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• ### SSL3 Heat Transfer

1. 1. MECHANISMS OF HEAT TRANSFER Lecture 3 Keith Vaugh BEng (AERO) MEng Reference text: Chapter 16 - Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 KEITH VAUGH
2. 2. KEITH VAUGH
3. 3. OBJECTIVESUnderstand the basic mechanisms of heat transfer,which are conduction, convection, and radiation, }and Fouriers law of heat conduction, Newtons lawof cooling, and the Stefan–Boltzmann law ofradiation KEITH VAUGH
4. 4. OBJECTIVESUnderstand the basic mechanisms of heat transfer,which are conduction, convection, and radiation,and Fouriers law of heat conduction, Newtons lawof cooling, and the Stefan–Boltzmann law of }radiationIdentify the mechanisms of heat transfer that occursimultaneously in practice KEITH VAUGH
5. 5. OBJECTIVESUnderstand the basic mechanisms of heat transfer,which are conduction, convection, and radiation,and Fouriers law of heat conduction, Newtons lawof cooling, and the Stefan–Boltzmann law of }radiationIdentify the mechanisms of heat transfer that occursimultaneously in practiceDevelop an awareness of the cost associated withheat losses KEITH VAUGH
6. 6. OBJECTIVESUnderstand the basic mechanisms of heat transfer,which are conduction, convection, and radiation,and Fouriers law of heat conduction, Newtons lawof cooling, and the Stefan–Boltzmann law of }radiationIdentify the mechanisms of heat transfer that occursimultaneously in practiceDevelop an awareness of the cost associated withheat lossesSolve various heat transfer problems encounteredin practice KEITH VAUGH
7. 7. }KEITH VAUGH
8. 8. HEATThe form of energy that can be transferredfrom one system to another as a result oftemperature difference. } KEITH VAUGH
9. 9. }KEITH VAUGH
10. 10. THERMODYNAMICS Concerned with the amount of heat transfer as a system undergoes a process from one equilibrium state to another. } KEITH VAUGH
11. 11. }KEITH VAUGH
12. 12. HEAT TRANSFER Deals with the determination of the rates of such energy transfers as well as variation of temperature. } KEITH VAUGH
13. 13. } KEITH VAUGH
14. 14. } The transfer of energy as heat is always from the higher-temperature medium to the lower- temperature one. Heat transfer stops when the two mediums reach the same temperature. Heat can be transferred in three different modes: Conduction Convection Radiation KEITH VAUGH
15. 15. }KEITH VAUGH
16. 16. CONDUCTIONThe transfer of energy from the more energeticparticles of a substance to the adjacent lessenergetic ones as a result of interactions betweenthe particles. } KEITH VAUGH
17. 17. CONDUCTIONThe transfer of energy from the more energeticparticles of a substance to the adjacent lessenergetic ones as a result of interactions betweenthe particles. } KEITH VAUGH
18. 18. CONDUCTIONThe transfer of energy from the more energeticparticles of a substance to the adjacent lessenergetic ones as a result of interactions betweenthe particles. }In gases and liquids, conduction is due to thecollisions and diffusion of the molecules duringtheir random motion. KEITH VAUGH
19. 19. CONDUCTIONThe transfer of energy from the more energeticparticles of a substance to the adjacent lessenergetic ones as a result of interactions betweenthe particles. }In gases and liquids, conduction is due to thecollisions and diffusion of the molecules duringtheir random motion. KEITH VAUGH
20. 20. CONDUCTIONThe transfer of energy from the more energeticparticles of a substance to the adjacent lessenergetic ones as a result of interactions betweenthe particles. }In gases and liquids, conduction is due to thecollisions and diffusion of the molecules duringtheir random motion.In solids, it is due to the combination of vibrationsof the molecules in a lattice and the energytransport by free electrons. KEITH VAUGH
21. 21. CONDUCTIONThe transfer of energy from the more energeticparticles of a substance to the adjacent lessenergetic ones as a result of interactions betweenthe particles. }In gases and liquids, conduction is due to thecollisions and diffusion of the molecules duringtheir random motion.In solids, it is due to the combination of vibrationsof the molecules in a lattice and the energytransport by free electrons. KEITH VAUGH
22. 22. Heat Conduction through alarge plane wall of thickness Δx and area A KEITH VAUGH
23. 23. The rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer area, but is inversely proportional to the thickness of the layer. Rate of heat conduction ∝ ( Area )( Temperature difference ) Thickness Heat Conduction through alarge plane wall of thickness Δx and area A KEITH VAUGH
24. 24. The rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer area, but is inversely proportional to the thickness of the layer. Rate of heat conduction ∝ ( Area )( Temperature difference ) Thickness & = kA T1 − T2 = −kA ΔT Qcond ( Watts ) Δx Δx Heat Conduction through alarge plane wall of thickness Δx and area A KEITH VAUGH
25. 25. The rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer area, but is inversely proportional to the thickness of the layer. Rate of heat conduction ∝ ( Area )( Temperature difference ) Thickness & = kA T1 − T2 = −kA ΔT Qcond ( Watts ) Δx Δx Heat Conduction through alarge plane wall of thickness & = −kA dT When x → 0 Qcond Fourier’s law of Δx and area A dx heat conduction KEITH VAUGH
26. 26. Fourier’s law of & = −kA dT Qcondheat conduction dx KEITH VAUGH
27. 27. Fourier’s law of & = −kA dT Qcondheat conduction dx In heat conduction analysis, A represents the area normal to the direction of heat transfer KEITH VAUGH
28. 28. Fourier’s law of & = −kA dT Qcond heat conduction dxThermal conductivity, k A measure of the abilityof a material to conduct heat. In heat conduction analysis, A represents the area normal to the direction of heat transfer KEITH VAUGH
29. 29. Fourier’s law of & = −kA dT Qcond heat conduction dxThermal conductivity, k A measure of the abilityof a material to conduct heat.Temperature gradient dT/dx The slope of thetemperature curve on a T-x diagram. In heat conduction analysis, A represents the area normal to the direction of heat transfer KEITH VAUGH
30. 30. Fourier’s law of & = −kA dT Qcond heat conduction dxThermal conductivity, k A measure of the abilityof a material to conduct heat.Temperature gradient dT/dx The slope of thetemperature curve on a T-x diagram. In heat conduction analysis, A represents the area normal to the direction of heatHeat is conducted in the direction of decreasing transfertemperature, and the temperature gradientbecomes negative when temperature decreaseswith increasing x. KEITH VAUGH
31. 31. Fourier’s law of & = −kA dT Qcond heat conduction dxThermal conductivity, k A measure of the abilityof a material to conduct heat.Temperature gradient dT/dx The slope of thetemperature curve on a T-x diagram. In heat conduction analysis, A represents the area normal to the direction of heatHeat is conducted in the direction of decreasing transfertemperature, and the temperature gradientbecomes negative when temperature decreaseswith increasing x.The negative sign in the equation ensures thatheat transfer in the positive x direction is apositive quantity. KEITH VAUGH
32. 32. Fourier’s law of & = −kA dT Qcond heat conduction dxThermal conductivity, k A measure of the abilityof a material to conduct heat.Temperature gradient dT/dx The slope of thetemperature curve on a T-x diagram. In heat conduction analysis, A represents the area normal to the direction of heatHeat is conducted in the direction of decreasing transfertemperature, and the temperature gradientbecomes negative when temperature decreaseswith increasing x.The negative sign in the equation ensures thatheat transfer in the positive x direction is apositive quantity. The rate of heat conduction through a solid is directly proportional to its thermal conductivity KEITH VAUGH
33. 33. KEITH VAUGH
34. 34. Experimental conﬁguration:Determination of the thermal conductivityof a material KEITH VAUGH
35. 35. Thermal conductivityExperimental conﬁguration:Determination of the thermal conductivityof a material KEITH VAUGH
36. 36. Thermal conductivity The rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.Experimental conﬁguration:Determination of the thermal conductivityof a material KEITH VAUGH
37. 37. Thermal conductivity The rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity of a material is a measure of the ability of the material to conduct heat.Experimental conﬁguration:Determination of the thermal conductivityof a material KEITH VAUGH
38. 38. Thermal conductivity The rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity of a material is a measure of the ability of the material to conduct heat. A high value for thermal conductivity indicates that the material is a good heat conductor, and a low value indicates that the material is a poor heat conductor or insulator.Experimental conﬁguration:Determination of the thermal conductivityof a material KEITH VAUGH
39. 39. Thermal conductivity The rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity of a material is a measure of the ability of the material to conduct heat. A high value for thermal conductivity indicates that the material is a good heat conductor, and a low value indicates that the material is a poor heat conductor or insulator. Good conductor Bad conductorExperimental conﬁguration:Determination of the thermal conductivity Diamond Rigid foamof a material Bad insulator Good insulator KEITH VAUGH
40. 40. Source: Cambridge Engineering Selector KEITH VAUGH
41. 41. Source: Cambridge Engineering Selector KEITH VAUGH
42. 42. KEITH VAUGH
43. 43. Range of thermal conductivity of various materials at room temperature KEITH VAUGH
44. 44. KEITH VAUGH
45. 45. Mechanisms of heat conduction in differentphases of a substance KEITH VAUGH
46. 46. The thermal conductivities of gases such as air vary by a factor of 104 from those of pure metals such as copper. Pure crystals and metals have the highest thermal conductivities, and gases and insulating materials the lowest. Note: thermal conductivity of an alloy is usually much lower than the thermal conductivity of the metals which it is composed of.Mechanisms of heat conduction in differentphases of a substance KEITH VAUGH
47. 47. KEITH VAUGH
48. 48. Mini AssignmentUsing Cambridge Engineering Selector (GRANTA) investigate }how thermal conductivities of alloys differ from the thermalconductivity of materials they are made from KEITH VAUGH
49. 49. Mini AssignmentUsing Cambridge Engineering Selector (GRANTA) investigatehow thermal conductivities of alloys differ from the thermalconductivity of materials they are made fromcompare at least 6 alloys }e.g. at room temperature Bronze (52 k, W×m-1×°C -1) = Copper (401 k, W×m-1×°C -1,) andAluminium (237 k, W×m-1×°C -1) KEITH VAUGH
50. 50. }KEITH VAUGH
51. 51. THERMAL DIFFUSIVITY } a measure of the capability of a substance or energy to be diffused or to allow something to pass by diffusion. KEITH VAUGH
52. 52. } KEITH VAUGH
53. 53. } A material that has a high thermal conductivity or a low heat capacity will have a large thermal diffusivity. The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat is conducted further. KEITH VAUGH
54. 54. } A material that has a high thermal conductivity or a low heat capacity will have a large thermal diffusivity. The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat is conducted further. Heat conducted k α= Heat stored = ρc p ( s) m2 KEITH VAUGH
55. 55. } A material that has a high thermal conductivity or a low heat capacity will have a large thermal diffusivity. The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat is conducted further. Heat conducted k α= Heat stored = ρc p ( s) m2 cp Speciﬁc heat, J/kg · °C: Heat capacity per unit mass ρcp Heat capacity, J/m3 · °C: Heat capacity per unit volume α Thermal diffusivity, m2/s: Represents how fast heat diffuses through material KEITH VAUGH
56. 56. }KEITH VAUGH
57. 57. CONVECTIONThe mode of energy transfer between a solidsurface and the adjacent liquid or gas that is inmotion, and it involves the combined effects ofconduction and ﬂuid motion. }The faster the ﬂuid motion, the greater theconvection heat transfer.In the absence of any bulk ﬂuid motion, heattransfer between a solid surface and the adjacentﬂuid is by pure conduction. KEITH VAUGH
58. 58. KEITH VAUGH
59. 59. KEITH VAUGH
60. 60. Fluid is forced to ﬂow over thesurface by external means suchas a fan, pump or the wind KEITH VAUGH
61. 61. Fluid is forced to ﬂow over the Fluid motion is caused by buoyancy forcessurface by external means such that are induced by density differences dueas a fan, pump or the wind to the variation of temperature in the ﬂuid KEITH VAUGH
62. 62. Fluid is forced to ﬂow over the Fluid motion is caused by buoyancy forces surface by external means such that are induced by density differences due as a fan, pump or the wind to the variation of temperature in the ﬂuidHeat transfer processes that involve change of phase of a ﬂuid are also considered tobe convection because of the ﬂuid motion induced during the process, such as the riseof the vapour bubbles during boiling or the fall of the liquid droplets duringcondensation. KEITH VAUGH
63. 63. Newton’s law of cooling&Qconv = hAs (Ts − T∞ ) ( Watts )h convection heat transfer coefﬁcient, W/m2 · °CAs the surface area through which convection heat transfer takes placeTs the surface temperatureT∞ the temperature of the ﬂuid sufﬁciently far from the surface. KEITH VAUGH
64. 64. Newton’s law of cooling&Qconv = hAs (Ts − T∞ ) ( Watts )h convection heat transfer coefﬁcient, W/m2 · °CAs the surface area through which convection heat transfer takes placeTs the surface temperatureT∞ the temperature of the ﬂuid sufﬁciently far from the surface.The convection heat transfer coefﬁcient h is anexperimentally determined parameter whose valuedepends on all the variables inﬂuencing convectionsuch as: the surface geometry the nature of ﬂuid motion the properties of the ﬂuid the bulk ﬂuid velocity KEITH VAUGH
65. 65. KEITH VAUGH
66. 66. RADIATIONThe energy emitter by matter in the form ofelectromagnetic waves (or photons) as a result of thechanges in the electronic conﬁguration of the atomsor molecules } KEITH VAUGH
67. 67. } KEITH VAUGH
68. 68. } Unlike conduction and convection, the transfer of heat by radiation does not require the presence of an intervening medium. KEITH VAUGH
69. 69. } Unlike conduction and convection, the transfer of heat by radiation does not require the presence of an intervening medium. In fact, heat transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth. KEITH VAUGH
70. 70. } Unlike conduction and convection, the transfer of heat by radiation does not require the presence of an intervening medium. In fact, heat transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth. In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. KEITH VAUGH
71. 71. } Unlike conduction and convection, the transfer of heat by radiation does not require the presence of an intervening medium. In fact, heat transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth. In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. All bodies at a temperature above absolute zero emit thermal radiation. KEITH VAUGH
72. 72. } Unlike conduction and convection, the transfer of heat by radiation does not require the presence of an intervening medium. In fact, heat transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth. In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. All bodies at a temperature above absolute zero emit thermal radiation. Radiation is a volumetric phenomenon, and all solids, liquids, and gases emit, absorb, or transmit radiation to varying degrees. KEITH VAUGH
73. 73. } Unlike conduction and convection, the transfer of heat by radiation does not require the presence of an intervening medium. In fact, heat transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth. In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. All bodies at a temperature above absolute zero emit thermal radiation. Radiation is a volumetric phenomenon, and all solids, liquids, and gases emit, absorb, or transmit radiation to varying degrees. However, radiation is usually considered to be a surface phenomenon for solids. KEITH VAUGH
74. 74. Stefan - Boltzmann law & Qemit ,max = σ AsTs4 ( Watts ) KEITH VAUGH
75. 75. Stefan - Boltzmann law & Qemit ,max = σ AsTs4 ( Watts )Stefan - Boltzmann constant σ = 5.670 × 10 −8 W 2 gK 4 m KEITH VAUGH
76. 76. Stefan - Boltzmann law & Qemit ,max = σ AsTs4 ( Watts )Stefan - Boltzmann constant σ = 5.670 × 10 −8 W 2 gK 4 mBlackbody - The idealised surface that emits radiation at the maximum rate KEITH VAUGH
77. 77. Stefan - Boltzmann law & Qemit ,max = σ AsTs4 ( Watts )Stefan - Boltzmann constant σ = 5.670 × 10 −8 W 2 gK 4 mBlackbody - The idealised surface that emits radiation at the maximum rateRadiation emitted by real surfaces & Qemit = εσ AsTs4 ( Watts ) KEITH VAUGH
78. 78. Stefan - Boltzmann law & Qemit ,max = σ AsTs4 ( Watts )Stefan - Boltzmann constant σ = 5.670 × 10 −8 W 2 gK 4 mBlackbody - The idealised surface that emits radiation at the maximum rateRadiation emitted by real surfaces & Qemit = εσ AsTs4 ( Watts )Emissivity ε - A measure of how closely a surface approximates ablackbody for which ε = 1 of the surface. 0 ≤ ε ≤ 1 KEITH VAUGH
79. 79. Stefan - Boltzmann law & Qemit ,max = σ AsTs4 ( Watts )Stefan - Boltzmann constant σ = 5.670 × 10 −8 W 2 gK 4 mBlackbody - The idealised surface that emits radiation at the maximum rateRadiation emitted by real surfaces & Qemit = εσ AsTs4 ( Watts )Emissivity ε - A measure of how closely a surface approximates ablackbody for which ε = 1 of the surface. 0 ≤ ε ≤ 1 Blackbody radiation represents the maximum amount of radiation that can be emitted from a surface at a speciﬁed temperature KEITH VAUGH
80. 80. The absorption of radiation incident on an opaque surface of absorptivityAbsorptivity α - The fraction of the radiation energy incident on a surface that isabsorbed by the surface.0≤α≤1A blackbody absorbs the entire radiation incident on it (α = 1)Kirchhoff’s law - The emissivity and the absorptivity of a surface at a giventemperature and wavelength are equal KEITH VAUGH
81. 81. KEITH VAUGH
82. 82. Net radiation heat transfer - The differencebetween the rates of radiation emitted by thesurface and the radiation absorbed.The determination of the net rate of heat transferby radiation between two surfaces is acomplicated matter since it depends on ✓ the properties of the surfaces ✓ their orientation relative to each other ✓ the interaction of the medium between the surfaces with radiation Radiation heat transfer between a surface and the surfaces surrounding it KEITH VAUGH
83. 83. Net radiation heat transfer - The differencebetween the rates of radiation emitted by thesurface and the radiation absorbed.The determination of the net rate of heat transferby radiation between two surfaces is acomplicated matter since it depends on ✓ the properties of the surfaces ✓ their orientation relative to each other ✓ the interaction of the medium between the surfaces with radiation Radiation heat transfer between a surface and the surfaces surrounding itWhen radiation and convection occursimultaneously between a surface and a gas & Qtotal = hcombined As (Ts − T∞ ) ( Watts )Combined heat transfer coefﬁcient hcombinedincludes the effects of both convection andradiation KEITH VAUGH
84. 84. Net radiation heat transfer - The differencebetween the rates of radiation emitted by thesurface and the radiation absorbed.The determination of the net rate of heat transferby radiation between two surfaces is acomplicated matter since it depends on ✓ the properties of the surfaces ✓ their orientation relative to each other ✓ the interaction of the medium between the surfaces with radiation Radiation heat transfer between a surface and the surfaces surrounding itWhen radiation and convection occursimultaneously between a surface and a gas & Qtotal = hcombined As (Ts − T∞ ) ( Watts )Combined heat transfer coefﬁcient hcombinedincludes the effects of both convection and } Radiation is usually signiﬁcant relative to conduction or natural convection, but negligible relative to forced convectionradiation KEITH VAUGH
85. 85. SIMULTANEOUS HEAT TRANSFER MECHANISMSHeat transfer is only by conduction in opaque solids, but by conduction andradiation in semitransparent solidsA solid may involve conduction and radiation but not convection. A solid mayinvolve convection and/or radiation on its surfaces exposed to a ﬂuid or othersurfacesHeat transfer is by conduction and possibly by radiation in a still ﬂuid (no bulkﬂuid motion) and by convection and radiation in a ﬂowing ﬂuidIn the absence of radiation, heat transfer through a ﬂuid is either by conductionor convection, depending on the presence of any bulk ﬂuid motionConvection = Conduction + Fluid motionHeat transfer through a vacuum is by radiation Although there are threeMost gases between two solid surfaces do not interfere with radiation. mechanisms of heat transfer, a medium may involve only two ofLiquids are usually strong absorbers of radiation. them simultaneously. KEITH VAUGH
86. 86. Conduction  Fourier’s law of heat conduction  Thermal Conductivity  Thermal DiffusivityConvection  Newton’s law of coolingRadiation  Stefan–Boltzmann lawSimultaneous Heat Transfer Mechanisms KEITH VAUGH