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this predicted value as an estimate of the uncertainty resulting from this effect, or we can use
the predicted value to correct the indicated value and assign a smaller uncertainty based on the
uncertainty in the correction.
Equation 8.31 and Equation 8.32, above, do not allow direct solution for the radiation error
because it contains the probe temperature raised to the fourth power. Any calculator or computerbased method for the solution of nonlinear equations may be employed to affect the solution,
although a trial-and-error approach converges rapidly to the correct temperature.
Radiation Shielding
Radiation shielding is a key concept in controlling radiative heat transfer; shielding for radiation is
analogous to insulation to reduce conduction heat transfer. A radiation shield is an opaque surface
interposed between a temperature sensor and its radiative surroundings so as to reduce electromagnetic wave interchange. In principle, the shield attains an equilibrium temperature closer to the
fluid temperature than the surroundings. Because the probe can no longer ‘‘see’’ the surroundings,
with the radiation shield in place, the probe temperature is closer to the fluid temperature. Additional
information on radiation error in temperature measurements may be found in Sparrow (14). The
following example serves to demonstrate radiation errors and the effect of shielding.
Example 8.14
Consider again Example 8.13, where the oven is maintained at a temperature of 800
C. Because of
energy losses, the walls of the oven are cooler, having a temperature of 500
C. For the present case,
consider the temperature probe as a small, spherical object located in the oven, having no thermal
conduction path to the ambient. (All energy exchange is through convection and radiation.) Under
these conditions, the probe temperature is 642.5
C, as found in Example 8.13.
Suppose a radiation shield is placed between the temperature probe and the walls of the furnace,
which blocks the path for radiative energy transfer. Examine the effect of adding a radiation shield
on the probe temperature.
KNOWN A radiation shield is added to a temperature probe in an environment with T 1 ¼
800
C and T w ¼ 500
C.
FIND The radiation error in the presence of the shield.
ASSUMPTIONS The radiation shield completely surrounds the probe, and the surroundings
may be treated as a blackbody.
SOLUTION The shield equilibrium temperature is higher than the wall temperature by virtue
of convection with the fluid. As a result, the probe ‘‘sees’’ a higher temperature surface, and the
probe temperature is closer to the fluid temperature, resulting in less measurement error.
For a single radiation shield placed so that it completely surrounds the probe, which is small
compared to the size of the enclosure and has an emissivity of 1, the equilibrium temperature of the
shield can be determined from Equation 8.30. The temperature of the shield is found to be 628
C.
Because the sensor now ‘‘sees’’ the shield, rather than the wall, the temperature measured by the
probe is 697
C, which is also determined from Equation 8.30.
362 Chapter 8 Temperature Measurements
14:54:2 Page 362
this predicted value as an estimate of the uncertainty resulting from this effect, or we can use
the predicted value to correct the indicated value and assign a smaller uncertainty based on the
uncertainty in the correction.
Equation 8.31 and Equation 8.32, above, do not allow direct solution for the radiation error
because it contains the probe temperature raised to the fourth power. Any calculator or computerbased method for the solution of nonlinear equations may be employed to affect the solution,
although a trial-and-error approach converges rapidly to the correct temperature.
Radiation Shielding
Radiation shielding is a key concept in controlling radiative heat transfer; shielding for radiation is
analogous to insulation to reduce conduction heat transfer. A radiation shield is an opaque surface
interposed between a temperature sensor and its radiative surroundings so as to reduce electromagnetic wave interchange. In principle, the shield attains an equilibrium temperature closer to the
fluid temperature than the surroundings. Because the probe can no longer ‘‘see’’ the surroundings,
with the radiation shield in place, the probe temperature is closer to the fluid temperature. Additional
information on radiation error in temperature measurements may be found in Sparrow (14). The
following example serves to demonstrate radiation errors and the effect of shielding.
Example 8.14
Consider again Example 8.13, where the oven is maintained at a temperature of 800
C. Because of
energy losses, the walls of the oven are cooler, having a temperature of 500
C. For the present case,
consider the temperature probe as a small, spherical object located in the oven, having no thermal
conduction path to the ambient. (All energy exchange is through convection and radiation.) Under
these conditions, the probe temperature is 642.5
C, as found in Example 8.13.
Suppose a radiation shield is placed between the temperature probe and the walls of the furnace,
which blocks the path for radiative energy transfer. Examine the effect of adding a radiation shield
on the probe temperature.
KNOWN A radiation shield is added to a temperature probe in an environment with T 1 ¼
800
C and T w ¼ 500
C.
FIND The radiation error in the presence of the shield.
ASSUMPTIONS The radiation shield completely surrounds the probe, and the surroundings
may be treated as a blackbody.
SOLUTION The shield equilibrium temperature is higher than the wall temperature by virtue
of convection with the fluid. As a result, the probe ‘‘sees’’ a higher temperature surface, and the
probe temperature is closer to the fluid temperature, resulting in less measurement error.
For a single radiation shield placed so that it completely surrounds the probe, which is small
compared to the size of the enclosure and has an emissivity of 1, the equilibrium temperature of the
shield can be determined from Equation 8.30. The temperature of the shield is found to be 628
C.
Because the sensor now ‘‘sees’’ the shield, rather than the wall, the temperature measured by the
probe is 697
C, which is also determined from Equation 8.30.
362 Chapter 8 Temperature Measurements