Chapter 18. Heat Transfer. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
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1 Chapter 18. eat Transfer A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007
2 TRANSFER OF EAT is minimized by multiple layers of beta cloth. These and other insulating materials protect spacecraft from hostile environmental conditions. (NASA)
3 Objectives: After finishing this unit, you should be able to: Demonstrate your understanding of conduction, convection,, and radiation, and give examples. Solve thermal conductivity problems based on quantity of heat, length of path, temperature, area, and time. Solve problems involving the rate of radiation and emissivity of surfaces.
4 eat Transfer by Conduction Conduction is the process by which heat energy is transferred by adjacent molecular collisions inside a material. The medium itself does not move. Conduction Direction From hot to cold.
5 eat Transfer by Convection Convection is the process by which heat energy is transferred by the actual mass motion of a heated fluid. eated fluid rises and is then replaced by cooler fluid, producing convection currents. Convection Convection is significantly affected by geometry of heated surfaces. (wall, ceiling, floor)
6 eat Transfer by Radiation Radiation is the process by which heat energy is transferred by electromagnetic waves. Radiation Atomic Sun No medium is required!
7 Kinds of eat Transfer Consider the operation of a typical coffee maker: Think about how heat is transferred by: Conduction? Convection? Radiation?
8 eat Current The heat current is defined as the quantity of heat Q transferred per unit of time in the direction from high temperature to low temperature. Steam Ice Q ( J / s) Typical units are: J/s, cal/s, and Btu/h
9 Thermal Conductivity The thermal conductivity k of a material is a measure of its ability to conduct heat. = eat current (J/s) A = Surface area (m 2 ) t = Temperature difference L = Thickness of material t 1 t 2 t = t 2 -t 1 QL A t Q kat J k Units 0 L s m C
10 The SI Units for Conductivity ot Cold k QL A t For Copper: k = 385 J/s m C 0 Taken literally, this means that for a 1-m length In of SI copper units,, typically whose small cross measures section for is 1 m 2 length and L and whose area A end must points be converted differ to in temperature to meters and by 1 C 0, square heat meters, will respectively, be conducted before at the substitution rate of 1 J/s. into formulas.
11 Older Units for Conductivity t = 1 F 0 h A=1 ft 2 Q=1 Btu L = 1 in. Older units, still active, use common measurements for area in ft 2 time in hours, length in seconds,, and quantity of heat in Btu s. Glass k = 5.6 Btu in./ft 2 h F 0 Taken literally, this means that for a 1-in. thick plate of glass whose area is 1 ft 2 and whose sides differ in temperature by 1 F 0, heat will be conducted at the rate of 5.6 Btu/h.
12 Thermal Conductivities Examples of the two systems of units used for thermal conductivities of materials are given below: Material J/sm C o Btu in/ft h F 2 0 Copper: Concrete or Glass: Corkboard:
13 Examples of Thermal Conductivity Comparison of eat Currents for Similar Conditions: L = 1 cm (0.39 in.); A = 1 m 2 (10.8 ft 2 ); t = 100 C 0 Aluminum: Copper: Concrete or Glass: Corkboard: 2050 kj/s 4980 Btu/h 3850 kj/s 9360 Btu/h 8.00 kj/s 19.4 Btu/h kj/s 9.72 Btu/h
14 Q Example 1: A large glass window measures 2 m wide and 6 m high. The inside surface is at 20 0 C and the outside surface is at 12 0 C. ow many joules of heat pass through this window in one hour?? Assume L = 1.5 cm and that k = 0.8 J/s m C 0. A = (2 m)(6 m) = 12 m 2 Q ka t ; Q ka t L L (0.8 J/m s C )(12 m )(8 C )(3600 s) m Q = 18.4 MJ 20 0 C 12 0 C A = 1 h Q =? t = t 2 -t 1 = 8 C m
15 Example 2: The wall of a freezing plant is composed of 8 cm of corkboard and 12 cm of solid concrete. The inside surface is at C and the outside surface is C. What is the interface temperature t i? Note: A A Cork Concrete C t i 25 0 C 0 0 k1 ti ( 20 C) k 2 25 C - t i L L k1( ti 20 C) k2(25 C - ti) L L 1 2 A Steady Flow 8 cm 12 cm
16 Example 2 (Cont.): Finding the interface temperature for a composite wall. 0 0 k1( ti 20 C) k2(25 C - ti) L L 1 2 Rearranging factors gives: k k 1L 2 ( 0 0 t 20 C) (25 C - t ) 2L i i C t i 25 0 C A Steady Flow 8 cm 12 cm k k 0 1L 2 (0.04 W/m C )(0.12 m) 0 2L 1 (0.8 W/m C )(0.08 m) 0.075
17 Example 2 (Cont.): Simplifying, we obtain: 0 0 (0.075)( ti 20 C) (25 C - ti) 0.075t i C = 25 0 C - t i From which: tt i i = C Knowing the interface temperature t i allows us to determine the rate of heat flow per unit of area, /A C t i 25 0 C A Steady Flow 8 cm 12 cm The quantity /A is same for cork or concrete: Q ka t ; k t L A L
18 Example 2 (Cont.): Constant steady state flow. Over time /A is constant so different k s cause different t s C t i 25 0 C Cork: t = C - (-20 0 C) = 41.9 C 0 Concrete: t = 25 0 C C = 3.1 C 0 A Q ka t ; k t L A L Steady Flow 8 cm 12 cm Since /A is the same, let s s just choose concrete alone: 0 0 kt (0.8 W/mC )(3.1 C ) A A W/m L 0.12 m
19 Example 2 (Cont.): Constant steady state flow. A W/m Cork: t = C - (-20 0 C) = 41.9 C 0 Concrete: t = 25 0 C C = 3.1 C 0 Note that 20.7 Joules of heat per second pass through the composite wall. owever, the temperature interval between the faces of the cork is 13.5 times as large as for the concrete faces C t i 25 0 C A Steady Flow 8 cm 12 cm If If A = 10 m 2,, the heat flow in in 1 h would be? 745 kw
20 Radiation The rate of radiation R is the energy emitted per unit area per unit time (power per unit area). Rate of Radiation (W/m 2 ): R Q P A A R P A e T 4 Emissivity, e :: 0 > e > 1 Stefan-Boltzman Constant :: = 5.67 x W/m K 4
21 Example 3: A spherical surface 12 cm in radius is heated to C.. The emissivity is What power is radiated? A 4R 4 (0.12 m) 2 2 A = m 2 T = ; T = 900 K P e AT P (0.12)(5.67 x 10 W/mK )(0.181 m )(900 K) 4 Find Power Radiated A C Power Radiated from Surface: P = 808 W
22 Summary: eat Transfer Conduction: eat energy is transferred by adjacent molecular collisions inside a material. The medium itself does not move. Radiation is the process by which heat energy is transferred by electromagnetic waves. Convection is the process by which heat energy is transferred by the actual mass motion of a heated fluid.
23 Summary of Thermal Conductivity The thermal conductivity k of a material is a measure of its ability to conduct heat. = eat current (J/s) A = Surface area (m 2 ) t = Temperature difference L = Thickness of material t 1 t 2 t = t 2 -t 1 QL A t Q kat J k Units 0 L s m C
24 Summary of Radiation The rate of radiation R is the energy emitted per unit area per unit time (power per unit area). Rate of Radiation (W/m R 2 ): R Q P A A R P A e T 4 Emissivity, e :: 0 > e > 1 Stefan-Boltzman Constant :: = 5.67 x W/m K 4
25 Summary of Formulas QL A t Q kat J k Units 0 L s m C Q ka t ; k t L A L P e AT 4 R Q P P 4 R e T A A A
26 CONCLUSION: Chapter 18 Transfer of eat
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