Convection Heat Transfer Process GATE Notes- Toppers Portal

Convection Heat Transfer Notes

Convection Definition

It is the process of heat transfer within a fluid by mixing one portion of the fluid with another.
It is possible only in a fluid medium and is directly linked with the transport of the medium itself.
The 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(t_s-t_f)

Q = Rate of Convective heat transfer

A = Area exposed to heat transfer

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

t_s = Surface Temperature

t_f = 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.

Read More- Modes of Heat Transfer

Types of Convection

Free Convection 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 the 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)

Read More- Radiation: What is Shape Factor?

Dimensionless Numbers related to Convection Processes

Grashoff Number

It is used only in the 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

(ρ²βgΔθL³)/µ²

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

The ratio of kinematic viscosity to thermal diffusivity

Pr = (µc_p)/K

K = thermal conductivity

c_p = 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 a 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.