# Heat transfer

Heat transfer occurs when energy moves between locations or materials because the temperatures of the two differ.<sup>[1](https://openstax.org/books/university-physics-volume-2/pages/1-1-temperature-and-thermal-equilibrium)</sup> It is fundamental to everyday activities such as home heating and cooking, to industrial processes, and to the design of engines, refrigerators, and spacecraft.<sup>[2](https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry)</sup> Heat always flows from a hotter region to a cooler one, and when the temperatures become equal the net transfer stops.<sup>[3](https://openstax.org/books/physics/pages/11-2-heat-specific-heat-and-heat-transfer)</sup>

| Key fact | Detail |
|---|---|
| Mechanisms | Three modes: conduction (direct contact), convection (bulk motion of a fluid), and radiation (electromagnetic waves); all three can operate simultaneously.<sup>[3](https://openstax.org/books/physics/pages/11-2-heat-specific-heat-and-heat-transfer)</sup> |
| Sensible heat | \( Q = mc\Delta T \), where \( c \) is specific heat; water's specific heat is 4186 J/(kg·°C), about five times that of glass.<sup>[2](https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry)</sup><sup> • </sup><sup>[3](https://openstax.org/books/physics/pages/11-2-heat-specific-heat-and-heat-transfer)</sup> |
| Conduction rate | \( P = kA(T_h - T_c)/d \): proportional to thermal conductivity \( k \), area \( A \), and temperature difference, inversely proportional to thickness \( d \).<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> |
| Radiation rate | \( P_{\text{net}} = \sigma e A (T_2^4 - T_1^4) \), with the Stefan-Boltzmann constant \( \sigma = 5.67 \times 10^{-8} \) J/s·m²·K⁴ and emissivity \( e \leq 1 \).<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> |
| Insulation metric | The R factor is \( d/k \); the rate of conductive heat transfer is inversely proportional to R, and US R-values are quoted in ft²·°F·h/Btu.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> |
| Vacuum constraint | In a vacuum, heat moves only by radiation, with no conduction or convection; radiation is the only mode by which a spacecraft can reject waste heat.<sup>[5](https://www.nasa.gov/smallsat-institute/sst-soa/thermal-control/)</sup> |
| Phase change | Heat absorbed or released in melting or boiling, \( Q = mL_f \) or \( Q = mL_v \), changes no temperature: ice melts at 333 kJ/kg and water boils at 2256 kJ/kg at 1 atm.<sup>[6](https://openstax.org/books/university-physics-volume-2/pages/1-5-phase-changes)</sup> |

## Heat as energy in transit

Heat and temperature are distinct quantities. Temperature measures the average kinetic energy of a substance's molecules and predicts the direction of transfer; heat is energy in transit that exists only while it moves across a boundary. Neither heat nor work is a property a system can contain or store.<sup>[7](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)</sup> In thermodynamic terms, heat added to a system and work done by it change the system's internal energy according to the first law, \( \Delta E_{\text{int}} = Q - W \); the change in internal energy between two states is the same whatever path the system takes.<sup>[8](https://openstax.org/books/university-physics-volume-2/pages/3-3-first-law-of-thermodynamics)</sup>

For a substance that changes temperature without changing phase, the heat transferred is approximated by \( Q = mc\Delta T \). The specific heat \( c \) is the heat needed to raise the temperature of 1.00 kg of a substance by 1.00 °C, and it must be looked up for each material and phase: aluminum 900, copper 387, ice (averaged from −50 °C to 0 °C) 2090, and liquid water 4186 J/(kg·°C).<sup>[2](https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry)</sup> Water's high specific heat, among the largest of any material, is important for sustaining life on Earth.<sup>[2](https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry)</sup>

## Conduction

Conduction transfers heat through direct molecular interaction, within a solid or between solids in contact, without any bulk movement of the material.<sup>[7](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)</sup> Microscopically, molecules in the hotter region have higher average kinetic energy, and collisions pass energy to cooler neighbors; in metals, free valence electrons also carry energy through collisions.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup>

The conduction rate through a slab follows Fourier's law, \( P = kA(T_h - T_c)/d \). It rises with the temperature difference and the cross-sectional area and falls with the material's thickness, and the thermal conductivity \( k \) sets how well the material conducts: aluminum is about 220 W/m·°C, while polystyrene foam is about 0.035 W/m·°C.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> The ratio \( d/k \), called the R factor, is large for a good insulator, and R factors for layers in series simply add.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> The best insulators, including fiberglass, wool, goosedown, and polystyrene foam, all contain many small pockets of air, taking advantage of air's poor thermal conductivity.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> In buildings, insulation works by trapping these air pockets in walls, ceilings, and floors, and a thermal boundary of insulation, windows, and doors reduces both energy waste and occupant discomfort.<sup>[9](https://bsesc.energy.gov/energy-basics/heat-flow)</sup>

## Convection

Convection transfers heat by the macroscopic motion of a fluid, so it occurs only in liquids and gases, in which molecules are free to move.<sup>[10](https://www1.eere.energy.gov/education/pdfs/basics_thermodynamicsguidestudent.pdf)</sup> When motion is driven by density differences produced by temperature gradients within the fluid, it is natural convection, as when a hot water radiator warms a room; when a pump or fan drives the flow, it is forced convection, as in a heat exchanger.<sup>[7](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)</sup>

Convection is harder to analyze than conduction because no single material property describes it; the transfer depends on fluid velocity, viscosity, surface roughness, and flow type, so it is treated empirically through a convective heat transfer coefficient \( h \).<sup>[7](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)</sup> Typical values span a wide range: free convection in air runs from 0.5 to 1000 W/(m²·K), forced convection in water and other liquids from 50 to 10000 W/(m²·K), and boiling water from 3000 to 100000 W/(m²·K).<sup>[11](https://www.engineeringtoolbox.com/amp/convective-heat-transfer-d_430.html)</sup> Convection also shapes weather: water vapor carried upward by convection condenses in thunderheads, releasing energy that drives the cloud as much as 20.0 km into the stratosphere in a positive-feedback process that also powers hurricanes.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup>

## Radiation

Radiation transfers heat by electromagnetic waves emitted because of a body's temperature, and it needs no medium: the Sun warms Earth across largely empty space, with no possibility of conduction or convection en route.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> Most thermal radiation lies in the infrared part of the spectrum, though some falls in the visible region.<sup>[7](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)</sup> For spacecraft applications the thermal radiation band is taken as 0.1 to 100 µm in wavelength, and analyses commonly split it into solar wavelengths below 3 µm and infrared wavelengths above 3 µm.<sup>[5](https://www.nasa.gov/smallsat-institute/sst-soa/thermal-control/)</sup>

The net radiative exchange between an object and its surroundings is \( P_{\text{net}} = \sigma e A (T_2^4 - T_1^4) \), where \( e \) is the emissivity, a dimensionless number with a maximum of 1.0 for an ideal black body.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup><sup> • </sup><sup>[7](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)</sup> Because the rate depends on the fourth power of absolute temperature, higher temperatures produce much more radiation, and especially more at shorter wavelengths, which is why a stove element glows red to orange while blast-furnace steel glows yellow to white.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup> [Human skin](https://www.edgepedia.org/human-skin) is a very good infrared absorber and emitter, with an emissivity of 0.97, so an unclothed person in a 22.0 °C room radiates heat at about 99 W, a significant loss against a resting metabolic production of about 125 W.<sup>[4](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)</sup>

## Phase change as a special case

Heat transfer with a change of phase is sometimes treated as a fourth mechanism, though it is really a specialized case of the other three in which the material changes state.<sup>[12](https://ntrs.nasa.gov/api/citations/20150002905/downloads/20150002905.pdf)</sup> During melting, boiling, freezing, or condensation, the transferred heat goes into breaking or forming intermolecular bonds rather than raising temperature, so the temperature stays constant until the transition completes.<sup>[6](https://openstax.org/books/university-physics-volume-2/pages/1-5-phase-changes)</sup> The quantities involved are large: melting ice absorbs 333 kJ/kg, boiling water at 100 °C absorbs 2256 kJ/kg, and sweat evaporating at body temperature removes about 2430 kJ/kg, roughly 10 percent more than at the boiling point, which is the basis of evaporative cooling in hot weather.<sup>[6](https://openstax.org/books/university-physics-volume-2/pages/1-5-phase-changes)</sup>

## Engineering applications

Heat exchangers, devices that transfer thermal energy from one fluid to another without mixing them, combine all the modes: convection on each side of a tube wall and conduction through the wall itself.<sup>[7](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)</sup> Their performance is summarized by an overall heat transfer coefficient \( U \), which combines the two fluid-side coefficients and the wall's conductivity; typical values range from about 5 W/(m²·K) for gases at atmospheric pressure in tubular exchangers to 1000–4000 W/(m²·K) for liquid-to-liquid plate exchangers and 1500–4000 W/(m²·K) for steam condensing against cooling water.<sup>[13](https://www.engineeringtoolbox.com/heat-transfer-coefficients-exchangers-d_450.html)</sup>

In spacecraft thermal control the modes separate cleanly. Inside a pressurized cabin, conduction and convection usually dominate, and analysts often neglect radiant exchange with only minor loss of accuracy; outside, in vacuum, radiation is the only way to reject waste heat, so radiators, coatings, and multilayer insulation manage the balance between absorbed solar heating and emitted infrared radiation.<sup>[12](https://ntrs.nasa.gov/api/citations/20150002905/downloads/20150002905.pdf)</sup><sup> • </sup><sup>[5](https://www.nasa.gov/smallsat-institute/sst-soa/thermal-control/)</sup> On Earth's surface, the energy budget works the same way at planetary scale: evaporation removes about 25 percent of incoming solar energy from the surface, convection about 5 percent, and net thermal infrared radiation about 17 percent.<sup>[14](https://science.nasa.gov/earth/earth-observatory/climate-and-earths-energy-budget/)</sup>

## References

1. [Temperature and Thermal Equilibrium, University Physics Volume 2, OpenStax](https://openstax.org/books/university-physics-volume-2/pages/1-1-temperature-and-thermal-equilibrium)
2. [Heat Transfer, Specific Heat, and Calorimetry, University Physics Volume 2, OpenStax](https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry)
3. [Heat, Specific Heat, and Heat Transfer, Physics, OpenStax](https://openstax.org/books/physics/pages/11-2-heat-specific-heat-and-heat-transfer)
4. [Mechanisms of Heat Transfer, University Physics Volume 2, OpenStax](https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer)
5. [Thermal Control, State-of-the-Art of Small Spacecraft Technology, NASA](https://www.nasa.gov/smallsat-institute/sst-soa/thermal-control/)
6. [Phase Changes, University Physics Volume 2, OpenStax](https://openstax.org/books/university-physics-volume-2/pages/1-5-phase-changes)
7. [DOE Fundamentals Handbook, Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2 of 3 (DOE-HDBK-1012/2-92)](https://www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf)
8. [First Law of Thermodynamics, University Physics Volume 2, OpenStax](https://openstax.org/books/university-physics-volume-2/pages/3-3-first-law-of-thermodynamics)
9. [Heat Flow, Building Science Education, U.S. Department of Energy](https://bsesc.energy.gov/energy-basics/heat-flow)
10. [Thermodynamics Student Guide, U.S. Department of Energy](https://www1.eere.energy.gov/education/pdfs/basics_thermodynamicsguidestudent.pdf)
11. [Convective Heat Transfer, The Engineering ToolBox](https://www.engineeringtoolbox.com/amp/convective-heat-transfer-d_430.html)
12. [Human Spaceflight: Thermal Control Interface, NASA Technical Reports Server](https://ntrs.nasa.gov/api/citations/20150002905/downloads/20150002905.pdf)
13. [Heat Exchangers: Overall Heat Transfer Coefficients, The Engineering ToolBox](https://www.engineeringtoolbox.com/heat-transfer-coefficients-exchangers-d_450.html)
14. [Climate and Earth's Energy Budget, NASA Science](https://science.nasa.gov/earth/earth-observatory/climate-and-earths-energy-budget/)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Classical physics › Thermodynamics*

*Initially written Sep 17, 2026 · Reviewed: Sep 17, 2026; Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*

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