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Heat Transfer
Conduction, Convection & Radiation

Explore the three fundamental mechanisms by which thermal energy moves from one place to another: through direct contact, fluid motion, and electromagnetic waves.

High School Physics

What Is Heat Transfer?

Heat is thermal energy that flows from a region of higher temperature to a region of lower temperature. This flow never reverses spontaneously: it always proceeds down the temperature gradient.

Understanding these three modes explains everything from why a metal spoon gets hot in soup to how the Sun warms the Earth across the vacuum of space.

The Three Modes at a Glance

Conduction
Energy passes through direct molecular contact. Vibrating particles bump into neighbours, transferring kinetic energy along a solid.
Convection
Energy moves via bulk fluid motion. Warmer, less-dense fluid rises while cooler fluid sinks, creating circulation currents.
Radiation
Energy travels as electromagnetic waves. No medium is required: radiation can cross a perfect vacuum.

Why Does It Matter?

Every engineering system that involves temperature relies on understanding heat transfer. From building insulation to spacecraft thermal shields, choosing the right materials and designs depends on knowing which mode dominates.

1
Cooking: A pan conducts heat to food, boiling water convects, and a broiler radiates.
2
Weather: Convection currents drive wind patterns and thunderstorms across the globe.
3
Space: With no air in the vacuum, radiation is the only way heat reaches Earth from the Sun.

Conduction: Fourier's Law

Hot \(T_H\) Cold \(T_C\) Heat flow \(\dot{Q}\) Length \(L\) Cross-section area \(A\)

Convection: Newton's Law of Cooling

Warm rises Cool sinks Heat source Surface area \(A_s\)

Radiation: Stefan-Boltzmann Law

\(T\) Absorber Electromagnetic waves No medium required

Key Distinction: Medium Requirements

Property Conduction Convection Radiation
Medium needed? Solid (best) Fluid (liquid/gas) None (vacuum OK)
Mechanism Molecular vibration Bulk fluid motion EM waves
Speed Slow in solids Moderate Speed of light
Key variable \(k\) (conductivity) \(h\) (coefficient) \(\varepsilon\) (emissivity)

How to Identify the Mode

1
Is there a vacuum? If heat crosses empty space with no material medium, it must be radiation.
2
Is a fluid moving? If a liquid or gas is circulating (rising/sinking or being blown), it is convection.
3
Are two solids in contact? If heat passes through a solid from one end to another (or between touching surfaces), it is conduction.
4
Multiple modes? Many real scenarios involve two or three modes at once. A pot on a stove: conduction through the metal, convection in the boiling water, radiation from the flame.

Example 1: Conduction Through a Wall

\(35\,^\circ\text{C}\) \(20\,^\circ\text{C}\) \(L = 0.25\;\text{m}\) \(k = 0.8\;\text{W/(m}\cdot\text{K)},\quad A = 10\;\text{m}^2\)

Example 2: Convection from a Heated Plate

\(T_s = 120\,^\circ\text{C}\) \(T_\infty = 25\,^\circ\text{C}\) (air) \(h = 15\;\frac{\text{W}}{\text{m}^2\cdot\text{K}}\) \(A_s = 0.5\;\text{m}^2\)

Example 3: Radiation from a Hot Sphere

A steel sphere with emissivity \(\varepsilon = 0.6\), surface area \(A = 0.02\;\text{m}^2\), is heated to \(T = 500\;\text{K}\). Find the radiated power.

Natural vs Forced Convection

Natural Convection
Driven by buoyancy: warm fluid rises, cool fluid sinks. No external device needed. Example: hot air rising above a radiator heater.
Forced Convection
Driven by an external force such as a fan, pump, or wind. Much higher \(h\) values. Example: a computer fan blowing air over a CPU.

Thermal Conductivity \(k\) Values

Material \(k\) (\(\text{W/(m}\cdot\text{K)}\)) Classification
Diamond 2000 Excellent conductor
Copper 401 Excellent conductor
Steel 50 Good conductor
Glass 1.0 Poor conductor
Wood 0.15 Insulator
Styrofoam 0.03 Excellent insulator

The \(T^4\) Power Dependence

\(T\) (K) \(\dot{Q}\) (relative) 0 200 400 600 800 \(T^4\) (radiation) Linear (for comparison)

Common Mistakes

✕ Confusing Heat and Temperature
Heat is energy in transit (measured in joules or watts). Temperature is a measure of average kinetic energy. They are related but not the same.
✕ Radiation Requires a Medium
A common error: thinking radiation needs air or another medium. Radiation is electromagnetic and travels perfectly through a vacuum.
✕ Using Celsius in \(\sigma T^4\)
The Stefan-Boltzmann law requires absolute temperature in Kelvin. Using Celsius gives wildly wrong answers because \(T^4\) amplifies the error.

Summary Comparison

Feature Conduction Convection Radiation
Medium Solid (best) Fluid required None needed
Governing Law Fourier's Law Newton's Cooling Stefan-Boltzmann
Formula \(\displaystyle \frac{kA\Delta T}{L}\) \(\displaystyle hA_s\Delta T\) \(\displaystyle \varepsilon\sigma AT^4\)
Key Parameter \(k\) \(h\) \(\varepsilon\), \(\sigma\)
Everyday Example Hot spoon in soup Boiling water Warmth from a fire
Temp. Dependence Linear (\(\Delta T\)) Linear (\(\Delta T\)) \(T^4\) (very strong)

Question 1 of 5

A metal spoon left in a pot of hot soup becomes warm at the handle. Which mode of heat transfer is primarily responsible?

Question 2 of 5

Sunlight warms the Earth after travelling through the vacuum of space. This is an example of heat transfer by:

Question 3 of 5

A student doubles the absolute temperature of a black body. By what factor does its radiated power increase?

Question 4 of 5

In convection, heat is transferred by:

Question 5 of 5

A brick wall has \(k = 0.7\;\text{W/(m}\cdot\text{K)}\), area \(A = 12\;\text{m}^2\), and thickness \(L = 0.20\;\text{m}\). If the inside temperature is \(22\,^\circ\text{C}\) and the outside is \(2\,^\circ\text{C}\), what is the rate of heat loss?