Department of Chemical Engineering

National Institute of Technology, Warangal

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Academic Year: 2014-15, I Semester, II Biotech

Course : CH235 Fluid Mechanics and Heat Transfer

Instructor : Dr. V. Ramsagar

Radiation Radiation, which may be considered to be energy streaming through space at the speed of light, may originate in various ways.

Thermal Radiation: All substances at temperatures above absolute zero emit radiation that is independent of external agencies.

Joseph Stefan (1879)– total radiation emission per unit time & area over all wavelengths and in all directions:

s=Stefan-Boltzmann constant =5.67 x10-8 W/m2K4

24 mW TEb s

Radiation moves through space in straight lines, or beams, and only substances in sight of a radiating body can intercept radiation from that body.

The fraction of the radiation falling on a body that is reflected is called the reflectivity ρ. The fraction that is absorbed is called the absorptivity α. The fraction that is transmitted is called the transmissivity τ.

The sum of these fractions must be unity, or α+ρ+τ =1

Radiation as such is not heat.

A body that absorbs all incidient radiation is called a blackbody.Topics to be discussed: emission of radiation, absorption by opaque solids, radiation between surfaces, radiation to and from semitransparent materials

The radiation emitted by any given mass of material is independent of that being emitted by other material in sight of, or in contact with, the mass.

The net energy gained or lost by a body is the difference between the energy emitted by the body and that absorbed by it from the radiation reaching it from other bodies.

When bodies at different temperatures are placed in sight of one another inside an enclosure, the hotter bodies lose energy by emission of radiation faster than they receive energy by absorption of radiation from the cooler bodies, and the temperatures of the hotter bodies decrease.

WAVELENGTH OF RADIATION. Known electromagnetic radiations cover an enormous range of wavelengths, from the short cosmic rays having wavelengths of about 10-11 cm to longwave broadcasting waves having lengths of 1000 m or more.

Radiation of a single wavelength is called monochromatic.

Radiation of any wavelength from zero to infinity is, in principle, convertible into heat on absorption by matter.

the portion of the electromagnetic spectrum that is of importance inheat flow lies in the wavelength range between 0.5 and 50 µm. Visible light covers a wavelength range of about 0.38 to 0.78 µm.

The higher the temperature of the radiating body, the shorter the predominant wavelength of the thermal radiation emitted by it.

Monatomic and diatomic gases such as oxygen, argon, and nitrogen radiate weakly, even at high temperatures. Under industrial conditions, these gases neither emit nor absorb appreciable amounts of radiation.

Polyatomic gases, including water vapor, carbon dioxide, ammonia, sulfur dioxide, and hydrocarbons emit and absorb radiation appreciably at furnace temperatures but only in certain bands of wavelength.

Solids and liquids emit radiation over the entire spectrum.

EMISSIVE POWER. The monochromatic energy emitted by a radiating surface depends on the temperature of the surface and on the wavelength of the radiation.

The unit chosen for measuring the monochromatic radiation is based on the fact that, from a small area of a radiating surface, the energy emitted is "broadcast" in all directions through any hemisphere centered on the radiation area.

The monochromatic radiation emitted in this manner from unit area in unit time divided by the wavelength is called themonochromatic radiating power Wλ.

the total radiating power W:

EMISSIVITY. Ɛ

MONOCHROMATIC EMISSIVITY. Ɛλ

If the monochromatic emissivity of a body is the same for all wavelengths, the body is called a gray body.

EMISSIVITIES OF SOLIDS. Emissivity usually increases with temperature. Emissivities of polished metals are low, in the range 0.03 to 0.08.

PRACTICAL SOURCE OF BLACKBODY RADIATION. No actual substance is a black body, although some materials, such as certain grades of carbon black, do approach blackness.

An experimental equivalent of a black body is an isothermal enclosure containing a small peephole.

The overall absorptivity of the interior surface is unity.

LAWS OF BLACKBODY RADIATION. A basic relationship for blackbody radiation is the Stefan-Boltzmann law.Wb α T4

Planck's law: The distribution of energy in the spectrum of a blackbody

Eq can be written using the Cl and C2 constants

the maximum monochromatic radiating power is attained at a definite wavelength, denoted by λmax

Wien's displacement law states that λmax is inversely proportional to the absolute temperature

ABSORPTION OF RADIATION BY OPAQUE SOLIDSMost solids (other than glasses, certain plastics, quartz, and some minerals) absorb radiation of all wavelengths so readily that, except in thin sheets, the transmissivity is zero.

absorption of radiation by an opaque solid is a surface phenomenon, not a volume phenomenon.

The heat generated by the absorption can flow into or through the mass of an opaque solid only by conduction.

REFLECTIVITY AND ABSORPTIVITY OF OPAQUE SOLIDS.sum of the reflectivity and the absorptivity is unity.

The reflectivity of an opaque solid depends on the temperatureand character of the surface, the material of which the surface is made, the wavelength of the incident radiation, and the angle of incidence.

Types of Reflections: specular and diffuse

Specular: characteristic of smooth surfaces, the reflectedbeam makes a definite angle with the surface, and the angle of incidence equals the angle of reflection.

reflectivity from these surfaces approaches unity

Diffuse Reflection: from rough surfaces or from dull, or matte, surfaces.

reflect diffusely in all directions, there is no definite angle of reflection, and the absorptivity can approach unity.

Most industrial surfaces of interest to the chemical engineer give diffuse reflection important simplifying assumption can usually be made that reflectivity and absorptivity are independent of angle of incidence.

This assumption is equivalent to the cosine law for a perfectly diffusing surface the intensity of the radiation leaving the surface is independent of the angle from which the surface is viewed.

The reflectivity may vary with the wavelength of the incident radiation.

The absorptivity of the entire beam is then a weighted average of the monochromatic absorptivities and depends upon the entire spectrum of the incident radiation.

The absorptivity of a gray body, like the emissivity, is the same for allwavelengths.

If the surface of the gray body gives diffuse radiation or reflection, its monochromatic absorptivity is also independent of the angle of incidence of the radiant beam.

The total absorptivity equals the monochromatic absorptivity and is also independent of the angle of incidence.

KIRCHHOFF'S LAW

At temperature equilibrium, the ratio of the total radiating power of any body to its absorptivity depends only upon the temperature of the body.

Ex: any two bodies in temperature equilibrium with common surroundings.

when any body is at temperature equilibrium with its surroundings, its emissivity and absorptivity are equal.

The radiant heat flux (q) is incident onto the body and allowed to come into temperature equilibrium.

E is the emissive power of the body, α is absorptivity of the of the body at equilibrium temperature, and A is the area of the body.

EA = αqA

Eb = q

E/Eb= α

except for blackbodies or gray bodies, absorptivity and emissivity are not equal if the body is not in thermal equilibrium with its surroundings.

The absorptivity and emissivity, monochromatic or total, of a blackbody are both unity.

RADIATION BETWEEN SURFACES

Total radiation for a unit area of an opaque body of area A1 emissivity ε1 and absolute temperature T1

(1)Most surfaces emit radiation also receive radiation from other surfaces at different temperatures.

Some of this incoming radiation is absorbed and must be allowed for in determining the total flux of radiant energy.

example, a steam line in a room is surrounded by the walls, floor, and ceiling of the room, all of which are radiating to the pipe, and although the pipe loses more energy than it absorbs from its surroundings, the net loss by radiation is less than that calculated from Eq. 1.

In Radiation HT our objective is to obtain a controlled rate of net heat exchange between one or more hot surfaces, called sources, and one or more cold surfaces, called sinks.

Examples: radiation between two surfaces is where each surface can see only the other

Parallel Planes (block surface)

The net loss of energy per nnit area by the first plane and the net gain by the second is

Engineering problems:One or both of the surfaces of interest see other surfaces.an element of surface in a concave area sees a portion of its own surface. No actual surface is exactly black, and the emissivities of the surfaces must often be considered.

ANGLE OF VISION

2π sr (steradians) is the maximum angle of vision that can be subtended at any area element by a plane surface in sight of the element.

The total radiating power of an area element is defined to take this fact into account.

Muffle furnace: the radiation from the hot floor, or source, is intercepted partly by the row of tubes across the top of the furnace, which form the sink, and partly by the refractory walls and the refractory ceiling behind the tubes. The refractory in such assemblies is assumed to absorb and emit energy at the same rate, so the net energy effect at the refractory is zero.

rate of energy reception by element dA1 of radiation originating at dA2

The net rate of transfer dq12 between the two area elements

QUANTITATIVE CALCULATION OF RADIATION BETWEEN BLACK SURFACES

The factor F is called the view factor or angle factor; it depends upon the geometry of the two surfaces, their spatial relationship with each other, and the surface chosen for A.

Factor F12 may be regarded as the fraction of the radiation leaving area A1 that is intercepted by area A2•

If surface A1 can see only surface A2, the view factor F12 is unity.

If surface A1 sees a number of other surfaces and if its entire hemispherical angle of vision is filled by these surfaces.

The factor F11 covers the portion of the angle of vision subtended by other portions of body A1.

If the surface of A1 cannot see any portion of itse lf, F11 is zero.

Example: consider a small black body of area A2 having no cavities and surrounded by a large black surface of area A1.

The factor F21 , is unity.

View Factors Relations: Radiation analysis on an enclosure consisting of N surfaces requires the evaluation of N 2 view factors.

The reciprocity relation

The summation rule

The superposition rulethe view factor from a surface i to a surface j is equal to the sum of the view factors from surface i to the parts of surface j

Note that the reverse of this is not true.

F1 → (2, 3) = F1 → 2 + F1 → 3

F1 → 3 = F1 → (2, 3) - F1 → 2

𝐹 (2,3¿→ 1=𝐴2𝐹 2 →1+𝐴3 𝐹 3→ 1

𝐴2+𝐴3

The symmetry rule

The symmetry rule can be expressed as two (or more) surfaces that possess symmetry about a third surface will have identical view factors from that surface

N = 2 and this enclosure involves N 2 = 22 = 4 view factors, which are F11, F12, F21, and F22. We have to determine F11 = 0, since no radiation leaving surface 1 strikes itself F12 = 1, since all radiation leaving surface 1 strikes surface 2

A1 F12 = A2 F21

Determine the view factors from the base of the pyramid shown in Figure to each of its four side surfaces. The base of the pyramid is a square, and its side surfaces are isosceles triangles.

the symmetry rule,

F12 = F13 = F14 = F15

∑𝑗=1

5

𝐹1 𝑗=¿ 𝐹11+𝐹12+𝐹13+𝐹 14+𝐹 15=1¿

the summation rule

F11 = 0

Determine the view factor from any one side to any other side of the infinitely long triangular duct whose cross section is given in Figure

N 2 = 32 = 9

12 𝑁 (𝑁−1 )=1

2 ×3 (3− 1 )=3

F11 = F22 = F33 = 0

𝐹 11+𝐹 12+𝐹 13=1

 

 

 

reciprocity relations A1F12 = A2F21, A1F13 = A3F31, and A2F23 = A3F32

 

 

𝐴1𝐹 12+ 𝐴2 𝐹 23=𝐴2

𝐴1𝐹 13+ 𝐴2𝐹 23=𝐴3

3 Equations and 3 unknowns

𝐹 12=𝐴1+𝐴2− 𝐴3

2 𝐴1=𝐿1+𝐿2− 𝐿3

2𝐿1

𝐹 13=𝐴1+𝐴3 −𝐴2

2 𝐴1=𝐿1+𝐿3 −𝐿2

2𝐿1

𝐹 23=𝐴2+ 𝐴3−𝐴1

2 𝐴2=𝐿2+𝐿3 −𝐿1

2𝐿2

NONBLACK SURFKCESradiation between nonblack surfaces, in the general case where absorptivity and emissivity are unequal and both depend upon wavelength and angle of incidence

example is a small body that is not black surrounded by a blacksurface. Let the areas of the enclosed and surrounding surfaces be A1 and A2, respectively, and let their temperatures be T1 and T2

Areas A1 and A2

A2 is black bodyA1 is non black

The radiation from surface A2 falling on surface A1 is σA2F21T2

4

The net energy loss by surface A1 is

In general, for gray surfaces

For Black Surfaces For Gray Surfaces

the overall interchange factors are functions of Ɛ1 and Ɛ2

Two large parallel planes: In simple cases the factor F can be calculated directly.

Consider two Iarge gray parallel planes at absolute temperatures T1 and T2 , Ɛ1 and Ɛ2

the total amount of radiation originating at surface 1 that is absorbed by surface 2

Some of the energy originating at surface 2, as shown in Fig., is reflectedby surface 1 and returns to surface 2, where part of it is absorbed.

Example 14.1. A chamber for heat curing large aluminum sheets, lacquered black on both sides, operates by passing the sheets vertically between two steel plates 150 mm apart. One of the plates is at 300°C and the other, exposed to the atmosphere, is at 25°C. (a) What is the temperature of the lacquered sheet? (b)What is the heat transferred between the walls

when equilibrium has been reached? Neglect convection effects.

Emissivity of steel is 0.56; emissivity of lacquered sheets is 1.0.

Determine the net heat transfer by radiation between two surfaces A and B, expressed as watts per square meter of area B, if the temperatures of A and B are 500 and 200°C respectively, and the emissivity's of A and B are 0.90 and 0.25, respectively. Both surfaces are gray. (a)Surfaces A and B are infinite parallel planes 3 m apart. (b)Surface A is a spherical shell 3 m in diameter, and surface

B is a similar shell concentric with A and 0.3 m in diameter.