2 marks)

A

LMTD: The four temperatures (in/out for the cold and hot flows) and the area are given. The heat transfer can be computed.

Effectiveness-NTU: The heat transfer can be computed without knowing the outlet temperatures

8
Q

Discuss what the fouling factor, R_f , represents and why it is often used in the study of heat exchangers. (2 marks)

A

The fouling factor R_f represents the additional resistance to heat transfer as a result of the layer of deposits and accumulation of deposits on the internal surfaces of the heat exchanger.

9
Q

Was Planck more impressed by Clausius’ or by Kirchhoff’s style of teaching? (3 marks)

A

More Clausius

10
Q

Who discovered a simple mathematical relationship that described the effect of a change in temperature on the distribution of blackbody radiation? (4 marks)

A

Wien

11
Q

Explain the physical meaning of the summation rule (2 marks)

A

conservation of energy. Radiation leaving any surface i of an enclosure must be received completely by the other surfaces

12
Q

What is the physical significance of the Biot number? Justify your answer. (2 marks)

A

The Biot number represents the ratio of conduction resistance within the body to convection resistance at the surface of the body

13
Q

Is the Biot number likely to be larger for highly conducting solids or poorly conducting ones? Justify your answer. (2 marks)

A

The Biot number is more likely to be larger for poorly conducting solids since such bodies have larger resistances against heat conduction

14
Q

What is the definition and the physical significance of the Prandtl number? Carefully explain the physical meaning of all the quantities you use in the definition of Prandtl number. (2 marks)

A

The Prandtl number is defined as the ratio between the kinematic viscosity and the thermal diffusivity. It expresses the ratio of molecular diffusion with respect to the thermal diffusion

15
Q

Define emissivity and explain its physical significance. (2 marks)

A

Emissivity is the ratio of the radiation emitted by a surface to the radiation emitted by a blackbody at the same temperature

16
Q

What is a blackbody? Explain its physical significance. (2 marks)

A

A blackbody is a perfect emitter and absorber of radiation. A blackbody does not actually exist. It is an idealised body that emits the maximum amount of radiation that can be emitted by a surface at a given temperature

17
Q

How do real bodies differ from blackbodies? Discuss your answer thoroughly. (2 marks)

A

A real surface emits and absorbs less radiation than a blackbody

18
Q

Define thermal diffusivity and explain its significance in heat transfer. (2 marks)

A

The thermal diffusivity is defined as α=k/ρc. It expresses the ratio between the conduction of heat and the storage of thermal energy

19
Q

For a surface, how is radiosity defined? Explain your answer. (2 marks)

A

Radiosity J is the rate at which radiation energy leaves a unit area of a surface by emission and reflection in all directions

20
Q

What was the focus of Planck’s research as he began his academic career? (2 marks)

A

Thermodynamics, particularly the second law, became the focus of Planck’s research as he began his academic career

21
Q

What were the three crucial pieces of information that Planck had to construct his formula for the energy spectrum of blackbody radiation? (3 marks)

A

i) Wien’s law accounted for the intensity of radiation at short wavelengths
ii) It failed in the infrared where Rubens and Kurlbaum had found that intensity was proportional to the temperature
iii) Wien’s displacement law was correct

22
Q

Indicate what the similarity variable is and explain its mathematical significance, i.e. explain why it allows simplifying the problem. (3 marks)

A

The similarity variable is η. The physical problem depends on both x and t, so two independent variables, but by use of η, the temperature depends on only one independent variable, η

23
Q

Explain what is meant by critical radius of insulation. Explain why it is irrelevant for heat transfer through flat large walls. Justify your answer. (2 marks)

A

In cylindrical and spherical geometries, it is not always a good idea to add more insulating material because, although the conduction resistance for sure increases, the outer surface of the body increases, which means that convection increases. There is a critical radius below which the heat transfer actually increases as insulating material is added.

24
Q

θ’‘−(m^2)θ=0
Clearly describe the physical meaning of the two terms in the above differential equation. Justify your answer fully. (4 marks)

A

Heat is conducted through the fin and it is transferred outside the fin by convection. No radiation. The first term (second derivative) indicates heat conduction, and the second one heat convection

25
Q

What does the correction factor depend on? (2 marks)

A

Depends on the geometry of the heat exchanger and the inlet and outlet temperatures of the hot and cold fluid streams