Math cad effective radiation heat transfer coefficient.xmcd

MathCAD - Effective Radiation Heat Transfer Coefficient.xmcd

Effective Radiation Heat Transfer Coefficientby Julio C. Banks, PE

Reference"Principles of Heat Transfer" 7th Ed. Frank Kreith, et. alISBN-13: 978-0-495-66770-4, or ISBN-10: 0-495-66770-6. Pp. 21-23.

The intent of this paper is to simplify the given in order to have the actual, nor apparent,order. It should be noted that all radiative heat transfer calculations must utilize theabsolute temperatures, oR, or K.

Note: The author has found it to be practical to distinguish Q, and q as "Total heattransfer flow" and "Heat transfer flux", respectively. This clarification is very importantin the modeling of convection with advection, Some authors fail to name the transferof thermal energy via a moving (working) fluid as qa wCp ΔTc=

FIGURE 1.11 Schematic diagram of radiation between body 1 and enclosure 2.

qrQr

A= hr T1 T2 = T1 T2 1( )

Were hr ε1 σT1

4T2

4 T1 T2 = 2( )

σ 5.67 108

W

m2

K4

The parameter hr is called the "effective radiation heat transfer coefficient" or, forsimplicity, "radiation heat transfer coefficient"

Julio C. Banks, PE [email protected] page 1 of 4


The temperature ration in Eq. 2 can be simplified by the following procedure

T14

T24

T1 T2 T1

2T2

2 T12

T22

T1 T2 =T1 T2 T1 T2 T1

2T2

2 T1 T2 =

Simplifying we get .

T14

T24

T1 T2 T1 T2 T12

T22 =

Finally. Eq. 2 becomes Eq. 3 as follows

hr ε1 σ T1 T2 T12

T22 = 3( )

Example 1.4 A long, cylindrical electrically heated rod, 2 cm in diameter, is installed in a vacuumfurnace as shown in Fig. 1.12. The surface of the heating rod has an emissivity of0.9 and is maintained at 1000 K, while the interior walls of the furnace are black andare at 800 K. Calculate the net rate at which heat is lost from the rod per unit lengthand the radiation heat transfer coefficient.



Tube diameter: D 0.02m

Tube length: L 1.0m

Emissivity: ε1 0.9

Temperatures: T1 103K T2 800K

The heat flux will be calculated first to emphasize that the total heat transfer is apost-process value from the heat transfer system simulation. Once the heat balancesimulation is completed the pertinent areas are calculated to scale the heat flux and thus obtain the total heat transfer.

Calculate the radiation heat transfer coefficient, hr

hr ε1σ T1 T2 T12

T22 151

W

m2K

Notice that the use of heat transfer flux, q, is much easier to visualize because the heat transfer coefficient when multiplied by the surface area and the temperaturedifference, ΔT,, results in the "total" heat transfer, Q.

Heat flux: qr hr T1 T2 30.1kW

m2

Post ProcessThe surface area of the tube must be calculated in order for the total heat transfer, Qr,to be obtained.

Surface area: A1 π D L 6.28 102 m

2

Heat transfer: Qr A1qr 1.89kW



The use of the concept of radiation heat transfer coefficient can be used as adeterminantn of the importrance of radiation mode of heat transfer when compared to the heat transfer coeeficient of existing free or forced convectionin the heat transfer system. A rule of thumb is that if the radiation heat transferis comparable to that of free convection or exceeds 5% of the exisitng forcedconvection, then radiation shoud be included in the calculations. The radiationheat transfer can be calculated, in advance (a priori) using the temperaturedof the component in thermal radiation exchange. A radiation heat transfercoefficient plot is constructed for the example jiust calculated by maintaing the source temeprare, T1, constant and arbitrarily changing the sink temperatureas follows:

hr T2 ε1σ T1 T2 T12

T22

T2 0.2T1 0.25T1 0.8T1

200 300 400 500 600 700 80060

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160Effective Radiation Heat Transfer Coefficient

hr T2 W

m2K

T2

K


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