Dimensionless Numbers in Heat Transfer

Many correlations in heat transfer are based on dimensionless numbers, which are used to establish similitude among cases which might seem very different. Four significant dimensionless numbers in heat transfer course are discussed in this article:

  1. Reynolds Number
  2. Nusselt Number
  3. Prandtl Number
  4. Grashof Number

Reynolds Number:

The Reynolds number is the ratio of fluid flow momentum rate (fluid’s inertia force) to viscous force.

Reynolds number formula

The Reynolds number is used to determine whether flow is laminar or turbulent.

Nusselt Number:

The Nusselt number characterizes the similarity of heat transfer at the interface between wall and fluid in different systems. Nusselt number is basically a ratio of convective heat transfer coefficient to conductance.

nusselt number

Where, ‘h’ is the convective heat transfer coefficient of the flow,
‘L’ is the characteristic length,
‘k’ is the thermal conductivity of the fluid.

Prandtl Number:

The Prandtl number is the ratio of momentum diffusivity to thermal diffusivity of a fluid:

Prandtl number

Where, ‘v‘ is kinematic viscosity,
‘∝’ is thermal diffusibility,
‘μ’ is dynamic viscosity,
‘ρ’ is density,
‘k’ is thermal conductivity,
‘cp‘ is specific heat.

It is solely dependent upon the fluid properties:

  • For gases, Pr = 0.7 to 1.0.
  • For water, Pr = 1 to 10.
  • For liquid metals, Pr = 0.001 to 0.03.
  • For oils. Pr = 50 to 2000.

Grashof Number:

The Grashof number is used to determine the heat transfer coefficient under free convection conditions. It is basically a ratio between the buoyancy forces and viscous forces.

Grashof number

Heat transfer requires circulation, therefore, the Grashof number (and heat transfer coefficient) will rise as the buoyancy forces increase and the viscous forces decrease.

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