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Heat and Mass Transfer Mechanical Engineering

Ajai S | Lecturer/MECH

4.1

UNITIV

Thermal radiation is the process by which the surface of an object radiates its thermal energy in the form of electromagnetic waves. An example of thermal radiation is the infrared radiation emitted by a common household radiator or electric heater. A person near a raging bonfire will feel the radiated heat of the fire, even if the surrounding air is very cold. Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation. Solar radiation heats the earth during the day, while at night the earth re-radiates some heat back into space.

Figure 1: Hot metalwork from a blacksmith & a lady near a fire.

The yellow-orange glow is the visible part of the thermal radiation emitted due to the high temperature. Everything else in the picture is glowing with thermal radiation as well, but less brightly and at longer wavelengths that the human eye cannot see. A far-infrared camera will show this radiation.



4.2

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object. The long wavelength limit is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length, although in principle the spectrum is infinite and continuous.

Figure 2: Electromagnetic-Spectrum



4.3

Stefan-Boltzman Law

The Sefan-Boltzman law relates the total amount of radiation emitted by an object to its temperature:

E=T4

where: E = total amount of radiation emitted by an object per square meter (Watts m-2) is a constant called the Stefan-Boltzman constant = 5.67 x 10-8 Watts m-2 K-4 T is the temperature of the object in K Consider the earth and sun: Sun: T = 6000 K so E = 5.67 x 10-8 Watts m-2 K-4 (6000 K)4 = 7.3 x 107 Watts m-2

Planck's law is written as



4.4

Weins Law

Most objects emit radiation at many wavelengths However, there is one wavelength max where an object emits the largest

amount of radiation

T max = 2897 mm (T is the temperature of the object in K)

Figure3: Weins Law



4.5

Figure4: Radiation curves for the Sun and Earth

Figure5: Radiation curve for the Sun - a closer look



4.6

Radiative Equilibrium

If the temperature of an object is constant with time, the object is in radiative equilibrium at its radiative equilibrium temperature (Te)

Figure6: Radiative Equilibrium

Radiative Equilibrium for the Earth

Energy gained through absorption of short wave radiation is equal to the emitted long wave radiation

Figure7



4.7

Emissivity

The radiation from real sources is always less than that from a blackbody. Emissivity () is a measure of how a real source compares with a blackbody. It is defined as the ratio of the radiant power emitted per area to the radiant power emitted by a blackbody per area.

Kirchoff's Law

Kirchoffs Law states that the emissivity of a surface is equal to its absorptance, where the absorptance () of a surface is the ratio of the radiant power absorbed to the radiant power incident on the surface.

Emissivity = absorptivity at each wavelength for all materials. (l)=(l)

Therefore, a good absorber is also a good emitter of radiation. So snow also absorbs very little visible light, but a lot of infrared light That is why we can see coming down on a dimly lighted ski-slope

Black body is an idealized object that absorbs all electromagnetic radiation that falls on it. No electromagnetic radiation passes through it and none is reflected. Because no light (visible electromagnetic radiation) is reflected or transmitted, the object appears black when it is cold. However, a black body emits a temperature-dependent spectrum of light. This thermal radiation from a black body is termed black-body radiation.

E=T4



4.8

Gray Body Radiation Heat Transfer

Bodies that emit less thermal radiation than a blackbody have surface emissivities less than 1. If the surface emissivity is independent of wavelength, then the body is called a "gray" body, in that no particular wavelength (or color) is favored.

The net heat transfer from a small gray body at absolute temperature T with surface emissivity to a much larger enclosing gray (or black) body at absolute temperature Te is given by,

Radiation View Factors

The above equations for blackbodies and graybodies assumed that the small body could see only the large enclosing body and nothing else. Hence, all radiation leaving the small body would reach the large body. For the case where two objects can see more than just each other, then one must introduce a view factor F and the heat transfer calculations become significantly more involved.

The view factor F12 is used to parameterize the fraction of thermal power leaving object 1 and reaching object 2. Specifically, this quantity is equal to,

Likewise, the fraction of thermal power leaving object 2 and reaching object 1 is given by,

The case of two blackbodies in thermal equilibrium can be used to derive the



4.9

following reciprocity relationship for view factors,

Thus, once one knows F12, F21 can be calculated immediately.

Radiation view factors can be analytically derived for simple geometries and are tabulated in several references on heat transfer (e.g. Holman, 1986). They range from zero (e.g. two small bodies spaced very far apart) to 1 (e.g. one body is enclosed by the other).

Radiation Heat Transfer Between Black Surfaces of Arbitrary Geometry

In general, for any two objects in space, a given object 1 radiates to object 2, and to other places as well, as shown in Figure a.

Figure a: Radiation between two bodies

Figure b: Radiation between two arbitrary surfaces



4.10

We want a general expression for energy interchange between two surfaces at different temperatures. This is given by the radiation shape factor or view factor,

. For the situation in Figure b,

= fraction of energy leaving 1 which reaches 2

= fraction of energy leaving 2 which reaches 1

, are functions of geometry only

For body 1, we know that is the emissive power of a black body, so the energy

leaving body 1 is . The energy leaving body 1 and arriving (and being

absorbed) at body 2 is . The energy leaving body 2 and being absorbed

at body 1 is . The net energy interchange from body 1 to body 2 is

(i)

Suppose both surfaces are at the same temperature so there is no net heat exchange. If so,

but also . Thus



4.11

Equation (i) is the shape factor reciprocity relation. The net heat exchange between the two surfaces is

Example: Concentric cylinders or concentric spheres

Figure c: Radiation heat transfer for concentric cylinders or spheres

The net heat transfer from surface 1 to surface 2 of Figure c is

We know that , i.e., that all of the energy emitted by 1 gets to 2. Thus

This can be used to find the net heat transfer from 2 to 1.

View factors for other configurations can be found analytically or numerically. Shape factors are given in textbooks and reports (they are tabulated somewhat like Laplace transforms), and examples of the analytical forms and numerical values of shape factors for some basic engineering configurations are given in Figures d through g, taken from the book by Incropera and DeWitt.



4.12

Figure d: Total emittances for different surfaces [from: A Heat Transfer Textbook, J. Lienhard]



4.13

Figure e: View Factors for Three-Dimensional Geometries [from: Fundamentals of Heat Transfer, F.P. Incropera and D.P. DeWitt, John Wiley and Sons]



4.14

Figure f: View factor for aligned parallel rectangles [from: Fundamentals of Heat Transfer, F.P. Incropera and D.P. DeWitt, John Wiley and Sons]

Figure g: View factor for coaxial parallel disks [from: Fundamentals of Heat Transfer, F.P. Incropera and D.P. DeWitt, John Wiley and Sons]



4.15

Principles of radiation protection

Radiation protection can be divided into occupational radiation protection, which is the protection of workers; medical radiation protection, which is the protection of patients; and public radiation protection, which is protection of individual members of the public, and of the population as a whole. The types of exposure, as well as government regulations and legal exposure limits are different for each of these groups, so they must be considered separately.

There are three factors that control the amount, or dose, of radiation received from a source. Radiation exposure can be managed by a combination of these factors:

1. Time: Reducing the time of an exposure reduces the effective dose proportionally. An example of reducing radiation doses by reducing the time of exposures might be improving operator training to reduce the time they take to handle a source.

2. Distance: Increasing distance reduces dose due to the inverse square law. Distance can be as simple as handling a source with forceps rather than fingers.

3. Shielding: Adding shielding can also reduce radiation doses. The radiation getting through falls exponentially with the thickness of the shield. In x-ray facilities, the plaster on the rooms with the x-ray generator contains barium sulfate and the operators stay behind a leaded glass screen and wear lead aprons. Almost any material can act as a shield from gamma or x-rays if used in sufficient amounts.

Practical radiation protection tends to be a job of juggling the three factors to identify the most cost effective solution.

Shielding design

Shielding reduces the intensity of radiation exponentially depending on the thickness.

This means when added thicknesses are used, the shielding multiplies. For example, a practical shield in a fallout shelter is ten halving-thicknesses of packed



4.16

dirt, which is 90 cm (3 ft) of dirt. This reduces gamma rays by a factor of 1/1,024, which is 1/2 multiplied by itself ten times. Halving thicknesses of some materials, that reduce gamma ray intensity by 50% (1/2.

Material Halving Thickness, inches

Halving Thickness, cm

Density, g/cm

Halving Weight, g/cm

lead 0.4 1.0 11.3 12 concrete 2.4 6.1 3.33 20 steel 0.99 2.5 7.86 20 packed soil 3.6 9.1 1.99 18 water 7.2 18 1.00 18 lumber or other wood

11 29 0.56 16

depleted uranium 0.08 0.2 19.1 3.9 air 6000 15000 0.0012 18

Column Halving Weight in the chart above indicates mass of material, required to cut radiation by 50%, in grams per square centimetre of protected area.

The effectiveness of a shielding material in general increases with its density.

Gas Radiation

Radiation in absorbing-emitting media When a medium is transparent to radiation, radiation propagating through such a

media remains unchanged

However gases such as CO, NO, CO2, SO2, H2O and various hydrocarbons

absorb and emit radiation over certain wavelength regions called absorption bands

We will discuss a very simple analysis of radiation exchange in an absorbing and

emitting medium, exchange between a body of hot gas and its black enclosure.



4.17

Beers Law If Io is the intensity of radiation at the source and I is the observed intensity after a given path, then optical depth is defined by the following equation:

Figure8 Characterization of Participating Media

Figure9: Radiation heat transfer in gas turbine combustors

References:

1://apollo.lsc.vsc.edu/classes/met130/notes/chapter2/ebal2.html. 2://www.efunda.com/formulae/heat_transfer/radiation/blackbody.cfm 3://en.wikipedia.org/wiki/Black_body 4: web.iitd.ac.in/~prabal/gas-radiation.pdf 5: Heat and Mass Transfer - A Practical Approach by Yugnus-A-Cengel.

Radiation Heat Transfer Between Black Surfaces of Arbitrary GeometryExample: Concentric cylinders or concentric spheresPrinciples of radiation protectionShielding design

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