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Modified Rayleigh Number Formula:
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The Modified Rayleigh Number is a dimensionless number associated with buoyancy-driven flow, also known as free or natural convection. It accounts for the effects of Bingham plastic behavior in fluid flow systems.
The calculator uses the Modified Rayleigh Number formula:
Where:
Explanation: This formula modifies the standard Rayleigh number to account for Bingham plastic behavior in fluids, where the Bingham number represents the ratio of yield stress to viscous stress.
Details: The Modified Rayleigh Number is crucial for analyzing convective heat transfer in non-Newtonian fluids, particularly those exhibiting Bingham plastic behavior. It helps predict the onset of convection and heat transfer characteristics in such fluids.
Tips: Enter the Rayleigh Number and Bingham Number as positive dimensionless values. Both values must be valid (Rayleigh Number > 0, Bingham Number ≥ 0).
Q1: What is the physical significance of the Modified Rayleigh Number?
A: It represents the ratio of buoyancy forces to viscous forces in Bingham plastic fluids, modified to account for the yield stress behavior.
Q2: How does the Bingham Number affect the Modified Rayleigh Number?
A: As the Bingham Number increases, the Modified Rayleigh Number decreases, indicating reduced convective instability due to the yield stress effect.
Q3: What types of fluids require this modified calculation?
A: This calculation is essential for Bingham plastic fluids such as certain slurries, pastes, gels, and other materials that exhibit yield stress behavior.
Q4: What are typical applications of this calculation?
A: Applications include chemical processing, food industry, petroleum engineering, and any field dealing with non-Newtonian fluid heat transfer.
Q5: Are there limitations to this equation?
A: This equation assumes ideal Bingham plastic behavior and may need modification for fluids with more complex rheological properties.