---
title: "Newton's law of cooling and convection coefficient"
subject: "Heat Transfer"
chapter: 3
key: "semester_5/heat_transfer:newtons-law-cooling-convection-coefficient"
source: https://www.bctengineer.com/q/semester_5/heat_transfer/newtons-law-cooling-convection-coefficient
site: BCT Engineering
---

# Newton's law of cooling and convection coefficient

Heat Transfer · Chapter 3: Convection Heat Transfer

- Asked in: year not given, 4 marks
- Video: [Newton's Law of Cooling | Conduction | Heat Transfer | #zafarsir #freeengineeringcourses #free #imp](https://www.youtube.com/watch?v=daJdFXNe99M) — Impact Academy Official
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/heat_transfer/newtons-law-cooling-convection-coefficient
- Whole chapter: https://www.bctengineer.com/md/semester_5/heat_transfer/chapter-3

## Question

State Newton's law of cooling. Define the convective heat transfer coefficient and list the factors on which it depends. Give typical ranges of h for natural convection of air, forced convection of air, forced convection of water and boiling water.

## Short answer

Newton's law: Q = hA(T_s - T_inf). The convective coefficient h is the heat flux per unit temperature difference, depending on flow type, fluid properties, geometry, and phase. Typical ranges: natural convection air 2-25, forced air 25-250, forced water 250-15000, boiling water 2500-100000 W/m^2K.

## Answer

**Newton's law of cooling:** the rate of convective heat transfer between a surface and a fluid is proportional to the surface area and to the temperature difference between the surface and the fluid:

$$
Q = hA\,(T_s - T_\infty)
$$

#### Convective heat transfer coefficient
$h$ (W/m$^2$ K) is the heat flow per unit area per unit temperature difference between the surface and the bulk fluid. It is not a property of the fluid alone; it depends on the whole flow situation. It is found from $h = -k_f\,(\partial T/\partial y)_{wall}/(T_s-T_\infty)$, which links it to the fluid conductivity and the temperature gradient at the wall.

#### Factors affecting $h$
- Type of flow: natural or forced, laminar or turbulent.
- Fluid properties: density, viscosity, thermal conductivity, specific heat, expansion coefficient.
- Fluid velocity and temperature difference.
- Geometry: shape, size, orientation and roughness of the surface.
- Phase change (boiling, condensation) raises $h$ very much.

#### Typical ranges

| Situation | $h$ (W/m$^2$ K) |
|---|---|
| Natural convection, air | 2 to 25 |
| Forced convection, air | 25 to 250 |
| Forced convection, water | 250 to 15 000 |
| Boiling water | 2500 to 100 000 |
| Condensing steam | 5000 to 100 000 |

## Check yourself

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

1. Newton's law of cooling states Q is proportional to:
   A. Surface area and surface-to-fluid temperature difference
   B. Area and the fourth power of temperature
   C. Temperature gradient and k
   D. Velocity only
   Answer: A. Q = hA(Ts - Tinf). (Key point: Newton's law)

2. Which statement about h is correct?
   A. It is a fixed property of the fluid
   B. It depends on the whole flow situation, not the fluid alone
   C. It depends only on temperature
   D. It is the same for all geometries
   Answer: B. h depends on flow type, properties, velocity, geometry and phase change. (Key point: Nature of h)

3. Which order of h (low to high) is right?
   A. Forced air, natural air, boiling water, forced water
   B. Boiling water, forced water, forced air, natural air
   C. Natural air, forced air, forced water, boiling water
   D. Natural air, forced water, forced air, boiling water
   Answer: C. Ranges: 2-25, 25-250, 250-15000, 2500-100000 W/m^2K. (Key point: Typical ranges)

## Related in Heat Transfer

- [Natural and forced convection compared](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Afree-versus-forced-convection) — Heat Transfer, chapter 3
- [Dimensional analysis of forced convection](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Abuckingham-pi-forced-convection) — Heat Transfer, chapter 3
- [Convective mass transfer and analogies](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Aconvective-mass-transfer-analogy-correlations) — Heat Transfer, chapter 7
- [Factors affecting heat transfer and its applications](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Afactors-applications-heat-transfer) — Heat Transfer, chapter 1
- [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
- [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

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- [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
- [Insulating layer: minimum outside heat transfer coefficient](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Ainsulating-layer-min-outside-h-300c) — Fundamental of Thermodynamics & Heat Transfer, chapter 7, asked 2×
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