Heat Transfer - Problem Sets

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  1. In a counter-current heat exchanger, an oil stream is cooled from 450 K to 410 K by water inlet and outlet temperatures of 300 K and 350 K respectively. The exchanger consists a number of tubes of 1 m length each. It is now desired to cool the oil to 390 K (instead of 410 K) while maintaining the flow rate of oil, flow rate of water, inlet temperature of oil and water, and the number of tubes at the same values as before. Calculate the length of each tube required for this purpose. Assume that the physical properties remain unchanged.

  2. A horizontal steam pipe 20 m long, 50 mm internal diameter, 60 mm outside diameter losses 13.5 kW heat to the surroundings at 310 K. The pipe carries steam at 500 K. Given that the convective heat transfer coefficient hc = 1.65 (ΔT)0.25 W/m2.K and the Stefan-Boltzmann constant = 5.67 x 10-8 W/m2.K4. Find the emissivity of the bare surface of the pipe.

  3. Saturated steam at 130oC is flowing through a steel pipe of 0.021 m inside diameter and 0.027m outside diameter. The pipe is insulated outside with 0.038 m thick insulation. The ambient air outside the insulation is at 27oC. Calculate
      1. the rate of heat loss per meter length of tube
      2. the overall heat transfer coefficient based on inside surface area of steel pipe.
    Additional data:
    Thermal conductivity of steel = 45 W/m.K
    Thermal conductivity of insulation = 0.064 W/m.K
    Convective heat transfer coefficient inside the steel pipe = 5678 W/m2.K
    Convective heat transfer coefficient outside the insulation = 11 W/m2.K.

  4. Saturated steam at 6.9 x 104 Pa pressure and 90oC saturation temperature condenses on a vertical pipe of 0.025 m outside diameter and 0.3 m length. The average condensing heat transfer coefficient on the tube is 12000 W/m2.K. Other data:
    Outside surface temperature of the pipe = 86oC
    Enthalpy of saturated steam = 2659 kJ/kg
    Enthalpy of condensate = 375 kJ/kg
    Viscosity of condensate at the film temperature = 3.24 x 10-4 Pa.s
    Assume the flow of the condensate is laminar:
      1. Calculate the rate of steam condensation
      2. Check whether the flow is laminar.

  5. Water, flowing in a steel pipe of diameter 0.02 m, is to be cooled from 40oC to 30oC. The velocity of water in the steel pipe is 1.5 m/s. The inside surface temperature of the steel pipe is maintained at 25oC. The physical properties of water at mean bulk temperature of the fluid are: Specific heat = 4.174 kJ/kg.oK
    Density = 995 kg/m3
    Thermal conductivity = 0.623 W/m.K
    Viscosity = 7.65 x 10-4 Pa.s
    Calculate:
    1. The convective heat transfer coefficient for water
    2. The length of the tube required.

  6. Consider three infinite parallel plates. Plate 1 is maintained at 1227oC and plate 3 is maintained at -174oC. Emissivities are equal to that of a black body. Plate 2 is placed between plates 1 and 3, and receives no heat from external sources. What is the temperature of plate 2?

  7. A nickel-steel rod 8 cm OD originally at a temperature of 300oC is suddenly immersed in a liquid at 100oC for which the convective heat transfer coefficient is 100 W/m2.K. Determine the time required for the rod to reach a temperature of 150oC. (Hint: Calculate the Biot number and make the necessary assumption).

    Properties of nickel-steel:

    k = 80 W/m.K

    ρ = 8000 kg/m3

    Cp = 0.5 kJ/kg.K

  8. In a 1-1 shell and tube heat exchanger , a fluid flowing through the tubes in turbulent flow, is being heated by means of steam condensing on the shell side. It is proposed to increase the tube side coefficient by one of the following methods:
      1. replace the existing tubes by the same number of tubes with half the original diameter but twice the length.
      2. Increase the number of tube passes to 2.

    Assuming that the fluid flow rate remains high enough to ensure a Reynolds number of over 10,000 in all cases, indicate the method you would select. Justify your selection in brief (in not more than five lines).

  9. 10,000 kg/hr of an aqueous feed containing 1% dissolved solids is to be concentrated to 20% solids, in a single effect evaporator. The feed enters at 25oC. The steam chest is fed with saturated steam at 110oC. The absolute pressure maintained in the evaporator is such that the water will boil at 55oC. The heat transfer area available is 50 m2. The boiling point elevations are as follows:

    10. Feed: 0.2oC
    20% solution: 15oC

    The overall heat transfer coefficient, under normal operating conditions would be 2500 W/m2.oC

    Estimate the heat load on the condenser, assuming no sub cooling of condensate.

  10. A light motor oil with the following characteristics is to be heated from 65 to 120oC in a 6 mm id pipe of 5 m long. The pipe is at 175oC. How much oil can be heated in this pipe in kg/hr? What coefficient can be expected?

    11. Data for the oil:

    Thermal conductivity = 0.142 W/m.oC

    Specific heat = 2 kJ/kg.oC

    Viscosity (Temperature oC): 6.0 (65) ; 3.3 (120) ; 1.37 (175) cP

  11. A thermopane window consists of two sheets of glass each 6 mm thick, separated by a layer of stagnant air also 6 mm thick. Find the percentage reduction in heat loss from this pane as compared to that of a single sheet of glass 6 mm thickness. The temperature drop between inside and outside remains same at 15oC. Thermal conductivity of glass is 30 times that of air.

  12. An asbestos pad, square in cross-section, measures 0.05 m on a side and increases linearly to 0.1 m on the side at the other end (see the figure). The length of the pad is 0.15 m.

    If the small end is held at 600 K and the larger end at 300 K. What will be the heat flow rate if the other four sides are insulated. Assume one directional heat flow. Thermal conductivity of asbestos is 0.173 W/m.K.

  13. The outside surface temperature of a pipe ( radius = 0.1m ) is 400 K. The pipe is losing heat to atmosphere, which is at 300 K. The film heat transfer coefficient is 10 W/(m2.K). To reduce the rate of heat loss, the pipe is insulated by a 50 mm thick layer of asbestos ( k = 0.5 W/(m.K) ). Calculate the percentage reduction in the rate of heat loss.

  14. In a 1 - 1 counter flow shell and tube heat exchanger, a process stream (CP = 4.2 kJ/(kg.K) ) is cooled from 450 to 350 K using water ( CP = 4.2 kJ/(kg.K) ) at 300 K. The process stream flows on the shell-side at a rate of 1 kg/s and the water on the tube-side at a rate of 5 kg/s. If the heat transfer coefficients on the shell and tube sides are 1000 W/(m2.K) and 1500 W/(m2.K), respectively, determine
    (a) the required heat transfer area.
    by what factor will the required area change if the flow is concurrent?
    Neglect tube wall resistance and fouling resistances.

  15. An aqueous solution of a solute is concentrated from 5% to 20% (mass basis) in a single-effect short-tube evaporator. The feed enters the evaporator at a rate of 10 kg/s and at a temperature of 300 K. Steam is available at a saturation pressure of 1.3 bar. The pressure in the vapor space of the evaporator is 0.13 bar and the corresponding saturation temperature of steam is 320 K. If the overall heat transfer coefficient is 5000 W/(m2.K), calculate the
    (a) steam economy
    (b) heat transfer surface area.
      Enthalpy (kJ/kg) Heat of vaporization (kJ/kg)
    Saturated steam (1.3 bar; 380 K) ------ 2000
    Saturated steam (0.13 bar; 320 K) 2200 ------
    Feed (5% ; 300 K) 80 ------
    Concentrated liquor (20% ; 325 K) 400 ------

    Boiling point elevation is 5 K.

  16. A thermocouple junction may be approximated as a sphere of diameter 2 mm with thermal conductivity 30 W/(m.oC), density 8600 kg/m3 and specific heat 0.4 kJ/(kg.oC). The heat transfer coefficient between the gas stream and the junction is 280 W/(m2.oC). How long will it take for the thermocouple to record 98 percent of the applied temperature difference?

  17. A shell and tube steam condenser is to be constructed of 2.5 cm O.D., 2.2 cm I.D., single pass horizontal tubes with steam condensing at 54oC on the outside of the tubes. The cooling water enters at 20oC and leaves at 36oC at a flow rate of 1 kg/s. The heat transfer coefficient for the condensation of steam is 7900 W/(m2.oC). Calculate the tube length. If the latent heat of condensation is 2454 kJ/kg, calculate the condensation rate per tube. The properties of water are as follows: Specific heat 4180 J/(kg.oC)
    Viscosity 0.86 x 10-3 kg/(m.s)
    Thermal conductivity 0.61 W/(m.oC)
    The heat transfer coefficient for turbulent flow in a pipe may be determined by
    Nu = 0.023 Re0.8 Pr0.4

  18. A Rocket chamber can be assumed as a spherical steel chamber 30 cm dia. Within this fuel burns at a temperature of 1500oC. In order to protect the wall and reduce heat transfer a 5 cm alumina-brick layer (K = 3.5 W/m.K) is provided inside and two insulation layers (3 and 5 mm thick, and respective K's are 0.17 and 0.85 W/m.K) outside the chamber. Find out heat loss and intermediate wall temperatures when surrounding temperature was 100oC. If the insulation layers are reversed will there be any effect on heat transfer and interface temperatures?

  19. A steel sphere is of inner radius 40 cm and outer radius 45 cm is used to store liquid oxygen (B.P is minus 183oC). The sphere is covered with one layer of insulation whose K is 0.35 W/m.K and another insulation whose K is 0.098 W/m.K. The sphere is exposed to atmosphere of 25oC. Find out the rate of oxygen becoming vapor every minute. Latent heat of oxygen is 370 kJ/kg.

  20. A steam pipe 160 mm id and 170 mm od is covered with two layers of insulation. The thickness of the first layer is 30 mm and that of the second is 50 mm. The thermal conductivity values are 50, 0.15 and 0.08 kcal/m.hr.oC for the pipe, first insulation and second insulation respectively. The temperature of the inner surface of the steam pipe is 300oC and that of the outer surface of the insulation layer is 50oC. Determine the quantity of heat lost per meter length of steam pipe and the layer contact temperatures.

  21. Brick work of a furnace is built of layers of fire clay and red brick and the space between them is filled with common brick. Fire clay layer is 120 mm thick, common brick is 50 mm thick and the red brick layer is 250 mm thick. The thermal conductivity values for the materials are 0.93, 0.13 and 0.7 kcal/hr.m.oC respectively. Find the thickness of the red brick layer if the common brick layer is to be absent and the heat transfer remains the same. Take the fir clay thickness also remains the same.

  22. A heat exchanger heats 25,000 kg/hr of water entering at 80oC while cooling 20,000 kg/hr of water from 100oC to 80oC. Determine the heat transfer area necessary for (i) Parallel flow arrangement (ii) Counter flow arrangement. Given Overall heat transfer coefficient, U= 1,500 W/m2 K

  23. A brick wall of thermal conductivity 1.0 W/m.K is of 300 mm thickness, lined on the inner face with plaster of thermal conductivity 0.4 W/m.K and thickness 20 mm. If a temperature difference of 70 K is maintained between the two outer faces, what is the heat flow per unit area of the wall?

  24. A liquid metal flows at a rate of 5 kg/sec through a 5 cm diameter stainless steel tube. It enters at 425oC and is heated to 450oC as it passes through the tube. If a constant heat flux is maintained along the tube and the tube wall is at a temperature 20oC higher than the liquid metal bulk temperature, calculate the area required to effect the heat transfer. At constant heat flux, NNu = 4.82 + 0.0185 NPe0.827 relation holds good. Properties of the compound: μ = 1.34 x 10-3 kg/m.s; CP = 0.149 kJ/kg.K; k = 15.6 W/m.K; NPr = 0.013.

  25. A solid cube of side 30 cm at an initial temperature of 1000 K is kept in vacuum at absolute zero temperature. Calculate the time required to cool it to 500 K. The material has the following properties:

    26. Density = 2700 kg/m3

    Specific heat = 0.9 kJ/kg.K

    Emissivity = 0.1

    Stefan-Boltzmann constant, σ = 5.67 x 10-8 W/m2.K4.

  26. In a counter-current heat exchanger which has been in service for some time, due to formation of scale, the heat transfer rate is reduced to 85% of its original value based on clean surface. Assuming that the terminal temperatures of fluids are same in both cases, and the effective heat transfer area does not change appreciably due to scale formation, determine the overall fouling factor if clean overall heat transfer coefficient is 500 W/m2.K

  27. A pipe of 20 mm inner diameter and 30 mm outer diameter is insulated with 35 mm thick insulation. The thermal conductivity of insulating material is 0.15 W/m.K and the convective heat transfer coefficient of outside air is 3 W/m2.K. The temperature of bare pipe is 200oC and the ambient air temperature is 30oC. The heat transfer resistance of the pipe metal can be neglected.
    1. Comment with reasoning about the heat transfer rates with and without insulation.
    2. If the same insulating material is used, what is the minimum thickness above which there is a reduction in heat loss as compared to the bare pipe?
    3. For optimum design, what conductivity of insulating material do you suggest for the conditions given in the problem?
  28. It is desired to cool 10,000 kg/hr of hexane from 50oC to 30oC using water between 10 to 25oC. For this purpose a 1-2 shell and tube heat exchanger of the following details is available. The shell is 100 cm dia having 1650 tubes of 19 mm od, 15 mm id, kept in 25 mm triangular pitch with 125 mm baffle spacing. The properties of liquids are as follows:
      K, W/mK r, kg/m3 m, N.sec/m2 Cp, J/kgoC
    hexane 0.315 810 0.65 x 10-3 2500
    Water 0.63 995 0.9 x 10-3 4184
    The length of heat exchanger is 5 m.

  29. A trible effect forced circulation evaporator is used to concentrate 10,000 kg/hr aqueous sodium hydroxide solution from 10% to 40%. The feed is at 30oC. The last stage is kept of at 50 mm Hg absolute vacuum. Assuming the overall heat transfer coefficients 6000, 3600 and 2100 W/m2K and forward feed, find out heat transfer areas and steam economy. The steam is available at 123oC (latent heat = 2010 kJ/kg). Assume boiling point rise of liquid as 20oC and latent heat at other stages as 2100 and 2200 kJ/kg. The temperature in the last stage is 38oC.

  30. An organic liquid Cp = 0.5 cal/(g.oC) flowing at 1200 kg/hr in the inner tube (ID = 2.5 cm; OD = 3.0 cm) of a double pipe heat exchanger of 8 meter length is cooled from 90oC to 50oC with water flowing countercurrently on the jacket side. Assume U = 450 kcal/(hr.m2.oC). Calculate the length of a transfer unit based on the hot organic fluid and also the number of transfer units.

  31. Water is to be cooled from 20oC to 7oC using brine at an inlet temperature of -1oC with a temperature rise of 4oC. The brine and water flows are on the tube and shell sides respectively. Determine the total heat transfer area required for a cross flow arrangement assuming an average overall heat transfer coefficient of 850 W/(m2.oC) and design heat load of 5900 W.

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    Last Modified on: 04-Feb-2022

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