ICAM2 –Heat Transfer

ICAM (LILLE) - HEAT EXCHANGER COURSE

ICAM 2 - AUTUMN 2003

Heat Exchanger Examples – Sheet 1

  1. A hot fluid at 100°C enters a double-pipe heat exchanger and is cooled to 75°C. A cooler fluid at 5°C enters the exchanger and is warmed to 50°C. Determine the logarithmic mean temperature difference (LMTD) for both counter-flow and parallel-flow configurations. [59.4°C, 52.4°C]
  1. A hot fluid at 120°C enters a double-pipe heat exchanger and is cooled to 65°C. A cooler fluid enters the exchanger at 38°C and is to be warmed to 65°C. Determine the logarithmic mean temperature difference (LMTD) for both counter-flow and parallel-flow configurations. What are the physical consequences of these results? [39.4°C, 0°C]
  1. Water at a mass flow rate of 68 kg/min is heated from 35°C to 75°C by an oil having a heat capacity of 1.9 kJ/kg K. The fluids are used in a counter-flow double pipe heat exchanger and the oil enters the exchanger at 110°C and leaves at 75°C. If the overall heat transfer coefficient is 320 W/m2 K calculate the heat-exchanger area. [15.82 m2]

Data: Heat capacity of water = 4.18 kJ/kg K.

  1. Steam passes through a turbine into a condenser. Liquid water from the condensed steam is used to heat ethylene glycol. The water is available at 90°C with a mass flow rate of 2300 kg/hr. The ethylene glycol has temperature of 30°C and a mass flow rate of 5500 kg/hr. It is proposed to use a double-pipe heat exchanger made of standard 2 x 1¼ inch tubing such that the inside diameter of the outer tube is 5.1 cm and the outside and inside diameters of the inner tube are 3.5 cm and 3.3 cm respectively. The length of the exchanger is 6 m. Determine the outlet temperature of the ethylene glycol for counter-flow operation if the water is to be routed through the inner tube. [37.7°C]

Data: Fluid properties are evaluated at the average of the inlet temperatures {(90+30)/2 = 60°C}

For water at 60°C - density ρ = 0.985 x 103 kg/m3; thermal conductivity k = 0.651 W/m K; heat capacity cp = 4184 J/kg K; kinematic viscosity ν = 0.478 x 10-6 m2/s.

For ethylene glycol at 60°C - density ρ = 1.087 x 103 kg/m3; thermal conductivity k = 0.260 W/m K; heat capacity cp = 2562 J/kg K; kinematic viscosity ν = 4.75 x 10-6 m2/s.

Use the Dittus-Boelter equations to determine the appropriate heat transfer coefficients:

Dittus-Boelter equation - NuD = 0.023 (ReD)0.8 (Pr)n {where n = 0.4 for fluid being heated and

n = 0.3 for fluid being cooled} for turbulent flow in the tube.

  1. A bank of four diesel engines is used with alternators for the generation of electricity. The exhaust from the engines is discharged to the atmosphere. It is proposed to use all or part of the exhaust gas for heating air, which can then be used for space heating to reduce costs. From measurements of velocity it is determined that the mass flow rate of exhaust gas available from the engines is 90 kg/hr. The exhaust gas temperature is 600K. The air is available at 20°C and will not be useful unless it can be heated to at least 80°C at a mass flow rate of 100 kg/hr. A number of 4 x 3 double-pipe heat exchangers are available which are 2 m long and made of type K copper tubing with compression fittings. Determine (a) how many exchangers will be required, (b) the overall heat transfer coefficient of the exchangers and (c) the pressure drop for each stream. Assume a counter-flow arrangement. [One, 14.1 W/ m2 K, pipe 12.8 Pa, annulus 200 Pa]

Data: Fluid properties are evaluated at the average of the inlet and outlet temperatures.

For air at 323 K - density ρ = 1.088kg/m3; thermal conductivity k = 0.02814 W/m K; heat capacity cp = 1007 J/kg K; kinematic viscosity ν = 18.2 x 10-6 m2/s, thermal diffusivity = 0.26 x 10-4 m2/s, Prandtl number Pr = 0.703.

For CO2 gas at 500 K - density ρ = 1.0732kg/m3; thermal conductivity k = 0.03352 W/m K; heat capacity cp = 1013 J/kg K; kinematic viscosity ν = 21.67 x 10-6 m2/s, = 0.3084 x 10-4 m2/s, Prandtl number Pr = 0.702.

For 4x3 tubing, the inside diameter of the outer tube is 9.8 cm and the outside and inside diameters of the inner tube are 7.938 cm and 7.384 cm respectively.

Use the Dittus-Boelter equations to determine the appropriate heat transfer coefficients:

Dittus-Boelter equation - NuD = 0.023 (ReD)0.8 (Pr)n {where n = 0.4 for fluid being heated and

n = 0.3 for fluid being cooled} for turbulent flow in the tube.

  1. Instead of the double-pipe heat exchanger of Example 3, it is decided to use a shell and tube heat exchanger with the water making one shell pass and the oil making two tube-passes. Using the appropriate LMTD correction factor plot calculate the surface area required for this new exchanger, assuming that the overall heat transfer coefficient remains constant at 320 W/ m2 K. [19.53 m2]
  1. Process water at a mass flow rate of 3.78 kg/s is heated from 37.8°C to 54.4°C in a shell and tube heat exchanger. On the shell side one pass is used with waste water as the heating fluid entering the exchanger at 93.3°C at a mass flow rate of 1.89 kg/s. The overall heat transfer coefficient is 1420 W/ m2 K and the average water velocity in the 1.905 cm diameter tubes is 0.366 m/s. Because of space limitations the tube length must not be longer than 2.44 m. Using the appropriate LMTD correction factor plots calculate (a) the number of tube passes required, (b) the number of tubes per pass and (c) the length of the tubes subject to the above length restriction. [2 tube passes, 36 tubes per pass, 1.64 m]
  1. A simple counter-flow heat exchanger is used to preheat 3000 kg/h of air entering at 20°C. The air is heated by waste gases entering the exchanger at 800°C at a rate of 3400 kg/h. The area of the heat exchanger surface is 35 m2. The overall heat transfer coefficient is 30 W/m2 K. Calculate the exit temperatures of the waste gas and air using the NTU method. [514°C, 488°C].

Data: Mean heat capacities - Air = 1043 J/kg K, Waste gas = 1507 J/kg K

  1. A cross-flow heat exchanger is designed to be used as an oil cooler. Performance tests by the manufacturer have provided the following information:

Oil / Air
Inlet temperature / 88°C / 52°C
Outlet temperature / 70°C / 74°C
Mass flow rate / 18 kg/min / 31 kg/min
Unmixed / Unmixed

Check the reliability of this information by using it (a) to determine the UA product for the exchanger and then (b) to calculate the exit temperatures, assuming that only the inlet temperatures are known, and compare the results to those given above.

Data: Heat capacities - Oil (at 80°C) = 2131 J/kg K, Air (at 63°C) = 1008.5 J/kg K

Mike Patrick

September 2003

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