Answer ALL Questions

1.   (a)  Why do metals generally have higher thermal conductivities than non-metals? [2 marks]

(b) An exterior wall of a house may be approximated by a 10 cm layer of common

brick (k = 0.7 Wm-1K-1) followed by a 4 cm layer of gypsum plaster (k = 0.48 Wm-1K-1). What thickness of loosely packed rock-wool insulation (k = 0.065 Wm-1K-1) should be added to reduce the heat loss through the wall by 70

percent?                                                                                            [5 marks]

2.   (a)  Under   what   circumstances   might   the   semi-infinite   body   solution   be reasonable?                                                                                      [2 marks]

(b) A large block of steel (k = 45 Wm-1K-1 , α = 1.4x10-5 m2s-1) is initially at a uniform

temperature of 35˚C. The surface is exposed to a heat flux by suddenly raising the  surface  temperature  to  250  ˚C  and  holding  it  at  that  temperature throughout the treatment. Calculate the temperature at a depth of 2.5 cm after

a time of 0.5 min.                                                                              [5 marks]

3.   Hot air is flowing through a 10 cm diameter pipe that is 20 m long. The density of the hot air is 0.8826 kg m−3 , the viscosity is 2.286×10−5 kg m−1 s−1 . At what velocity would you expect the flow to transition from laminar to turbulent flow?

[3 marks]

4.   Two very large parallel planes with emissivities 0.3 and 0.8 exchange heat. Find the percentage reduction in heat transfer when a polished-aluminium radiation shield (ε = 0.04) is placed between them.                                               [5 marks]

5.   Suggest, with  reasons, what  mechanism of diffusion  (vacancy,  interstitial or interstitalcy) the following species diffusing within FCC gold might have:

(a)  He

(b) Ag

[2 marks]

6.   Below is a set of data collected for the mean square displacement of the Ag atom diffusing in the gold.   Use this to extract the diffusion constant of the Ag atom. Show your working.

[2 marks]

7.   (a)  Radioactive waste is leaking out of cylindrical canisters into the surrounding rock in a geological disposal facility.  Given a diffusion constant of 3.95x10-6 cm2s-1  and an initial concentration of 28.5 mol m-1  in the canisters,   what concentration of waste will be present 5 cm into the rock after 1 day?

[4 marks]

(b) A team monitors the waste stream and finds a far higher concentration than

predicted from the equations. They note that the radioactive waste is far hotter than the surrounding rock.  Suggest how this would affect the diffusion.

[1 mark]

(c)  Monitoring the different waste streams identifies several ions diffusing into the aluminosilicate garnet  mineral  (grossular - Ca3Al2Si3O12).   Using the data below and your own understanding, rank the expected order of diffusion for these species highest to lowest.  Explain your reasoning.

[3 marks]