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# Heat Transfer (10th Edition)Solutions for Chapter 8

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Chapter: Problem:
SAMPLE SOLUTION
Chapter: Problem:
• Step 1 of 19

(a)

The fused quartz transmits 90 percent of the incident thermal, therefore the transsmisivity is determined as.

Change the temperature of black body, T into Kelvin unit.

The temperature of black body is determined as 1073 K.

• Step 2 of 19

Determine the value of .

The low limit of is determined by using the following relation:

With is low limit of wave length and T is temperature of black body.

Substitute for and 1073 K for T.

The top limit of is determined by using the following relation:

With is top limit of wave length and T is temperature of black body.

Substitute for and 1073 K for T.

• Step 3 of 19

Determine the fraction of the total energy between 0 and by using the following relation:

â€¦â€¦ (1)

With is total emissive power of black body and is the emissive power of a black body per unit wave length that determined as:

With is wavelength, T is temperature, and are constants which are determined as:

The total emissive power of black body is determined as:

With is Stefan-Boltzmann constant that determined as:

Recall equation (1) and substitute for and for .

• Step 4 of 19

Calculate the fraction of the total energy between 0 and by using the following relation:

Substitutefor, for , for , for, and for .

The fraction of the total energy between 0 and is determined as 0.5318.

Or another method we can use the table of ratio fraction of radiation. From the table, the following values of the fraction are obtained.

 4200 0.51599 4300 0.53267

By using interpolation method the value of fraction of total energy at can be obtained.

Here,

The previous value of from the table is .

The next value of from the table is .

The previous value of the fraction is .

The next value of the fraction is .

Substitute for , for , for , for , and 0.53267 for .

By using interpolation method, the fraction of the total energy between 0 and is determined as 0.5313.

Hence we are using the value of 0.5318 as the fraction of the total energy between 0 and.

• Step 5 of 19

Since the fused quartz does not transmit the incident thermal radiation below , The fraction of the total energy between 0 and is determined as zero.

The total energy between and is calculated by using following equation:

Substitute for , 1073 K for T, 0 for , and 0.5318 for .

The total emitted energy between and is determined as .

• Step 6 of 19

The transmitted heat flux by fused quartz is calculated by using following equation.

Substitute 0.9 for and for .

Therefore, the transmitted heat flux by fused quartz is determined as.

• Step 7 of 19

(b)

Change the temperature of black body, T into Kelvin unit.

The temperature of black body is determined as 823 K.

Determine the value of .

The low limit of is determined by using the following relation:

Substitute for and 823 K for T.

The top limit of is determined by using the following relation:

Substitute for and 823 K for T.

Calculate the fraction of the total energy between 0 and by using the following relation:

Substitute for, for, for, and for ,

The fraction of the total energy between 0 and is determined as 0.3387.

• Step 8 of 19

Or another method, we can use the table of ratio fraction of radiation. From the table, the following values of the fraction are obtained.

 3200 0.31809 3300 0.34009

By using interpolation method the value of fraction of total energy at can be obtained.

With

The previous value of from the table is .

The next value of from the table is .

The previous value of the fraction is .

The next value of the fraction is .

Substitute for , for , for , 0.31809 for , and 0.34009 for .

By using interpolation method, The fraction of the total energy between 0 and is determined as 0.3383.

Hence we are using the value of 0.3387 as the fraction of the total energy between 0 and .

• Step 9 of 19

Since the fused quartz does not transmit the incident thermal radiation below , The fraction of the total energy between 0 and is determined as zero.

The total energy between and is calculated by using following equation:

Substitute for , 823 K for T, 0 for , and 0.3387 for .

The total emitted energy between and is determined as .

The transmitted heat flux by fused quartz is calculated by using following equation.

Substitute 0.9 for and for.

Therefore, the transmitted heat flux by fused quartz is determined as .

• Step 10 of 19

(c)

Change the temperature of black body, T into Kelvin unit.

The temperature of black body is determined as 523 K.

Determine the value of .

The low limit of is determined by using the following relation:

Substitute for and 523 K for T.

The top limit of is determined by using the following relation:

Substitute for and 523 K for T.

• Step 11 of 19

Calculate the fraction of the total energy between 0 and by using the following relation:

Substitute for , for , for , for , and for ,

The fraction of the total energy between 0 and is determined as 0.0818.

• Step 12 of 19

Or another method, we can use the table of ratio fraction of radiation. From the table, the following values of the fraction are obtained.

 2000 0.06672 2100 0.08305

By using interpolation method the value of fraction of total energy at can be obtained.

With

The previous value of from the table is .

The next value of from the table is .

The previous value of the fraction is .

The next value of the fraction is .

Substitute for , for , for , 0.06672 for , and 0.08305 for .

By using interpolation method, The fraction of the total energy between 0 and is determined as 0.0818.

Hence we are using the value of 0.0818 as the fraction of the total energy between 0 and .

Since the fused quartz does not transmit the incident thermal radiation below , The fraction of the total energy between 0 and is determined as zero.

The total energy between and is calculated by using following equation:

Substitute for , 523 K for T, 0 for , and 0.0818 for .

The total emitted energy between and is determined as .

• Step 13 of 19

The transmitted heat flux by fused quartz is calculated by using following equation.

Substitute 0.9 for and for .

Therefore, the transmitted heat flux by fused quartz is determined as.

• Step 14 of 19

(d)

Change the temperature of black body, T into Kelvin unit.

The temperature of black body is determined as 343 K.

• Step 15 of 19

Determine the value of .

The low limit of is determined by using the following relation:

Substitute for and 343 K for T.

The top limit of is determined by using the following relation:

Substitute for and 343 K for T.

• Step 16 of 19

Calculate the fraction of the total energy between 0 and by using the following relation:

Substitute for , for , for , for, and for ,

The fraction of the total energy between 0 and is determined as 0.0067.

• Step 17 of 19

Or another method, we can use the table of ratio fraction of radiation. From the table, the following values of the fraction are obtained.

 1300 0.00432 1400 0.00779

By using interpolation method the value of fraction of total energy at can be obtained.

With

The previous value of from the table is .

The next value of from the table is .

The previous value of the fraction is .

The next value of the fraction is .

Substitute for , for , for , 0.00432 for , and 0.00779 for .

By using interpolation method, The fraction of the total energy between 0 and is determined as 0.00068.

Hence we are using the value of 0.0067 as the fraction of the total energy between 0 and .

• Step 18 of 19

Since the fused quartz does not transmit the incident thermal radiation below , The fraction of the total energy between 0 and is determined as zero.

The total energy between and is calculated by using following equation:

Substitute for , for T, 0 for , and 0.0068 for .

The total emitted energy between and is determined as .

• Step 19 of 19

The transmitted heat flux by fused quartz is calculated by using following equation.

Substitute 0.9 for and for.

Therefore, the transmitted heat flux by fused quartz is determined as.

Corresponding Textbook

Heat Transfer | 10th Edition
9780073529363ISBN-13: 0073529362ISBN: Authors:
Alternate ISBN: 9780077414900
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