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The total thermal resistance is calculated using the equation R = R1 + R2 + R3.
True
For a turbulent flow, a low Reynolds number (Re) indicates higher heat transfer coefficients.
False
Newton’s law of cooling describes the relationship between heat transfer and the temperature difference between two bodies.
True
The Nusselt number (Nu) is unrelated to the Prandtl number (Pr).
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The equation Tb = Tb0 + (Vf cos(θ) / H) relates the temperature at the base to the temperature difference and flow velocity.
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Boiling in a BWR allows significant boiling with a direct steam cycle.
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Departure from nucleate boiling (DNB) leads to improved heat transfer efficiency.
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A Pressurized Water Reactor (PWR) operates with subcooled boiling and an indirect steam cycle.
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Saturated boiling in a BWR occurs at a pressure of 1035 psia and a saturation temperature of 400°F.
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Critical heat flux (CHF) is unaffected by boiling conditions.
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The equation that describes the relationship between the heat flux and the temperature difference along the channel involves the parameter Rh.
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A low Reynolds number (Re) in fluid dynamics is associated with turbulent flow regimes.
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The Dittus-Boelter equation is used to calculate heat transfer coefficients for both laminar and turbulent flows.
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Critical heat flux (CHF) can vary significantly depending on the boiling conditions present in the reactor system.
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The Nusselt number (Nu) has no direct relationship with the Prandtl number (Pr) in heat transfer equations.
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In a Pressurized Water Reactor (PWR), extensive boiling is allowed to promote heat transfer efficiency.
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The boiling crisis is defined as the transition from film boiling to nucleate boiling.
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Boiling patterns in heated pipes are observed by changing the flow velocity and measuring the heat flux.
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Departure from Nucleate Boiling (DNB) significantly enhances heat transfer in boiling processes.
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Jens and Lottes correlations are used to understand boiling under subcooled conditions.
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The boiling process governed by convection is less effective than that governed by conduction and radiation.
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A BWR operates under saturated boiling conditions at a pressure of 1035 psia.
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The critical heat flux (CHF) is influenced by the bulk boiling conditions explained through the GE correlations.
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The minimum Departure from Nucleate Boiling Ratio (DNBR) for a Pressurized Water Reactor (PWR) is 1.9.
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The melting temperature of uranium dioxide (UO2) is approximately 5000°F.
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A higher hot channel factor (HCF) is necessary to achieve maximum power in a reactor.
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The temperature for significant fission gas release in metal uranium is approximately 750°F.
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The thermal design of reactors aims to increase the critical heat flux to ensure safety.
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The maximum heat flux (qmax) is defined as the product of the av heat flux (qav) and the hot channel factor (F).
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Uranium carbide (UC) has a higher melting point than uranium dioxide (UO2).
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Study Notes
Previous Lectures
- Newton's law of cooling defined as ( q'' = h(T_c - T_b) ).
- Total thermal resistance consists of contributions from conduction, convection, and geometry, expressed as:
- ( R = \frac{1}{2k_f A} + \frac{1}{k_c A} + \frac{1}{hA} + \frac{1}{4\pi k_f H} + \frac{1}{2\pi k_c H} + hA ).
- Temperature changes along the channel are influenced by maximum heat transfer, shown in formulas related to ( R ) and flow velocity variables.
Boiling
- Boiling in reactors enhances heat transfer with:
- Lower coolant pressure resulting in improved heat transfer.
- Reduced cladding temperature.
- Boiling Water Reactor (BWR) allows extensive boiling with a direct steam cycle.
- Pressurized Water Reactor (PWR) operates under subcooled conditions and uses an indirect steam cycle.
Boiling Regimes
- Boiling patterns characterized by:
- Changes in surface temperature leading to heat flux measurement.
- The transition from nucleate boiling to film boiling, which results in reduced heat transfer.
- Effective heat transfer occurs when bubbles form on heated surfaces, enhancing convection while maintaining bubble transport to bulk coolant.
Boiling Crisis
- Departure from Nucleate Boiling (DNB) leads to film boiling, where heated rods experience reduced heat transfer due to steam vapor exposure.
- The critical heat flux (CHF) marks the transition point influencing the cooling efficiency.
- Empirical correlations for CHF exist for subcooled and bulk boiling conditions.
Thermal Design of Reactor
- Design objectives include maintaining fission products within the fuel and ensuring cladding integrity to prevent fuel melting.
- Notable melting temperatures for uranium compounds:
- UO2: ~5000°F (2760°C)
- Uranium Carbide (UCN): ~6500°F (3600°C)
- Metal Uranium: ~2070°F (1132°C)
DNB Ratio (DNBR)
- Safety margins to prevent DNB are defined as minimum values:
- BWR: Minimum DNBR of 1.9
- PWR: Minimum DNBR of 1.3
- The DNBR formula incorporates heat transfer rates and actual cooling power.
Hot Channel Factor (HCF)
- The hot channel factor defined as:
- ( F = \frac{q''{max}}{q''{avg}} ), with further relations ( F = F_N \cdot F_E ).
- Reactor power can be maximized by increasing CHF, decreasing HCF, and lowering minimum DNBR through improved design strategies.
Summary
- Heat generation and removal in nuclear reactors rely on conduction, convection, and thermal resistance principles.
- Key calculations and concepts are vital, with emphasis on boiling regimes, DNB, and HCF to ensure operational efficiency and safety in reactor thermal designs.
Previous Lectures
- Newton's law of cooling defined as ( q'' = h(T_c - T_b) ).
- Total thermal resistance consists of contributions from conduction, convection, and geometry, expressed as:
- ( R = \frac{1}{2k_f A} + \frac{1}{k_c A} + \frac{1}{hA} + \frac{1}{4\pi k_f H} + \frac{1}{2\pi k_c H} + hA ).
- Temperature changes along the channel are influenced by maximum heat transfer, shown in formulas related to ( R ) and flow velocity variables.
Boiling
- Boiling in reactors enhances heat transfer with:
- Lower coolant pressure resulting in improved heat transfer.
- Reduced cladding temperature.
- Boiling Water Reactor (BWR) allows extensive boiling with a direct steam cycle.
- Pressurized Water Reactor (PWR) operates under subcooled conditions and uses an indirect steam cycle.
Boiling Regimes
- Boiling patterns characterized by:
- Changes in surface temperature leading to heat flux measurement.
- The transition from nucleate boiling to film boiling, which results in reduced heat transfer.
- Effective heat transfer occurs when bubbles form on heated surfaces, enhancing convection while maintaining bubble transport to bulk coolant.
Boiling Crisis
- Departure from Nucleate Boiling (DNB) leads to film boiling, where heated rods experience reduced heat transfer due to steam vapor exposure.
- The critical heat flux (CHF) marks the transition point influencing the cooling efficiency.
- Empirical correlations for CHF exist for subcooled and bulk boiling conditions.
Thermal Design of Reactor
- Design objectives include maintaining fission products within the fuel and ensuring cladding integrity to prevent fuel melting.
- Notable melting temperatures for uranium compounds:
- UO2: ~5000°F (2760°C)
- Uranium Carbide (UCN): ~6500°F (3600°C)
- Metal Uranium: ~2070°F (1132°C)
DNB Ratio (DNBR)
- Safety margins to prevent DNB are defined as minimum values:
- BWR: Minimum DNBR of 1.9
- PWR: Minimum DNBR of 1.3
- The DNBR formula incorporates heat transfer rates and actual cooling power.
Hot Channel Factor (HCF)
- The hot channel factor defined as:
- ( F = \frac{q''{max}}{q''{avg}} ), with further relations ( F = F_N \cdot F_E ).
- Reactor power can be maximized by increasing CHF, decreasing HCF, and lowering minimum DNBR through improved design strategies.
Summary
- Heat generation and removal in nuclear reactors rely on conduction, convection, and thermal resistance principles.
- Key calculations and concepts are vital, with emphasis on boiling regimes, DNB, and HCF to ensure operational efficiency and safety in reactor thermal designs.
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Description
Explore the principles of thermal dynamics as they relate to boiling in nuclear reactors. Understand Newton's law of cooling, thermal resistance components, and the distinct boiling regimes in boiling water reactors (BWR) and pressurized water reactors (PWR). This quiz will test your grasp of heat transfer and the operational mechanisms of these reactors.
