Thermodynamics Heat Transfer

Transcription

1 Thermodynamics Heat Transfer Lana Sheridan De Anza College April 30, 2018

2 Last time heat transfer conduction Newton s law of cooling

3 Overview continue heat transfer mechanisms conduction over a distance convection radiation and Stephan s law

4 Heat Transfer When objects are in thermal contact, heat is transferred from the hotter object to the cooler object There are various mechanisms by which this happens: conduction convection radiation

5 Thermal Conduction over distance For Newton s law of cooling, we assumed we have a system at one temperature throughout, T, and an environment at another temperature T. What if we have a system that is in contact with two different environments (thermal reservoirs) at different temperatures? The system will conduct heat from one reservoir to the other. The system will not be the same temperature throughout.

6 Transfer Thermal Mechanisms Conduction in Thermal Processes over distance609 s your hand by means ame, the microscopic ositions. As the flame begin to vibrate with lide with their neighly, the amplitudes of m the flame increase ected. This increased he metal and of your The opposite faces are at different temperatures where T h T c. T h A ties of the substance estos in a flame indefough the asbestos. In uch as asbestos, cork, Energy transfer for T h T c Figure Energy transfer r conductors Rate of because heat transfer between surfaces: tals are good thermal ness Dx. that are relatively free power, P = Q T = ka arge distances. There- t x x T c through a conducting slab with a cross-sectional area A and a thick-

7 Thermal Conduction over distance Fourier s Law Imagining a subsection of the slab with an area A and an infinitesimal thickness dx: P = ka dt dx where k is the thermal conductivity and dt dx is called the temperature gradient. If k is large for a substance, the substance is a good conductor of heat. The units of k are W m 1 K 1.

8 P 5 kaa T h 2 T c b Thermal Conduction over distance The opposite ends of the rod are in thermal contact with Imagine a uniform energy rod of length reservoirs L, that different has been placed between two thermal reservoirs temperatures. for a long time. Assume for this bar k does not depend on temperature or position. L T h Energy transfer T c T h T c Insulation Figure Conduction of energy through The temperature at each point is constant in time and the a uniform, insulated rod of length L. gradient everywhere is dt dx = T h T c L the rate of energy transfer by conduction through the rod is

9 are in thermal contact with energy reservoirs at different temperatures. Thermal Conduction over distance L T h Energy transfer T c T h T c Insulation Then, Figure Conduction of energy through a uniform, insulated rod ( of length ) Th T L. c P = ka L the rate of energy transfer by conduction through the rod is P 5 kaa T h 2 T c b L

10 are in thermal contact with energy reservoirs at different temperatures. Thermal Conduction over distance L T h Energy transfer T c T h T c Insulation Then, Figure Conduction of energy through a uniform, insulated rod ( of length ) Th T L. c P = ka L the rate of energy transfer by conduction through the rod is What if there are many different bars for heat to be transferred through? P 5 kaa T h 2 T c b L

11 Thermal Conduction through multiple materials P 5 k For a compound slab containing s thermal conductivities k 1, k 2,..., the steady For situation state is (a): T h Rod 1 Rod 2 T c P = A(T h T c ) (L 1 /k 1 ) + (L 2 /k 2 ) P 5 a Rod 1 (See ex. 20.8) where T h and T c are the temperature stant) and the summation is over all s results For situation from a (b): consideration of two th b T h Rod 2 T c Figure (Quick Quiz 20.5) In which case is the rate of energy transfer larger? Q P uick = Quiz P P ( 2 You have two rods o formed from k1 A 1 different materials. T = + k ) 2A 2 (T different temperatures so h T that ener c ) L 1 L 2 can be connected in series as in Fig In which case is the rate of energy when the rods are in series. (b) The (c) The rate is the same in both cas

12 Thermal Conduction through multiple materials Compare: P = I = ( ) ka T L ( ) 1 V R On the LHS we have transfer rates, on the RHS differences that propel a transfer. L You can think of ka as a kind of resistance. k is a conductivity, like σ (electrical conductivity). Recall, R = ρl A = L σa.

13 Thermal Conduction through multiple materials For multiple thermal transfer slabs in series: P = 1 i (L i/(k i A)) T For multiple thermal transfer slabs in parallel: ( ) k i A i P = T L i i Now for convenient comparison, let r i = L i k i A i. Then r i is a thermal resistance, for the ith slab.

14 Thermal Conduction through multiple materials For multiple resistors in series: ( ) 1 I = i R V i For multiple thermal transfer slabs in series: ( ) 1 P = i r T i For multiple resistors in parallel: ( ) 1 I = V For multiple thermal transfer slabs in parallel: ( ) 1 P = T i i R i r i

15 Thermal Conduction and Ohm s Law Fourier s work on thermal conductivity inspired Ohm s model of electrical conductivity and resistance!

16 L 1 /k 1 L 2 /k 2 Thermal Conductivity Question Eq to apply to any number n of materials making up The figure P cond shows A(T H T the face C ) and. interface temperatures (18-37) of a composite slab consisting (L/k) of four materials, of identical gn in the thicknesses, denominator through tells which us to the add heat the transfer values is of steady. L/k for Rank all the materials according to their thermal conductivities, greatest first. T 7 the face and 25 C 15 C 10 C 5.0 C 10 C res of a comting of four a b c d al thicknesses, through which the heat transfer is steady. Rank the matheir thermal conductivities, greatest first. (A) a, b, c, d (B) (b and d), a, c (C) c, a, (b and d) the flame (D) (b, of c, a candle d), aor a match, you are watching thermal sported upward by convection. Such energy transfer occurs as air or water, comes in contact with an object whose tem- 1 Halliday, Resnick, Walker, page 495.

17 L 1 /k 1 L 2 /k 2 Thermal Conductivity Question Eq to apply to any number n of materials making up The figure P cond shows A(T H T the face C ) and. interface temperatures (18-37) of a composite slab consisting (L/k) of four materials, of identical gn in the thicknesses, denominator through tells which us to the add heat the transfer values is of steady. L/k for Rank all the materials according to their thermal conductivities, greatest first. T 7 the face and 25 C 15 C 10 C 5.0 C 10 C res of a comting of four a b c d al thicknesses, through which the heat transfer is steady. Rank the matheir thermal conductivities, greatest first. (A) a, b, c, d (B) (b and d), a, c (C) c, a, (b and d) the flame (D) (b, of c, a candle d), aor a match, you are watching thermal sported upward by convection. Such energy transfer occurs as air or water, comes in contact with an object whose tem- 1 Halliday, Resnick, Walker, page 495.

18 Thermal Conduction and Insulation Engineers generally prefer to quote R-values for insulation, rather than using thermal conductivity, k. For a particular material: R = L k This is its length-resistivity to heat transfer. A high value of R indicates a good insulator. The units used are ft 2 F h / Btu. (h is hours, Btu is British thermal units, 1 Btu = 1.06 kj)

19 Convection In liquids and gases convection is usually a larger contributor to heat transfer. In convection, the fluid itself circulates distributing hot (fast moving) molecules throughout the fluid. When there is gravity present, convection current circulations can occur.

20 Convection Hot fluid expands, and since it is less dense, it will have a greater buoyant force and rise. Cooler, denser fluid will tend to sink.

21 Convection Heat loss by convection from a person s hand: This type of convection is called free convection.

22 Forced Convection External energy can also drive convection by means of a pump or fan. This is used in convection ovens to evenly heat food. It is also used in cooling systems to keep cool air flowing over hot components.

23 Summary heat transfer mechanisms: conduction, convection, radiation Collected Homework due Monday, May 7. Homework Serway & Jewett: Ch 20, onward from page 615. OQs: 11; CQs: 1, 9; Probs: 43, (45, 47,) 51, 55