Modes of Heat Transfer
Heat transfer is the movement of thermal energy from a region of higher temperature to a region of lower temperature through three distinct mechanisms: conduction (direct molecular collisions in solids/fluids), convection (bulk movement of fluid carrying thermal energy), and radiation (electromagnetic wave emission requiring no medium). Each mode operates by different physical laws — Fourier's Law for conduction, Newton's Law of Cooling for convection, and the Stefan-Boltzmann Law for radiation — and all three often occur simultaneously in real engineering systems such as furnaces, heat exchangers, and building insulation.
Key Formula
Q_cond = −kA(dT/dx) | Q_conv = hA(T_s − T∞) | Q_rad = εσAT⁴
LaTeX: Q_{cond} = -kA\frac{dT}{dx}, \quad Q_{conv} = hA(T_s - T_\infty), \quad Q_{rad} = \varepsilon \sigma A T^4
| Symbol | Meaning | Unit |
|---|---|---|
| k | Thermal conductivity of material | W/(m·K) |
| h | Convective heat transfer coefficient | W/(m²·K) |
| ε | Emissivity of surface (0 to 1) | dimensionless |
| σ | Stefan-Boltzmann constant (5.67 × 10⁻⁸) | W/(m²·K⁴) |
| A | Surface area through which heat transfers | m² |
| T | Absolute temperature of the surface | K |
Worked Example
Problem
A metal rod (k = 50 W/m·K, cross-section A = 0.01 m²) has a temperature difference of 100 K across a length of 0.5 m. Calculate the conductive heat transfer rate.
Solution
Step 1: Use Fourier's Law: Q = −kA(ΔT/Δx). Step 2: ΔT/Δx = 100 K / 0.5 m = 200 K/m (temperature gradient). Step 3: Q = −50 × 0.01 × (−200) = 50 × 0.01 × 200. Step 4: Q = 100 W (magnitude; heat flows from hot to cold end).
Answer
Conductive heat transfer rate Q = 100 W
Comparison of the Three Modes of Heat Transfer
| Property | Conduction | Convection | Radiation |
|---|---|---|---|
| Governing Law | Fourier's Law | Newton's Law of Cooling | Stefan-Boltzmann Law |
| Medium Required | Solid or stationary fluid | Moving fluid (liquid or gas) | None (vacuum possible) |
| Driving Potential | Temperature gradient | Temperature difference | Temperature (T⁴) |
| Key Coefficient | Thermal conductivity k | Heat transfer coefficient h | Emissivity ε |
| Typical Applications | Metals, walls, PCBs | Cooling fins, HVAC, oceans | Solar energy, furnaces |
| Rate Dependency | Linear with ΔT | Linear with ΔT | Fourth power of T |
Interactive Tools
PhET Energy Forms and Changes
Visualise heat transfer by conduction and convection in interactive scenarios
Open ToolKhan Academy – Heat Transfer
Video lessons covering conduction, convection, and radiation with examples
Open ToolWolfram Alpha
Calculate heat transfer rates using Fourier's, Newton's, or Stefan-Boltzmann formulae
Open Tool
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Related Terms
First Law of Thermodynamics
The First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another, making it a statement of conservation of energy applied to thermodynamic systems. For any process, the change in internal energy of a system equals the heat added to the system minus the work done by the system on its surroundings. This principle underpins the analysis of engines, refrigerators, and all energy-conversion devices in engineering and science.
Entropy
Entropy is a thermodynamic state function that quantifies the degree of disorder, randomness, or the number of microstates available to a system at a given macrostate. Macroscopically, it is defined via the Clausius inequality as the ratio of reversible heat exchange to absolute temperature; microscopically, Boltzmann's formula connects it to the number of microscopic configurations. Entropy always increases in irreversible processes in isolated systems, driving systems toward equilibrium and explaining the thermodynamic arrow of time.
Absolute Zero
Absolute zero is the lowest theoretically possible temperature, defined as 0 K (−273.15°C or −459.67°F), at which a system would have minimum possible internal energy and all classical thermal motion ceases. At absolute zero, quantum mechanical effects dominate: particles occupy their lowest quantum energy states (zero-point energy), meaning even at 0 K some residual energy remains due to Heisenberg's uncertainty principle. The Third Law of Thermodynamics establishes that absolute zero can be approached asymptotically but never actually reached in a finite number of cooling steps.
"Heat" derives from Old English "hætu." "Conduction" from Latin "conducere" (to lead together); "convection" from Latin "convectio" (a carrying together, from "convehere"); "radiation" from Latin "radiatio" (a shining, from "radius" — ray). Fourier established the mathematical theory of conduction in his 1822 work "Théorie analytique de la chaleur."