---
title: "Modes of heat transfer with rate equations"
subject: "Heat Transfer"
chapter: 1
key: "semester_5/heat_transfer:modes-of-heat-transfer"
source: https://www.bctengineer.com/q/semester_5/heat_transfer/modes-of-heat-transfer
site: BCT Engineering
---

# Modes of heat transfer with rate equations

Heat Transfer · Chapter 1: Review on Basic Concepts of Heat Transfer

- Asked in: year not given, 5 marks
- Video: [Heat Transfer - Conduction, Convection, and Radiation](https://www.youtube.com/watch?v=bRZwzy0xvhM) — The Organic Chemistry Tutor
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/heat_transfer/modes-of-heat-transfer
- Whole chapter: https://www.bctengineer.com/md/semester_5/heat_transfer/chapter-1

## Question

Explain the three modes of heat transfer. Write the rate equation of each mode and give one engineering example of each.

## Short answer

Heat is transferred by conduction (Fourier's law Q = -kA dT/dx, e.g., furnace wall), convection (Newton's law Q = hA(Ts − T∞), e.g., radiator), and radiation (Stefan–Boltzmann Q = εσA(Ts⁴ − Tsur⁴), e.g., solar heat).

## Answer

Heat transfer is the transfer of thermal energy because of a temperature difference. It occurs by conduction, convection and radiation, and in most practical problems two or three modes act together.

#### Conduction
Energy moves from a hotter to a colder part of a body (or between bodies in contact) by molecular vibration, free-electron motion and collisions, without bulk movement of matter. It is the only mode in an opaque solid. The rate is given by Fourier's law:

$$
Q = -kA\frac{dT}{dx}
$$

where $k$ is thermal conductivity (W/m K), $A$ the area normal to heat flow and $dT/dx$ the temperature gradient. The minus sign shows that heat flows toward falling temperature.
Example: heat flow through a furnace wall.

#### Convection
Energy is carried by the motion of a fluid over a surface. It is conduction plus bulk fluid motion. If the motion is caused by a fan or pump it is **forced** convection; if it is caused by density differences it is **natural** convection. Newton's law of cooling gives the rate:

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

where $h$ is the convective heat transfer coefficient (W/m$^2$ K).
Example: cooling of an engine radiator by air, or a hot cup of tea cooling in a room.

#### Radiation
Energy is emitted by every body above absolute zero as electromagnetic waves. It needs no medium and also works in vacuum. For a real surface:

$$
Q = \varepsilon\sigma A\,(T_s^4 - T_{sur}^4)
$$

with $\sigma = 5.67\times10^{-8}\ \text{W/m}^2\text{K}^4$, $\varepsilon$ the emissivity and temperatures in kelvin.
Example: heat received from the sun, heat loss from a boiler furnace to its surroundings.

| Mode | Needs medium | Driving force | Law |
|---|---|---|---|
| Conduction | Yes (stationary) | $\Delta T$ | Fourier |
| Convection | Yes (moving fluid) | $\Delta T$ | Newton |
| Radiation | No | $T_1^4 - T_2^4$ | Stefan-Boltzmann |

## Check yourself

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

1. Which equation is the rate law of conduction, and what does its minus sign mean?
   A. Q = -kA dT/dx; heat flows toward falling temperature
   B. Q = hA(Ts - Tinf); heat flows toward the fluid
   C. Q = eps sigma A(T^4 - Tsur^4); heat flows toward the surface
   D. Q = -kA dT/dx; heat flows toward rising temperature
   Answer: A. Fourier's law has a minus sign so that Q is positive in the direction of decreasing temperature. (Key point: Fourier's law)

2. What does convection add to plain conduction in a fluid?
   A. Electromagnetic waves
   B. Bulk motion of the fluid
   C. Free-electron motion
   D. Molecular vibration in a fixed lattice
   Answer: B. Convection is conduction plus bulk fluid motion, forced (fan/pump) or natural (density differences). (Key point: Convection)

3. Which statement about radiation is correct?
   A. It needs a stationary solid medium
   B. It needs a moving fluid
   C. It needs no medium and works in vacuum
   D. It occurs only above 0 degrees C
   Answer: C. Radiation is by electromagnetic waves, emitted by every body above absolute zero, and works in vacuum. (Key point: Radiation)

## Related in Heat Transfer

- [General heat conduction equation in Cartesian coordinates](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Ageneral-heat-conduction-equation-cartesian) — Heat Transfer, chapter 2
- [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
- [Heat exchanger types and LMTD derivation](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Aclassification-heat-exchangers-lmtd-derivation) — Heat Transfer, chapter 6
- [Effectiveness-NTU analysis of a heat exchanger](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Aeffectiveness-ntu-counterflow-oil-water) — Heat Transfer, chapter 6
- [Composite furnace wall heat loss](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Acomposite-furnace-wall-interface-temperatures) — Heat Transfer, chapter 2
- [Heat loss from insulated steam pipe](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Ainsulated-steam-pipe-heat-loss) — Heat Transfer, chapter 2

## Related in other subjects

- [Derive one-dimensional heat equation](https://www.bctengineer.com/question.md?key=semester_4%2Fapplied_mathematics%3Aheat-eq-derive) — Applied Mathematics, chapter 3, asked 5×
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- [Air compressor: heat transfer rate](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Acompressor-air-heat-transfer-rate) — Fundamental of Thermodynamics & Heat Transfer, chapter 4