HEAT TRANSFER AND FLUID FLOW ASSIGNMENT

Use steam tables where necessary to find thermo physical properties of water.

The following equations and data may be useful:

Surface area of a cylinder of length H and radius r = 2πrH

Surface area of a sphere = 4πr² = πd²

Stefan-Boltzmann constant, σ = 5.67 x 10^-8 W m^-2K^-4

Latent heat of melting of ice = 333.5 kJ kg^-1

Temperature in kelvins ≈ Temperature in ^oC plus 273.

g = 9.81ms^-2

P_atm = 1.013x10⁵ Pa

1. Heat Transfer and Fluid Flow: Subjects for all Seasons.

a) During the hot Summer one year, a loving and indulgent father set up a swimming pool in the garden for his children.

The swimming pool is 3 m in diameter and filled with water to a depth of 0.8 m, using a pump that operates with a delivery pressure of 2 bar gauge.  The power rating of the pump is 500 W.  Assuming that the pump motor operates with 60% efficiency, estimate how long it will take to fill the pool.

b) The Autumn that year was particularly wet with torrential rain.  Water from the rain collected in a tank from which it drained at a flow rate of 360 kg h^-1. It drained through a pipe initially of 5 cm in diameter, which then narrowed to 5 mm in diameter. Assuming the water is at 10°C, calculate the Reynolds number for the flow in the wide and narrow parts of the pipe.  Is the flow turbulent or laminar in each case?

c) The year ended with a particularly heavy Winter, and a 21 cm thick layer of snow fell onto the roof of some student accommodation, providing extra insulation.  The roof is 4 m by 7 m, and is made of material 32 mm thick with a thermal conductivity of 0.04 W m^-1K^-1. The thermal conductivity of snow is 0.3 W m^-1K^-1. 

Calculate the rate of heat transfer through the roof and snow, if the air in the room is at 10^oC, the outside air is -15^oC, the heat transfer coefficient between the air in the room and the inside of the roof is 25 W m^-2K^-1, and between the surface of the snow and the outside air is 6 W m^-2K^-1. Calculate the temperature at the interface between the snow and the roof (to the nearest ^oC).

d) The following Spring, high pressure and fine weather returned to the UK, the snow melted in the sunshine, and people's thoughts turned to warmth, optimism and the diverse relevance of pressure.

i) The high atmospheric pressure bringing the good weather reaches a value of 1031 mbar. Calculate the height of mercury (density 13560 kg m^-3) in the weatherman's barometer.

ii) The snow has a density of 300 kg m^-3. If the solar radiation absorbed by the snow was typically around 500 W m^-2 at that time of year, estimate how long it would take the snow on the roof in part (c) to melt?

2. Having purchased a steam stripper to help with removing wallpaper while redecorating a bedroom, Professor Campbell now decides to use the steam stripper to help with defrosting his freezer. The steam stripper comprises a tank of water with an electrical element (basically a kettle) to generate the steam, from which a long rubber tube conveys the steam to the head, which Professor Campbell directs at the ice in the freezer that he is trying to melt.

The power rating of the electrical heating element is equal to (the sum of the seven numbers in your Student ID number) divided by 10, in kW.  (e.g. if your student ID is 1372523, the sum of these is 1+3+7+2+5+2+3 = 23, so the power rating is 2.3 kW.)  Show this calculation here:

Power rating = kW

Professor Campbell fills the tank with about a volume of water approximately equal to (the average of the last three numbers in your Student ID number, rounded to the nearest litre). (e.g. if your student ID is 1372523, the average of the last three numbers is (5+2+3)/3=3.333, so the volume of water added is 3 L.)  Show this calculation here:

Volume of water = L

a) Estimate the time it would take from switching the power on to steam beginning to be generated.

b) Once the water is boiling, calculate the rate of production of steam.

c) Estimate how much ice could be melted from the generated steam from one tank of water, if the transfer of heat from condensing steam to melting ice was 100% efficient.  Assume that all the water initially in the tank can be evaporated into steam, and that heat losses from the tank and from the pipe conveying the steam are negligible, such that all of the electrical power goes into generating steam, and all of the steam is available to melt ice.  (Don't forget that the steam condenses, and gives up the latent heat of condensation, then cools to 0°C, giving up more heat.)

d) The internal diameter of the tube conveying the steam to the stripper head is 0.7 cm. Determine the density of steam at atmospheric pressure using steam tables (show your working).  Then, calculate the volumetric flow rate and average velocity of the steam flowing in the pipe.

3. Create an interesting example question related to heat transfer and/or fluid flow, and prepare a model answer for it.

You can type up your question and model answer and paste them into the space below if you prefer.  You should aim to create a question that requires the use of at least three equations to answer it.

4. [from Hannah Wilkes, 1st year Chemical Engineering student, 2015.]

Frosty the snowman was very proud to be the tallest snowman on the street. However, being a snowman is a chilly business, so Frosty decides to celebrate his brilliance with a large bucket of hot tea.

Given that Frosty's body is at a constant temperature of 0°C and the snow that Frosty is made from consists of 90% air and 10% ice:

a) What volume of Frosty melts when he drinks the 5 litre bucket of tea at 60°C?

Latent heat of melting ice: 333.5 kJ kg^-1

Density of ice: 900 kg m^-3

b) Frosty begins to panic and attempts to reverse his shrinkage by drinking the contents of the puddle that has formed underneath him, using a 2 m length straw. How much power (in watts) does Frosty exert by sucking up the total volume of the puddle in 30 seconds?  (Note that the puddle is made up of the 5 litres of tea plus the snow that melted.).