1. Mechanisms of Heat Transfer, Chapter 1 Dr.Eng. Hamdy A. Kandil 17 th February 2013 1 Lecture 1

2. Course Description- Evaluation Prepared by: Dr.Eng. Hamdy Kandil C7-113 Lecturer: Ass.Prof.Dr.Eng. Mohamed Salama C6-106 TA: Engs. Seif and Fady Textbooks: 1- Yunus A. Cengel, Heat and Mass Transfer, A Practical Approach 3rd edition (SI Units), McGraw Hill, ISBN 10-007- 125739-X 2- Yunus A. Cengel, Robert H. Turner, Fundamentals of Thermal-Fluid sciences, 2nd edition, McGraw Hill, 2005, ISBN 0-07-118152-0. 3- Incropera, DeWitt, Bergman and Lavine, Fundamentals of Heat and Mass Transfer, 6 th edition, John Wiley, 2007. Grading System: 40% Final, 25% midterm, 20% quizzes, 15% assignments and project. 2 Lecture 1

3. Course Schedule 3 Lecture 1 LectureDateWeekLectureDateWeek Lec. 7 7-48: (5/4 - 10/4) Lec. 1 17-21: (15/2 - 20/2) Lec. 8 14-49: (12/4 – 17/4) Lec. 2 24-22: (22/2 – 27/2) Easter10: (19/4 –24/4) Lec. 3 3-33: (1/3 – 6/3) Lec. 9 28-411: (26/4 –1/5) Lec. 4 10-34: (8/3 – 13/3) Lec. 10 5-512: (3/5 – 8/5) Lec. 5 17-35: (15/3 – 20/3) Last Lecture13:(10/5 – 15/5) Lec. 6 24-36: (22/3 – 27/3) Revision Week14:(17/5 – 22/5)Mid-Term7: (29/3 – 3/4)

4. Lecture Strategy Please 3- make your mobile Silent 1- Smile 2- Respect the lecture time 4 Lecture 1

5. What is heat transfer? Heat is a form of energy that can be transferred from one system to another as a result of temperature difference. The science that deals with the determination of the rates of such energy transfer is heat transfer. In practice we are more concerned about the rate of heat tranfer (heat tranfer per unit time) than the amount of heat transfer, e.g. Heat treatment of metals: (a) quenching and (b) annealing. 5 Lecture 1

6. 1- Radiation 2-conduction 3-convection Mechanisms of Heat Transfer Barn Water 6 Lecture 1

7. MECHANISMS OF HEAT TRANSFER Heat can be transferred in three different ways: conduction, convection, and radiation. All modes of heat transfer require the existence of a temperature difference, and all modes of heat transfer are from the high- temperature medium to a lower temperature one. 7 Lecture 1

8. Conduction, Convection & Thermal Radiation Conduction refers to the transport of energy in a medium due to a temperature gradient. In contrast, the convection refers to heat transfer that occurs between a surface and a fluid (at rest or in motion) when they are at different temperatures. Thermal radiation refers to the heat transfer that occurs between two surfaces at different temperatures. It results from the energy emitted by any surface in the form of electromagnetic waves. 8 Lecture 1

9. Conduction 9 Lecture 1

10. Physical Mechanism of Conduction Temperature is a measure of the kinetic energies of the molecules. In a liquid or gas, the kinetic energy of the molecules is due to the random motion of the molecules as well as the vibrational and rotational motions. When two molecules possessing different kinetic energies collide, part of the kinetic energy of the more energetic (higher temperature) molecule is transferred to the less energetic (lower temperature) particle, In solids, heat conduction is due to two effects: the lattice vibrational waves induced by the vibrational motions of the molecules positioned at relatively fixed position in a periodic manner called a lattice, and the energy transported via the free flow of electrons in the solid. The thermal conductivity of a solid is obtained by adding the lattice and the electronic components. The thermal conductivity of pure metals is primarily due to the electronic component, whereas the thermal conductivity of nonmetals is primarily due to the lattice component. 10 Lecture 1

11. The lattice component of thermal conductivity strongly depends on the way the molecules are arranged. For example, the thermal conductivity of diamond, which is a highly ordered crystalline solid, is much higher than the thermal conductivities of pure metals, as can be seen from Table 1-1. 11 Lecture 1

12. Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. Conduction can take place in solids, liquids, or gases. In gases and liquids, conduction is due to the collisions of the molecules during their random motion. In solids, it is due to the combination of vibrations of molecules in a lattice and the energy transport by free electrons. A cold canned drink in a warm room eventually warms up to the room temperature as a result of heat transfer from the room to the drink through the aluminum can by conduction 12 Lecture 1

13. Conduction It is observed that the rate of heat conduction through a layer of constant thickness Δx is proportional to the temperature difference ΔT across the layer and the area A normal to the direction of heat transfer, and is inversely proportional to the thickness of the layer, Δx. where the constant of proportionality k t is the thermal conductivity of the material, which is a measure of the ability of a material to conduct heat (Table 1-1). Materials such as copper and silver, which are good electric conductors, are also good heat conductors, and therefore have high k t values. Materials such as rubber, wood, and styrofoam are poor conductors of heat, and therefore have low k t values. 13

14. Heat Transfer depends on the thermal conductivity of the material 14

15. The range of thermal conductivity of various materials at room temperature. 15 Lecture 1

16. In the limiting case of  x → 0, the equation above reduces to the differential form x hot wallcold wall temperature profile which is known as Fourier’s law of heat conduction. It indicates that the rate of heat conduction in a direction is proportional to the temperature gradient in that direction. Heat is conducted in the direction of decreasing temperature, and the temperature gradient becomes negative when temperature decreases with increasing x. Therefore, a negative sign is added in the Eq. to make heat transfer in the positive x direction a positive quantity. 16 Lecture 1

17. Example: The Cost of Heat Loss through a Roof The roof of an electrically heated home is 6 m long, 8 m wide, and 0.25 m thick, and is made of a flat layer of concrete whose thermal conductivity is k 0.8 W/m · °C. The temperatures of the inner and the outer surfaces of the roof one night are measured to be 25°C and 0°C, respectively, for a period of 10 hours. Determine: (a) the rate of heat loss through the roof that night and (b) the cost of that heat loss to the home owner if the cost of electricity is $0.2/kWh. 17 Lecture 1 25 C 0 C

18. Solution: (a) Noting that heat transfer through the roof is by conduction and the area of the roof is: A= 6 m×8 m=48 m 2. The steady rate of heat transfer through the roof is determined to be Q · =kA(T 1 -T 2 )/L= (0.8)(48 )(25-0)/0.25= 3840 W= 3.84 kW (b) The amount of heat lost through the roof during a 10-hour period and its cost are determined from Q = Q ·  t =(3.84 kW)(10 h) = 38.4 kWh Cost/day = (Amount of energy)(Unit cost of energy) = (38.4 kWh)($0.2/kWh) =$7.68 Cost/month = (cost/day)×(30day/month)= $7.68×30=$230.4 Why is the bill so high? 18 Lecture 1

19. Thermal Diffusivity The thermal diffusivity is a measure of how quickly a material can carry heat away from a hot source. Since material does not just transmit heat but must be warmed by it as well,  involves both the conductivity, k, and the volumetric heat capacity, ρ c p. 19 Lecture 1

20. Convection 20 Lecture 1

21. Convection Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion. The faster the fluid motion, the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid is by pure conduction. The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid, but it also complicates the determination of heat transfer rates. Consider the cooling of a hot block by blowing of cool air over its top surface. Energy is first transferred to the air layer adjacent to the surface of the block by conduction. This energy is then carried away from the surface by convection; that is, by the combined effects of conduction within the air and the motion of the air, which removes the heated air near the surface and replaces it by the cooler air. 21 Lecture 1

22. Forced and Free Convection Convection is called forced convection if the fluid is forced to flow in a tube or over a surface by external means such as a fan, pump, or the wind. In contrast, convection is called free (or natural) convection if the fluid motion is caused by buoyancy forces induced by density differences due to the variation of temperature in the fluid. For example, in the absence of a fan, heat transfer from the surface of the hot egg will be by natural convection since any motion in the air in this case will be due to the rise of the warmer (and thus lighter) air near the surface and the fall of the cooler (and thus heavier) air to fill its place. 22 Lecture 1

23. Forced and Free Convection The cooling of a boiled egg by forced and natural convection. 23 Lecture 1

24. Newton’s law of cooling The rate of heat transfer by convection is determined from Newton’s law of cooling, expressed as where h is the convection heat transfer coefficient, A is the surface area through which heat transfer takes place, Ts is the surface temperature, and T f is bulk fluid temperature away from the surface. The convection heat transfer coefficient h is not a property of the fluid. It is an experimentally determined parameter whose value depends on all the variables that influence convection such as: the surface geometry, the nature of fluid motion, the properties of the fluid, and the bulk fluid velocity. 24 Lecture 1

25. Convection Typical values of h, in W/m 2 ·K, are in the range of 2–25 W/m 2 ·K for the free convection of gases, 50–1000 W/m 2 ·K for the free convection of liquids, 25–250 W/m 2 ·K for the forced convection of gases, 50–20,000 W/m 2 ·K for the forced convection of liquids, and 2500–100,000 W/m 2 ·K for convection in boiling and condensation processes. 25 Lecture 1

26. Unlike conduction and convection, heat transfer by radiation can occur between two bodies, even when they are separated by a medium colder than both of them. Radiation 26 Lecture 1

27. Radiation Radiation is the energy emitted by matter in the form of electromagnetic waves as a result of the changes in the electronic configurations of the atoms or molecules. Unlike conduction and convection, the transfer of energy by radiation does not require the presence of an intervening medium. In fact, energy transfer by radiation is fastest (at the speed of light) in a vacuum. This is exactly 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. It differs from other forms of electromagnetic radiation such as X-rays, gamma rays, microwaves, radio waves, and television waves that are not related to temperature. All bodies at a temperature above absolute zero emit thermal radiation. 27 Lecture 1

28. Radiation is a volumetric phenomenon, and all solids, liquids, and gases emit, absorb, or transmit radiation of varying degrees. However, radiation is usually considered to be a surface phenomenon for solids that are opaque to thermal radiation such as metals, wood, and rocks since the radiation emitted by the interior regions of such material can never reach the surface, and the radiation incident on such bodies is usually absorbed within a few microns from the surface. The maximum rate of radiation that can be emitted from a surface at an absolute temperature T s is given by the Stefan– Boltzmann law as where A is the surface area and  = 5.67 * 10- 8 W/m 2 · K 4 is the Stefan–Boltzmann constant. The idealized surface that emits radiation at this maximum rate is called a blackbody, and the radiation emitted by a blackbody is called blackbody radiation. 28

29. Emissivity,  The radiation emitted by all real surfaces is less than the radiation emitted by a blackbody at the same temperatures and is expressed as where  is the emissivity of the surface. The property emissivity, whose value is in the range 0    1, is a measure of how closely a surface approximates a blackbody for which  = 1. 29 Lecture 1

30. Emissivity,  30 Lecture 1

31. Another important radiation property of a surface is its absorptivity, , which is the fraction of the radiation energy incident on a surface that is absorbed by the surface. Its value is in the range 0    1. A blackbody absorbs the entire radiation incident on it. That is, a blackbody is a perfect absorber (  = 1) as well as a perfect emitter (  = 1). In general, both  and  of a surface depend on the temperature and the wavelength of the radiation. Kirchhoff’s law of radiation states that the emissivity and the absorptivity of a surface are equal at the same temperature and wavelength. In most practical applications, the dependence of  and  on the temperature and wavelength is ignored, and the average absorptivity of a surface is taken to be equal to its average emissivity.  =  Absorptivity,  31 Lecture 1

32. Absorpitivity The rate at which a surface absorbs radiation is determined from where Q inc is the rate at which radiation is incident on the surface and  is the absorptivity of the surface. For opaque (nontransparent) surfaces, the portion of incident radiation that is not absorbed by the surface is reflected back. 32 Lecture 1

33. Absorption and Emission of Radiation Energy out = Energy in Emitted energy/Incident energy = Emissivity = . 33

34. Black Bodies Summer clothing: white reflects radiant energy better than black. Until equilibrium is reached, white stripes on roads are at a lower temperature than unpainted asphalt. Wrap an ice-cube in black cloth and another in aluminum foil and place both in the sunshine. What will happen? 34 Lecture 1

35. The difference between the rates of radiation emitted by the surface and the radiation absorbed is the net radiation heat transfer. If the rate of radiation absorption is greater than the rate of radiation emission, the surface is said to be gaining energy by radiation. Otherwise, the surface is said to be losing energy by radiation. In general, the determination of the net rate of heat transfer by radiation between two surfaces is a complicated matter since it depends on the properties of the surfaces, their orientation relative to each other, and the interaction of the medium between the surfaces with radiation. 35 Lecture 1

36. However, in the special case of a relatively small surface of emissivity  and surface area A at absolute temperature T s that is completely enclosed by a much larger surface at absolute temperature T surr separated by a gas (such as air) that does not intervene with radiation (i.e., the amount of radiation emitted, absorbed, or scattered by the medium is negligible), the net rate of radiation heat transfer between these two surfaces is determined from In this special case, the emissivity and the surface area of the surrounding surface do not have any effect on the net radiation heat transfer. 36 Lecture 1

37. Not all three can exist simultaneously in a medium. For example, heat transfer is only by conduction in opaque solids, but by conduction and radiation in semitransparent solids. Thus, a solid may involve conduction and radiation but not convection. However, a solid may involve heat transfer by convection and/or radiation on its surfaces exposed to a fluid or other surfaces. For example, the outer surfaces of a cold piece of rock will warm up in a warmer environment as a result of heat gain by convection (from the air) and radiation (from the sun). But the inner parts of the rock will warm up by conduction. Simultaneous Heat Transfer Mechanisms 37 Lecture 1

38. Heat transfer is by conduction and possibly by radiation in a still fluid and by convection and radiation in a flowing fluid. In absence of radiation, heat transfer through a fluid is either by conduction or convection, depending on the presence of any bulk fluid motion. Convection can be viewed as combined conduction and fluid motion through a fluid Thus, when we deal with heat transfer through a fluid, we have either conduction or convection, but not both. Also, gases are practically transparent to radiation, except that some gases are known to absorb radiation strongly at certain wavelengths. Liquids, on the other hand, are usually strong absorbers of radiation. Combined Heat transfer coefficient: Q total = h comb (Ts – T  ) 38 Lecture 1

39. Example : Consider a person standing in a breezy room at 20°C. Determine the total rate of heat transfer from this person if the exposed surface area and the average outer surface temperature of the person are 1.6 m 2 and 29°C, respectively, and the convection heat transfer coefficient is 6 W/m 2 · °C. Convection can be viewed as combined conduction and fluid motion. Solution : Heat is transfered from the person by convection and radiation. From the above table the emissivity of human skin is 0.95, Q · conv =hA s (T s -T)= Q · rad 39