---
title: "Natural and forced convection compared"
subject: "Heat Transfer"
chapter: 3
key: "semester_5/heat_transfer:free-versus-forced-convection"
source: https://www.bctengineer.com/q/semester_5/heat_transfer/free-versus-forced-convection
site: BCT Engineering
---

# Natural and forced convection compared

Heat Transfer · Chapter 3: Convection Heat Transfer

- Asked in: year not given, 6 marks
- Video: [Free Convection vs Forced Convection | Heat Transfer |](https://www.youtube.com/watch?v=DPT5PDqkwLc) — Seal School
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/heat_transfer/free-versus-forced-convection
- Whole chapter: https://www.bctengineer.com/md/semester_5/heat_transfer/chapter-3

## Question

Differentiate between natural (free) and forced convection. Explain the mechanism of natural convection from a heated vertical plate, and show using dimensional analysis why the Nusselt number in natural convection depends on the Grashof and Prandtl numbers.

## Short answer

Natural convection is driven by density differences due to temperature, forced by external means. On a heated vertical plate, fluid rises, forming a buoyancy-driven boundary layer. Dimensional analysis yields Nu = f(Gr,Pr) because buoyancy force gβΔT replaces velocity, giving groups hL/k, ρ^2 gβΔT L^3/μ^2, and μc_p/k.

## Answer

#### Differences

| Point | Natural convection | Forced convection |
|---|---|---|
| Cause of motion | Density difference due to temperature | Pump, fan or wind |
| Velocity | Low, self-generated | High, controlled |
| Governing group | $Gr$, $Ra$ | $Re$ |
| Typical $h$ in air (W/m$^2$K) | 2 to 25 | 25 to 250 |
| Correlation | $Nu = f(Gr,Pr)$ | $Nu = f(Re,Pr)$ |
| Power needed | None | Pumping/fan power |

#### Mechanism on a heated vertical plate
Fluid next to the hot plate is heated, expands, becomes lighter and rises. Cooler fluid from the surroundings replaces it and a buoyancy-driven boundary layer forms.
```text
      ^  ^  ^    rising warm
   |  |         turbulent
   |  |   -----------
   |  |    transition
   |  |   laminar layer
 hot plate --> grows with height
```
The layer starts laminar at the lower edge, grows in thickness, becomes turbulent when $Ra \gtrsim 10^9$, and $h$ then becomes nearly independent of height.

#### Dimensional analysis
Buoyancy force per unit mass is $g\beta\,\Delta T$, replacing the velocity $V$ of forced flow. Thus $h = f(L, \rho, \mu, k, c_p, g\beta\Delta T)$: 7 variables and 4 fundamental dimensions give 3 groups:

$$
\frac{hL}{k}= f\left(\frac{\rho^2 g\beta\Delta T L^3}{\mu^2},\ \frac{\mu c_p}{k}\right)\;\Rightarrow\; Nu = f(Gr, Pr)
$$

For a vertical plate, $Nu = 0.59\,(Gr\,Pr)^{1/4}$ for laminar flow and $Nu = 0.10\,(Gr\,Pr)^{1/3}$ for turbulent flow.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What drives natural convection?
   A. A fan or pump
   B. Wind
   C. Pressure gradient from a compressor
   D. Density differences due to temperature
   Answer: D. Buoyancy from temperature-driven density differences. (Key point: Cause of motion)

2. On a heated vertical plate the boundary layer is:
   A. Laminar at the bottom, growing, turbulent when Ra exceeds about 10^9
   B. Turbulent at the bottom, laminar at top
   C. Always laminar
   D. Absent
   Answer: A. The layer grows with height and turns turbulent at high Ra. (Key point: Vertical plate mechanism)

3. In natural convection what replaces velocity V?
   A. Pressure
   B. Buoyancy term g beta delta T
   C. Specific heat
   D. Reynolds number
   Answer: B. This gives Nu = f(Gr, Pr). (Key point: Dimensional analysis)

## Related in Heat Transfer

- [Dimensional analysis of forced convection](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Abuckingham-pi-forced-convection) — Heat Transfer, chapter 3
- [Natural convection from a vertical plate](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Anatural-convection-vertical-plate-heat-loss) — Heat Transfer, chapter 3
- [Laminar forced convection over a heated flat plate](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Alaminar-flow-over-heated-plate-air) — Heat Transfer, chapter 3
- [Dimensionless numbers in convection](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Asignificance-dimensionless-numbers-convection) — Heat Transfer, chapter 3
- [Condensation of steam on a vertical plate](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Afilm-condensation-vertical-plate-numerical) — Heat Transfer, chapter 5

## Related in other subjects

- [Forced response depends on input, natural does not](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aforced-vs-natural-response-example) — Electrical Circuit Theory, chapter 3
- [Natural vs forced commutation](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Anatural-vs-forced-commutation) — Power Electronics, chapter 1
- [Natural vs artificial convection; heating curve](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Anatural-artificial-convection) — Electric Machine Design, chapter 2