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**Convection Heat Transfer Notes**

Contents

**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 10
^{9}.

**Prandtl Number**

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

Pr = molecular diffusivity of momentum / molecular diffusivity of heat

**OR**

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.

**Read More- Radiation: What is Shape Factor?**

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