1. Introduction
In thermodynamics, heat transfer refers to the transfer of energy between a system and its surroundings due to a temperature difference. It is one of the two main modes of energy transfer, the other being work transfer.
Heat is a path function — its value depends on the process path, not just the initial and final states. It is denoted by \( Q \) (total) or \( \delta Q \) (infinitesimal).
2. Definition
Heat transfer is the energy interaction that occurs solely because of a temperature difference between the system and surroundings.
It always occurs from a region of higher temperature to a region of lower temperature, in accordance with the second law of thermodynamics.
3. Sign Convention
- Heat transfer to the system is positive (\( Q > 0 \)).
- Heat transfer from the system is negative (\( Q < 0 \)).
- This is the common engineering convention in thermal sciences.
4. Modes of Heat Transfer
4.1 Conduction
- Transfer of heat through a solid or stationary fluid due to molecular vibration and free electron movement.
- Described by Fourier’s Law:
\[
q = -k \frac{dT}{dx}
\]
where \( q \) = heat flux (W/m²), \( k \) = thermal conductivity (W/m·K), \( dT/dx \) = temperature gradient.
- Example: Heat flow through a metal rod.
4.2 Convection
- Transfer of heat between a solid surface and a moving fluid (liquid or gas) in contact with it.
- Combination of conduction (at the surface) and bulk fluid motion.
- Described by Newton’s Law of Cooling:
\[
q = h (T_s - T_\infty)
\]
where \( h \) = convection heat transfer coefficient (W/m²·K), \( T_s \) = surface temperature, \( T_\infty \) = fluid temperature far from surface.
- Types: Natural (free) convection, Forced convection.
- Example: Cooling of a hot plate in still air (natural convection) or with a fan (forced convection).
4.3 Radiation
- Transfer of heat via electromagnetic waves (infrared) without the need for a medium.
- Occurs between all bodies with temperature above absolute zero.
- Described by the Stefan–Boltzmann Law for a blackbody:
\[
q = \sigma T^4
\]
where \( \sigma \) = 5.670374419 × 10⁻⁸ W/m²·K⁴, \( T \) = absolute temperature (K).
- For real surfaces: \( q = \varepsilon \sigma T^4 \), where \( \varepsilon \) = emissivity (0–1).
- Example: Heat from the Sun reaching Earth.
5. Combined Modes
In many practical situations, more than one mode of heat transfer occurs simultaneously. For example, in a boiler tube, heat is transferred from hot gases to the tube wall by convection, through the tube wall by conduction, and from the inner wall to water/steam by convection.
6. Heat Transfer vs. Work Transfer
| Aspect |
Heat Transfer |
Work Transfer |
| Driving force |
Temperature difference |
Generalized force × displacement (e.g., pressure × volume change) |
| Energy form |
Disordered (random molecular motion) |
Ordered |
| Conversion |
Cannot be fully converted to work (limited by 2nd law) |
Can be fully converted to other work forms |
| Path/state function |
Path function |
Path function |
7. Practical Examples
- Conduction: Heat loss through building walls in winter.
- Convection: Cooling of engine coolant in a radiator.
- Radiation: Heat felt from a campfire.
- Combined: Heat transfer in a heat exchanger.
8. Enhancing or Reducing Heat Transfer
- Increase surface area (fins) to enhance convection.
- Use insulation to reduce conduction losses.
- Use reflective coatings to reduce radiative heat gain.
- Increase fluid velocity to enhance forced convection.
9. Key Points to Remember
- Heat transfer occurs only when there is a temperature difference.
- Three basic modes: conduction, convection, radiation.
- Often, modes act together in real systems.
- Governing laws: Fourier’s law, Newton’s law of cooling, Stefan–Boltzmann law.
- Sign convention: heat into system positive, heat out negative.