2012/G017 Problem Sheet – Steady and Unsteady State Heat Transfer 

1. Explain the difference between steady state and equilibrium.

2. What is the general form of a thermal energy balance equation and how can it besimplified for steady-state heat transfer?

3. In conduction what components make up the thermal resistance?

4. What is the difference between forced convection and natural convection?

5. Calculate the amount of heat lost through 2 m2 of a cold storage wall that is composedof three layers of material. The wall consists of 0.1016-m thick concrete block (x c  ) onthe outside, 0.1524-m thick polystyrene insulation (x  p ), and 0.0508-m thick fir wood(x f  ) on the inside. The inside wall of the cold room is – 40 0C and the outside wall is200C. (Ans: 26.05W)The thermal conductivities are k c  = 0.76 W /m K k  p = 0.038 W /m K k f = 0.11 W /m K 

6. A cleaning solution flowing at a rate of 0.2 kg s-1 is heated from 20 oC to 60 oC in ahorizontal pipe with inside diameter 2.5cm. The inside pipe surface temperature is90oC. Estimate the convective heat transfer coefficient if the pipe is 1m long. (Ans:2765 W m-2 K -1 )The physical properties of the solution at the average bulk fluid temperature (40  oC) are:density = 992 kg m-3; specific heat = 4.175 kJ kg -1 K -1; thermal conductivity = 0.633 W m-1 K -1;viscosity = 6.58 x 10 -4 Pa s. The viscosity of the solution at 90 oC = 3.09 x 10 -4 Pa s.

7. Milk is flowing into a pipe cooler and passes through a tube of 2.5 cm internaldiameter at a rate of 0.4 kg s-1. Its initial temperature is 49°C and it is wished to cool itto 18°C using a stirred bath of constant 10°C water round the pipe. What length of pipe would be required? Assume an overall coefficient of heat transfer from the bathto the milk of 900 J m-2 s-1 °C-1, and that the specific heat of milk is 3890 J kg -1 °C-1.(Ans: 29.03m)

8. Before you begin any calculation for transient temperature in a solid with fluid flowingover it, what parameter value should you check to reduce your work? What is thephysical meaning of this parameter?

9. Tomato juice is pasteurised in a steam-jacketed hemispherical stirred vessel beforedispensing into bottles. The radius of the vessel is 0.5m. Calculate the temperature of tomato juice (density= 980 kg m-3) after 5 min of heating. The convective heat-transfer coefficient in the steam jacket is 5000 W m-2 K-1. The inside surface temperature of thevessel is 90oC. The initial temperature of the tomato juice is 20 oC. Assume thespecific heat capacity of the juice is 3.95 kJ kg -1 K-1. (Ans: 83.3oC)

10. Explain how dimensionless (Heisler) charts can be used to solve unsteady state heattransfer problems in 2-D and 3-D situations?

© UCL BENG 2009/G017 12-13