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TRANSCRIPT
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Heat Transfer
Lecture-11
RADIATION
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THE VIEW FACTOR or SHAPE FACTOR (F)
The concept of radiation shape factor is useful in the analysis of radiation
heat exchange between two surfaces.
Radiation heat transfer between surfaces depends on the orientation of thesurfaces relative to each other as well as their radiation properties andtemperatures, as illustrated in Figure 1.
For example, a camper will make the most use of a campfire on a cold nightby standing as close to the fire as possible and by blocking as much of theradiation coming from the fire by turning her front to the fire instead of herside.
Likewise, a person will maximize the amount of solar radiation incident onhim and take a sunbath by lying down on his back instead of standing up on
his feet.
FIGURE 1 Radiation heat exchange
between surfaces depends on the
orientation of the surfaces relative to
each other, and this dependence on
orientation is accounted for by the
view factor.
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To account for the effects of orientation on radiation heat transfer betweentwo surfaces, we define a new parameter called the view factor, which is apurely geometric quantity and is independent of the surface properties and
temperature. It is also called the shape factor, configuration factor, andangle factor.
It is the fraction of the radiation energy that is emitted from one surface andintercepted by the other surface directly without intervening reflections.
It is represented by the symbol Fmn which means the shape factor from asurface Am to the other surface An.
Consider two black surfaces A1 and A2 at uniform temperature T1 and T2respectively between which there is a net interchange of thermal radiation.
The energy leaving the surface 1 and arriving at surface 2, is Eb1 A1 F12
and that between 2 and 1 is Eb2 A2 F21
The net energy exchange between A1 and A2 is
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FIGURE 2 The view factor from a surface to itself
is zero forplane orconvexsurfaces and nonzeroforconcave surfaces.
Consider a case of enclosure in which one surface is
exchanging radiation with all other Surfaces in the enclosure
including itself , if it happen to be a concave surface. This is due
to the fact that the it can view another part of it.
On contrary, a convex or flat surface cannot see any part of it.
The shape factor of a convex surface with its enclosure is
always unity as all the heat radiated by a convex surface will be
intercepted by its enclosure and not vice versa.
If n surfaces form an enclosure, than the energy radiated fromone surface is always intercepted by the other (n-1) surfaces,
and the surface it self if it is concave one.
F11 + F12 + F13F1n = 1
F21 + F22 + F23F2n = 1
Fn1 + Fn2 + Fn3Fnn = 1
F11 , F22 , Fnn are the shape factor with respect to
itself, shape factor with respect to itself is the faction of
incident energy emitted by the surface that gets
interpreted by itself.
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When the surface is concave it has shape factor with respect to itself but for plane
convex surfaces, shape factor with respect to itself is zero.
Therefore Fnn = 0 for convex or flat surface
and Fnn = 0 for concave surface
The reciprocity relationship
This relationship can be applied to any two surfaces
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Problem
Two parallel black plates 1 by 2.0 m are spaced 2 m apart, plate 1 is
maintained at 1273 K (1000 C) and plate 2 is maintained at 773 K (500
C). What is the net radiant heat exchange between the plates?
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View factor between identical, parallel, directly opposed rectangles
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Q March 14
Two parallel gray plates 1 by 2.0 m are spaced 1 m
apart, plate 1 (1=0.8) is maintained at 1273 K (1000 C)
and plate 2 (2=0.7) is maintained at 773 K (500 C).
Determine the net radiant heat exchange between theplates?
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Electrical network analogy for thermal radiation
systems
The electrical network analogy is an alternate approach for analyzing thermal
radiation between gray or black surfaces in which case a radiation problem is
transferred to an equivalent electrical problem. The terms used in the electrical
analogy approach are irradiation and radiosity. This method gives a simpler formula
for estimating the rate of flow by comparison with Ohms law.
equivalent potential difference between surfacesQ = equivalent thermal resistance of the system
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Radiosity-Irradiation Approach:
Radiosity (J) : It is the total radiation leaving a surface (i.e. the total amount of energy
leaving a surface) per unit time per unit area. It is the sum of energy emitted andenergy reflected by the surface.
Irradiation (G) It is the total amount of radiatioan incident upon a surface per unit timeper unit area.
Let us consider an elementary gray surface A1 at T having emissivity e1.
Let Eb be the eniissive power of the surface.
Let G be the total radiation incident upon the surface.
Let J be the radiosity which is the sum of the energy emitted and energy reflectedwhen no energy is transmitted.
Then, the net energy leaving a surface is the difference between the radiosity and theirradiation.
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Hence, the two surfaces which exchange heat may each be considered as having asurface resistance of (1-1/eA) and a shape resistance of 1/A1 F12 between theirradiosity potential.
To construct a network for the radiation heat transfer between the surfaces, we onlyneed to connect a surface resistance (1-1/eA) to each surface and a shaperesistance 1/AmFmn) between the radiosity potentials.
For example, in case of two surfaces which exchange heat with each other, theradiation network is as shown in Fig. 4 In this case, the net heat transfer/exchangewould be the ratio of the overall potential difference to the sum of resistances.
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Radiation Heat Transfer in Three-Surface Enclosures
We now consider an enclosure consisting of three opaque, diffuse, gray surfaces, as shown inFigure 1226. Surfaces 1, 2, and 3 have surface areas A1, A2, and A3; emissivities e1,e2, and e3; and uniform temperatures T1, T2, and T3, respectively.
The radiation network of this geometry is constructed by following the standard procedure: draw asurface resistance associated with each of the three surfaces and connect these surfaceresistances with space resistances, as shown in the figure.
Relations for the surface and space resistances are known. The three endpoint potentials Eb1,Eb2, and Eb3 are considered known, since the surface temperatures are specified.
Then all we need to find are the radiosities J1, J2, and J3. The three equations for thedetermination of these three unknowns are obtained from the requirement that the algebraic sumof the currents (net radiation heat transfer) at each node must equal zero. That is,
Once the radiosities J1, J2, and J3 are available, the net rate of radiation heat transfers at eachsurface can be determined.
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Schematic of a three-surface enclosure and the radiation network associated with it.
Ref: JP.Holman, 8.6: Heat Exchange Between NonblackbodiesExample 8-6 & 8-7
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Radiation Effect on Temperature Measurements
A temperature measuring device indicates the temperature of its sensor, which issupposed to be, but is not necessarily, the temperature of the medium that the sensor
is in.
When a thermometer (or any other temperature measuring device such as athermocouple) is placed in a medium, heat transfer takes place between the sensorof the thermometer and the medium by convection until the sensor reaches thetemperature of the medium.
But when the sensor is surrounded by surfaces that are at a different temperaturethan the fluid, radiation exchange will take place between the sensor and thesurrounding surfaces.
When the heat transfers by convection and radiation balance each other, the sensorwill indicate a temperature that falls between the fluid and surface temperatures.
Below we develop a procedure to account for the radiation effect and to determinethe actual fluid temperature.
Consider a thermometer that is used to measure the temperature of a fluid flowingthrough a large channel whose walls are at a lower temperature than the fluid (Fig.1). Equilibrium will be established and the reading of the thermometer will stabilizewhen heat gain by convection, as measured by the sensor, equals heat loss byradiation (or vice versa). That is, on a unit area basis,
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where
Tf = actual temperature of the fluid, K
Tth = temperature value measured by the thermometer, K
Tw = temperature of the surrounding surfaces, K
h = convection heat transfer coefficient, W/m2 K
e = emissivity of the sensor of the thermometer
The last term in Eq. is due to the radiation effectand represents the radiation correction. Note
that the radiation correction term is most significant when the convection heat transfer
coefficient is small and the emissivity of the surface of the sensor is large.
Therefore, the sensor should be coated with a material of high reflectivity (low emissivity) to
reduce the radiation effect.
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Q March 19
Odd id
Even
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