1.2 Heat transfer by radiation
Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) 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) and it suffers no attenuation in a vacuum. This is 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. Radiation is a volumetric phenomenon, and all solids, liquids, and gases emit, absorb, or transmit radiation to 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 Stefan–Boltzmann law as gives the maximum rate of radiation that can be emitted from a surface at an absolute temperature Ts (in K or R)
(3)
where ? = 5.67 * 10-8 W/m2 • K4 or 0.1714 * 10-8 Btu/h • ft2 • R4 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 (Fig. 3). The radiation emitted by all real surfaces is less than the radiation emitted by a blackbody at the same temperature,
and is expressed as
FIGURE 3 Blackbody radiation represents the maximum amount of radiation that can be emitted from a surface at a specified temperature
(4)
where is the emissivity of the surface. The property emissivity, whose value is in the range , is a measure of how closely a surface approximates a blackbody for which . 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. Like emissivity, its value is in the range Ablackbody absorbs the entire radiation incident on it. That is, a blackbody is a perfect absorber as it is a perfect emitter.
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 at a given temperature and wavelength are equal. In many practical applications, the surface temperature and the temperature of the source of incident radiation are of the same order of magnitude, and the average absorptivity of a surface is taken to be equal to its average emissivity. The rate at which a surface absorbs radiation is determined from (Fig. 4)
FIGURE 4 The absorption of radiation incident on an opaque surface of absorptivity .
(5)
where Q incident 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 not absorbed by the surface is reflected back. 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 .When a surface of emissivity and surface area As at an absolute temperature Ts is completely enclosed by a much larger (or black) surface at absolute
temperature Tsurr separated by a gas (such as air) that does not intervene with radiation, the net rate of radiation heat transfer between these two surfaces is given by (Fig. 5)
(6)
FIGURE 5 Radiation heat transfer between a surface and the surfaces surrounding it.
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. Radiation heat transfer to or from a surface surrounded by a gas such as air occurs parallel to conduction (or convection, if there is bulk gas motion) between
the surface and the gas. Thus the total heat transfer is determined by adding the contributions of both heat transfer mechanisms. For simplicity and convenience, this is often done by defining a combined heat transfer coefficient hcombined that includes the effects of both convection and radiation. Then the total heat transfer rate to or from a surface by convection and radiation
is expressed as
(7)
Example 2 Two infinite black plates at 800 and 300? exchange heat by radiation. Calculate the heat transfer per unit area. Given the Stefan-Boltzmann constant, with a value of 5.669 × 10 -8 W/ (m2.K4),
Solution. Equation (10) may be employed for this problem, so we find immediately
q/A = ? (T14 – T24)
= (5.669 10-8) (10734-5734)
= 69.03 kW/m2? ?[21,884 Btu/h•ft2]
Example 3 It is a common experience to feel “chilly” in winter and “warm” in summer in our homes even when the thermostat setting is kept the same. This is due to the so called “radiation effect” resulting from radiation heat exchange between our bodies and the surrounding surfaces of the walls and the ceiling. Consider a person standing in a room maintained at 22°C at all times. The inner surfaces of the walls, floors, and the ceiling of the house are observed to be at an average temperature of 10°C in winter and 25°C in summer. Determine the rate of radiation heat transfer between this person and the surrounding surfaces if the exposed surface area and the average outer surface temperature of the person are 1.4 m2 and 30°C, respectively
SOLUTION
The rates of radiation heat transfer between a person and the surrounding surfaces at specified temperatures are to be determined in summer and winter.
Assumptions
1 Steady operating conditions exist. 2 Heat transfer by convection is not considered. 3 The person is completely surrounded by the interior surfaces of the room. 4 The surrounding surfaces are at a uniform temperature.
Properties
The emissivity of a person is = 0.95 .
Analysis
The net rates of radiation heat transfer from the body to the surrounding walls, ceiling, and floor in winter and summer are
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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