Dimensionless Numbers in Heat Transfer to Know for Heat and Mass Transfer

Dimensionless numbers are key in heat transfer, helping us understand fluid behavior and heat exchange. They simplify complex relationships, allowing us to predict flow patterns, heat transfer efficiency, and the impact of various forces in different thermal scenarios.

1. Reynolds Number (Re)

   • Represents the ratio of inertial forces to viscous forces in a fluid flow.
   • Indicates whether the flow is laminar (Re < 2000) or turbulent (Re > 4000).
   • Essential for predicting flow patterns and heat transfer characteristics in fluids.

2. Prandtl Number (Pr)

   • Defines the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity.
   • Affects the thickness of the thermal boundary layer relative to the velocity boundary layer.
   • Important for characterizing heat transfer in fluids, especially in forced convection scenarios.

3. Nusselt Number (Nu)

   • Represents the ratio of convective to conductive heat transfer across a boundary.
   • Higher values indicate more effective convective heat transfer.
   • Used to determine heat transfer coefficients in various heat exchanger designs.

4. Grashof Number (Gr)

   • Measures the ratio of buoyancy forces to viscous forces in natural convection.
   • Critical for analyzing the stability of fluid motion in buoyancy-driven flows.
   • Helps predict the onset of natural convection in heated fluids.

5. Rayleigh Number (Ra)

   • Combines the effects of Grashof and Prandtl numbers, indicating the stability of natural convection.
   • Determines the transition from conduction to convection in a fluid layer.
   • Essential for understanding heat transfer in systems with significant temperature differences.

6. Biot Number (Bi)

   • Represents the ratio of internal thermal resistance to external thermal resistance.
   • Affects the temperature distribution within a solid body during heat transfer.
   • Important for determining whether lumped system analysis is applicable.

7. Fourier Number (Fo)

   • Measures the ratio of heat conduction rate to the rate of thermal energy storage.
   • Useful for analyzing transient heat conduction problems.
   • Helps in determining the time scale for heat transfer processes.

8. Peclet Number (Pe)

   • Combines the effects of convection and diffusion in heat transfer.
   • Indicates the relative importance of advective transport to diffusive transport.
   • Important for characterizing heat transfer in systems with both conduction and convection.

9. Stanton Number (St)

   • Represents the ratio of heat transferred to the thermal capacity of the fluid.
   • Useful for evaluating the effectiveness of heat exchangers and cooling systems.
   • Provides insight into the heat transfer performance in convective systems.

10. Eckert Number (Ec)

    • Measures the ratio of kinetic energy to enthalpy difference in a flow.
    • Important for analyzing heat transfer in high-speed flows where viscous heating is significant.
    • Helps in understanding the thermal effects of compressibility in fluid dynamics.