### Advanced Thermodynamics

1. Provide a brief yet concise answer to the following concept questions:

a. The heat conduction equation in a medium is given in its simplest form as indicated below. Describe all aspects of this system (i.e., shape, transient / steady-state, constant / varying properties etc. – NB more elements then listed to be considered)

b. Draw the thermal resistance network for a (i) a single-layer plane wall (ii) a five-layer composite wall and (iii) a three component wall where each material is in parallel and explain how the thermal resistance and heat transfer compares in each case. Include radiation and convection.

c. Sketch the velocity and thermal profiles of flow in a pipe at the regions indicated. Comment on the Nusselt number (hence heat transfer coefficient, and thus heat transfer) in each region.

###### To maximise heat transfer would you recommend the flow be laminar or turbulent

Entrance Developing, Fully developed, Re 10,000

Re 2000 2,000 Re 10,000

d. Sketch the convection currents for the following enclosures. In all cases THo3 = 40°C and T7oia = 30°C. Tilted enclosures have been rotated 45°. Comment on the effectiveness of the heat transfer between the two plates.

2. A 100-mm diameter cylindrical rod generates uniform internal heat at a rate of ^^)*n = 2x10s W m# and has a surface temperature of 125°C. The rod is in a room where the ambient temperature is 24°C and the combined convective and radiation heat transfer coefficient is 350 W/m2/K. The properties of the rod are, k = 30 W m • K, p = 1100 k^^ mG and ^^I = 800 J k^^ • K. Assuming steady state conditions, find

a. A unique expression for the temperature profile in the rod

b. Plot this temperature distribution

3. A building has a composite wall of plywood LS = 50mm, k = 0.72 W m • K, insulation Lb =

150mm, k = 0.046 W m • K, and gypsum plasterboard LI = 13mm, k = 0.81 W m • K as indicated

below. On a hot summer day the convection heat transfer coefficients are ho = 60 W m# • K and hi =

30 W m# • K. The inside and outside temperatures are 20°C and 32°C respectively.

##### The total wall surface area is 420 m#. Neglect Radiation.

a. Draw the thermal resistance network and determine the thermal resistance of the wall

b. Determine the total heat loss through the wall

c. The temperature of the insulation where it joins the plywood

d. Determine the percentage change in heat transfer through the wall if the insulation thickness is halved

4. A tube has an outer diameter of 15-mm, inner diameter of 12-mm and a length of 3.5-m. The internal surface temperature of the tube is maintained at 27°C. Water enters the tube from a large reservoir at m =

0.4 kg s and TT,i = 57°C

a. What is the outlet temperature of the water, TT,o Assume the water has an average mean

temperature of 37°C.

b. What is the exit temperature of the water if it is heated by passing air at T., = 130°C and V = 10 m/s in cross flow over the tube Assume an average film temperature of 105°C.

5. Thin sheets of steel (L = 5m, W = 10m, t = 5mm, ) exit a heat treatment facility with a uniform

temperature of 950°C. They are to be cooled in a room where the ambient temperature is 24°C. The

properties of the steel plate are: k = 28.5 W/m/K and p = 7822 kg/mG.

###### Calculate the heat transfer rate

if:

a. The sheets are suspended vertically

Fujii, T and Imura, H “Natural Convection Heat Transfer from a Plate with Arbitrary Inclination” International Journal of Heat and Mass Transfer, 15 (1972) p7.55

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