Convective heat transfer correlations: The ratio of the Nusselt number to the product of Reynolds number and Prandtl number equals which dimensionless group?
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AStanton number
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BBiot number
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CPeclet number
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DGrashof number
Answer
Correct Answer: Stanton number
Explanation
Introduction / Context:Dimensionless numbers simplify heat transfer analysis by grouping variables. Relating Nusselt (Nu), Reynolds (Re), and Prandtl (Pr) numbers helps compare convection problems across scales.
Given Data / Assumptions:
- Nusselt number: Nu = h * L / k.
- Reynolds number: Re = ρ * V * L / μ.
- Prandtl number: Pr = μ * c_p / k.
- Steady convection, characteristic length L, properties evaluated at film temperature.
Concept / Approach:The Stanton number, St, is defined as St = h / (ρ * V * c_p). Algebra shows St = Nu / (Re * Pr). Recognizing this identity clarifies how convective heat transfer coefficient relates to flow inertia and thermal diffusivity.
Step-by-Step Solution:
Write St = h / (ρ * V * c_p).Express Nu / (Re * Pr) = (hL/k) / [(ρVL/μ)(μc_p/k)] = h / (ρVc_p) = St.Therefore, Nu / (Re * Pr) equals the Stanton number.Verification / Alternative check:Check dimensions: all groups are dimensionless; the identity holds for any consistent unit system.
Why Other Options Are Wrong:
- Biot number compares internal conduction to surface convection, unrelated to Re or Pr directly.
- Peclet number is Re * Pr, not the ratio in question.
- Grashof number governs natural convection, independent of Re for forced convection.
Common Pitfalls:Confusing Peclet and Stanton numbers; remember St = Nu/(RePr).
Final Answer:Stanton number