The one-dimensional plane wall of Figure 3.1 is of thickness
(a)
The minimum and maximum heat fluxes through the wall for free convection in gases.
Answer to Problem 9.1P
The minimum heat fluxes through the wall for free convection in gasses is
Explanation of Solution
Given:
The thickness of the length is
The thermal conductivity is
The fluid temperature is
Minimum heat transfer coefficient is
Maximum heat transfer coefficient is
Concept used:
Write the expression for heat flux.
Here,
Calculation:
Substitute
Therefore, the expression for heat flux is shown below.
The minimum heat flux is obtained below.
Substitute
The maximum heat flux is obtained below.
Substitute
Conclusion:
Thus, the minimum heat fluxes through the wall for free convection in gases is
(b)
The minimum and maximum heat fluxes through the wall for free convection in liquids.
Answer to Problem 9.1P
The minimum heat fluxes through the wall for free convection in liquids is
Explanation of Solution
Given:
Minimum heat transfer coefficient is
Maximum heat transfer coefficient is
Calculation:
Substitute
The maximum heat flux is obtained below.
Substitute
Conclusion:
Thus, the minimum heat fluxes through the wall for free convection in liquids is
(c)
The minimum and maximum heat fluxes through the wall for forced convection in gases.
Answer to Problem 9.1P
The minimum heat fluxes through the wall for forced convection in gases is
Explanation of Solution
Given:
Minimum heat transfer coefficient is
Maximum heat transfer coefficient is
Calculation:
Substitute
The maximum heat flux is obtained below.
Substitute
Conclusion:
Thus, the minimum heat fluxes through the wall for forced convection in gases is
(d)
The minimum and maximum heat fluxes through the wall for forced convection in liquids.
Answer to Problem 9.1P
The minimum heat fluxes through the wall for forced convection in liquids is
Explanation of Solution
Given:
Minimum heat transfer coefficient is
Maximum heat transfer coefficient is
Calculation:
Substitute
The maximum heat flux is obtained below.
Substitute
Conclusion:
Thus, the minimum heat fluxes through the wall for forced convection in liquids is
(e)
The minimum and maximum heat fluxes through the wall for convection with phase change.
Answer to Problem 9.1P
The minimum heat fluxes through the wall for convection with phase change is
Explanation of Solution
Given:
Minimum heat transfer coefficient is
Maximum heat transfer coefficient is
Calculation:
Substitute
The maximum heat flux is obtained below.
Substitute
Conclusion:
Thus, the minimum heat fluxes through the wall for convection with phase change is
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