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# 11 Heat Transfer

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Heat Transfer Module

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### 11 Heat Transfer

1. 1. HEAT TRANSFER
2. 2. Content • Modes of heat transfer? • Fourier Law of heat conduction • Convective heat coefficient • Radiant heat coefficient • Overall heat transfer coefficient • Hands-on example
3. 3. Temperature • A measure of energy due to level of heat – Freezing point of water is 0 ˚ C – Boiling point of water is 100 ˚ C
4. 4. Common Temperature Scales
5. 5. What is Heat? Heat is the total internal kinetic energy due to molecular motion in an object Quantity of heat is BTU or Kilo Joule (kJ) • One BTU is the amount of heat required to raise 1 lb of water by 1 ˚ F • One calorie is required to raise 1 g of water by 1 ˚ C 1 cal = 4.187 J • 1 BTU= 1.055 kJ= 1055 J
6. 6. Heat Vs Temperature • Heat energy depends on mass. Temperature is independent of mass. – 2 litres of boiling water has more heat energy than 1 litre of boiling water • Temperature is not energy, but a measure of it • Heat is energy
7. 7. Heat is Energy When heat (ie energy) goes into a substance, one of two things can happen: 1. Temperature goes up 2. Change of state
8. 8. Temperature Goes Up • Heat that causes a rise in temperature e.g. heating water before boiling • The heat energy is used to increase the kinetic energy of the molecules in the substance • This is also known as the sensible heat
9. 9. Change Of State • Heat that brings about a change in potential energy of the molecules (temperature remains constant). Also called the latent heat.
10. 10. Specific Heat • It is the heat required to the temperature of 1 kg (lb) a substance by 1 ˚ K (F) • Example: water’s specific heat is 1 btu/ lb F (4.2 kJ/kg K) air’s specific heat is 0.24 btu/ lb F (1.0 kJ/kg K)
11. 11. Sizing Heating Capacity Quantity of heat required  mass x specific heat x T Example: What is the heat required to raise air temperature from 15 ˚C to 25 ˚C at a flow rate of 2000 l/s?
12. 12. Heat Transfer • If there is a temperature difference in a system, heat will always move from higher to lower temperatures What is actually flowing?
13. 13. Heat Transfer Modes There are 3 modes of heat transfer. 1. Conduction 2. Convection 3. Radiation
14. 14. Conduction • Heat transfer through a solid medium via direct contact • Expressed by Fourier’s Law
15. 15. Fourier’s Law T2 T1 dT q"  k Q dx X k = thermal conductivity (W/ m K) T = temperature (K) q” = heat flux (W/m2) Heat flow rate = q” x area (W)
16. 16. Fourier’s law at steady state dT q"   k (Fourier Law) dx Tout  Tin q"   k (Steady State) L Tout  Tin q"   L/k Heat transfer rate q Q  q" x Area of heat flow T2 T T   out in T1 L / kA R=L/k Unit thermal resistance
17. 17. Example 1 • Temperature of 35 C and 22 C are maintained on opposite sides of a steel floor of 6mm thick. Compute the heat flux through the floor. • Thermal conductivity for steel = 50 W/m K
18. 18. Thermal Conductivity, k (W/m K) Liquids Common Metals Water: 0.556 Copper: 385 Ammonia: 0.54 Aluminum: 221 Gases Steel: 50 Air : 0.024 Non-metals Water vapor: 0.021 Common brick: 0.6 Mineral wool: 0.04 Ceiling board: 0.06
19. 19. Quiz • Suppose a human could live for 2 h unclothed in air at 45 ˚F. How long could she live in water at 45 ˚F?
20. 20. Electrical- Thermal Analogy q T2 Electrical (Ohm' s Law) T1 Voltage Potential R=L/kA Current, I  Re sis tan ce Thermal Temperature difference Heat flux, q  Re sis tan ce
21. 21. Composite Wall Using the resistance concept, T 2 T1 q"  R1 R 2 x1 R1  k1 x2 R1 R2 T2 R2  T1 k2 Q
22. 22. Example 2 A wall of a Switchgear room consists the following: 6mm 100mm 25mm TNF panel k2 k = 0.02 W/m K 35 C q2 22 C Q Q Q Steel plate Firebatt k = 50 W/m K k = 0.04 W/m K Determine Q, if the wall is 3m x 4m ?
23. 23. Convection • Energy transfer by fluid motion • Two kinds of convection – Forced convection: Fluid is forced – Natural or free convection: fluid is induced by temperature difference
24. 24. Convective Heat Transfer y Ta Newton's Law of cooling q q"  hc (Ts  Ta ) air flow (Ts  Ta ) Ts q"  1 hC where: h c is convection coefficient (W/m2C), 1 Ts is surface temperature (C), Rc  T a is surrounding air temperature (C) hc Rc= unit convective resistance.
25. 25. Magnitude of Convection Coefficients Arrangement h, W/m2 K Btu/(h.ft2.F) Air, free (indoor) 10-30 1-5 Air, forced 30-300 5-50 (outdoor) Oil, forced 60-1800 10-300 Water, forced 300-6000 50-1000 Steam, condensing 6000-120000 1000-20000
26. 26. Example 3 The same as Example 2. Consider convection of the exposed surfaces, calculate Q. 6mm 100mm 25mm TNF panel k2 k = 0.02 W/m K 35 C q2 22 C Q Q Q Steel plate Firebatt k = 50 W/m K k = 0.04 W/m K
27. 27. Radiation • Energy emitted by object that is at any temperature above absolute zero • Energy is in the form electromagnetic waves • No medium needed and travel at speed of light Example : Hot Body Solar radiation Radiator
28. 28. Radiation • Important mode of heat at high temperatures, e.g. combustion furnace • At room temperature it may just be measurable. • Intensity depends on body temperature and surface characteristics
29. 29. Solar Radiation • Solar radiation is the radiation emitted by the sun due to nuclear fusion reaction • Solar Constant: The amount of solar energy arriving at the top of the atmosphere perpendicular to the sun’s rays. • = 1375 W m-2
30. 30. Solar Radiation Spectrum 99% of solar radiation is between 0.3 to 3 µm.
31. 31. Wien’s Law 2900 m  m T
32. 32. Wien’s Law
33. 33. The Black Body 4 E = AT • E =The amount of energy (W ) emitted by an object •  = Stefan-Boltzmann constant = 5.67 x 10-8 W m-2 K-4 • T = Temperature (K) • A= area (m2)
34. 34. The Grey Body For an actual body, E   Eb   A(T ) where 4   emissitivity  0.8 - 0.9 for common materials  0.02 - 0.07 for polished metals
35. 35. Net Radiant Heat • If a hot object is radiating to a cold surrounding, the radiation loss is q   A(Th 4  Tc 4 )
36. 36. Quiz How much energy does human body radiate? • Body temperature is 37 C • Body area is 1.5 m2 • ε= 0.7
37. 37. Radiant Heat Transfer • Unit thermal resistance for radiation is written as q"  hr ( T) 1 Rc  hr Radiation coefficient is a function of temperature, radiation properties and geometrical arrangement of the enclosure and the body in question.
38. 38. Combined convection and radiant Coefficient • The heat transfer is combination of convection and radiation q"  qc  qr q"  ( hc  hr )(T ) Combined thermal resistance, 1 R hc  hr
39. 39. Combined Surface Coefficients • Some practical values of surface coefficients: (source: ASHRAE Fundamentals 1989) Air velocity Emissivity, ε=0.9 3.5 m/s h = 22.7 W/m2 K 7 m/s h = 35 W/m2 K Still air h = 8.5 W/ m2 K
40. 40. Combined modes Thot Thot Outside R3=1/hhot T3 T3 k2 T2 k1 R2=L1/k1 + L2/K2 T1 Inside T1 R1=1/hcold Tcold T Tcold Resistance in parallel, R= R1 + R2 +R3
41. 41. Compute Thot R  R1  R 2  R 3 R3=1/hhot 1 L1 L 2 1 R  /  hcold k 1 k 2 hhot Thot  Tcold T2 q"  R2=L1/k1 + L2/k2 1 / hhot  1 / hcold  L1 / k 1  L 2 / k 2 T1  Tcold q"  T1 1 / hcold T2  Tcold R1=1/hcold q"  1 / hcold  L1 / k 1  L 2 / k 2 Tcold
42. 42. Overall Heat Transfer Coefficient • Heat transfer processes includes conduction, convection and radiation simultaneously • The total conduction heat transfer for a wall or roof is expressed as Q = A x U x ∆T where U is the overall heat transfer coefficient (or U- value) R  R1  R 2  R 3  ....... 1 U  R
43. 43. Example • Find the overall heat transfer coefficient of a flat roof having the construction shown in the figure.
44. 44. Solution T1 R1 R2 R3 R4 R5 R6 T2
45. 45. Solution Resistance Construction Unit resistance (m2 K/ W) R1 Outside air R2 steel R3 Mineral wool R4 Air space R5 Ceiling board R6 Inside air Total R
46. 46. Solution Overall heat transfer coefficien t 1 1 U   0.40 W/m K 2 R 2.48
47. 47. Heat Transfer Loop in a DX System
48. 48. Heat Exchanger Coil Heat is exchanged between 2 fluids. Q= UA ∆T For cross flow, Q= UA (LMTD)
49. 49. Heat Exchanger- Mean Temperature Difference Heat Transfer, Q  U x Area x LMTD GTD - LTD Q  U x Area x GTD Ln LTD
50. 50. Heat transfer optimization • We have the following relations for heat transfer: – Conduction: Q = k A ∆T /d – Convection: Q = A h c ∆T – Radiation: Q = A h r ∆T • As a result, when equipment designers want to improve heat transfer rates, they focus on: – Increasing the area A, e.g. by using profiled tubes and ribbed surfaces. – Increasing T (which is not always controllable). – For conduction, increasing k /d. – Increase h c by not relying on natural convection, but introducing forced convection. – Increase hr, by using “black” surfaces.