7/28/2019 13.Radition 2 letcure notes

1/18

Heat Transfer

Lecture-11

RADIATION

7/28/2019 13.Radition 2 letcure notes

2/18

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.

7/28/2019 13.Radition 2 letcure notes

3/18

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

7/28/2019 13.Radition 2 letcure notes

4/18

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.

7/28/2019 13.Radition 2 letcure notes

5/18

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

7/28/2019 13.Radition 2 letcure notes

6/18

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?

7/28/2019 13.Radition 2 letcure notes

7/18

View factor between identical, parallel, directly opposed rectangles

7/28/2019 13.Radition 2 letcure notes

8/18

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?

7/28/2019 13.Radition 2 letcure notes

9/18

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

7/28/2019 13.Radition 2 letcure notes

10/18

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.

7/28/2019 13.Radition 2 letcure notes

11/18

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.

7/28/2019 13.Radition 2 letcure notes

12/18

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.

7/28/2019 13.Radition 2 letcure notes

13/18

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

7/28/2019 13.Radition 2 letcure notes

14/18

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,

7/28/2019 13.Radition 2 letcure notes

15/18

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.

7/28/2019 13.Radition 2 letcure notes

16/18

Q March 19

Odd id

Even

7/28/2019 13.Radition 2 letcure notes

17/18

7/28/2019 13.Radition 2 letcure notes

18/18