Definition of Convection

  • It is the process of heat transfer within a fluid by mixing of one portion of fluid with another.
  • Convection is possible only in a fluid medium and is directly linked with the transport of medium itself.
  • Mixing motion of the fluid tells us about the effectiveness of heat transfer by convection method.
  • Newton’s Law of Cooling governs the convective heat transfer between a surface and an adjacent fluid.

Q= hA(ts-tf)

Q = Rate of Convective heat transfer

A = Area exposed to heat transfer

h = Coefficient of Convective heat transfer (W/m2 °C)

ts = Surface Temperature

tf = Fluid Temperature

Factors on which ‘h’ depend

  • A geometry of Surface.
  • Nature of fluid flow.
  • Thermodynamic and transport properties (e.g. viscosity, density etc.).
  • Prevailing thermal conditions.


Free or Natural Convection

  • When fluid flows or circulates by virtue of the natural differences in densities of hot and cold fluids.
  • The difference in density of the hot and cold fluids causes the fluid to flow in an upward direction.
  • The force causing this flow is known as buoyancy force.
  • Nu = f(Gr, Pr)
  • Nusselt’s Number (Nu) = (convective heat transfer/conductive heat transfer)

Forced Convection

  • When fluid is circulated with the help of an external agent e.g. Pumping etc.
  • Nu = f(Re, Pr)

Dimensionless Numbers related to Convection processes-

Grashoff Number

  • It is used only in natural convection heat transfer process.
  • It is the ratio of the product of inertia force and buoyancy force to the square of viscous force.

Gr = (Inertia Force* Buoyancy Force) / (Viscous Force)2


g = Acc. Due to gravity

β = Coefficient of Volume Expansion

Δθ = Temperature difference

ρ = density of the fluid

L = Characteristic Length of the geometry

µ = Dynamic or Absolute Viscosity

γ = Kinematic Viscosity of the fluid (ρ/ µ)

  • Grashoff Number provides the main criteria in determining whether the fluid flow is laminar or turbulent in Natural Convection.
  • Grashoff Number plays the same role in free convection as Reynolds Number in forced convection.
  • For Vertical plates, critical Grashoff Number is 109.

Prandtl Number

  • The thermal boundary layer is best described by Prandtl Number.

Pr = molecular diffusivity of momentum / molecular diffusivity of heat


Ratio of kinematic viscosity to thermal diffusivity

Pr = (µcp)/K

K = thermal conductivity

cp = Specific Heat

  • The Prandtl Numbers of fluids range from less than 0.01 for liquid metals to more than 100000 for heavy oils.
  • Heat diffuse quickly in liquid metals (Pr<<1) and very slowly in oils (Pr>>1) relative to momentum.

Reynolds Number

  • It is the ratio of inertia force to viscous force.

Re = ρVL/µ

ρ = fluid density

V= velocity of fluid

  • Reynolds number tells the relative predominance of inertia force over the viscous force.
  • It is an important criterion in forced convection heat transfer.
  • A Higher value of Re means a greater contribution of inertia force.

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