Dimensionless groups in heat transfer Confirm whether the Prandtl number is defined as: Pr = μ * cp / k.

Introduction / Context:The Prandtl number connects momentum and thermal diffusivities and is fundamental in convection correlations such as for boundary layers, internal duct flow, and external flow over plates.

Given Data / Assumptions:

• Dynamic viscosity μ (Pa·s), specific heat at constant pressure cp (J/kg·K), thermal conductivity k (W/m·K).
• Continuum behavior; properties evaluated at film temperature.

Concept / Approach:Prandtl number: Pr = ν / α, where ν = μ/ρ is kinematic viscosity and α = k/(ρcp) is thermal diffusivity. Eliminating ρ gives Pr = (μ/ρ) / (k/(ρcp)) = μ * cp / k.

Step-by-Step Solution:Start from Pr = ν / α.Substitute ν = μ/ρ and α = k/(ρcp).Simplify: Pr = (μ/ρ) * (ρcp/k) = μcp/k.Thus the given definition is correct.

Verification / Alternative check:Check units: μcp/k is dimensionless, satisfying the requirement for a similarity parameter.

Why Other Options Are Wrong:

• Limiting validity to gases or liquids is incorrect; the definition is general.
• Temperature restrictions are not part of the definition, though property variation with temperature affects numerical values.

Common Pitfalls:Confusing Pr with Reynolds or Nusselt numbers; mixing up cp and cv; using inconsistent units causing numerical errors.

Final Answer:Yes