Heat Transfer: Conduction

• Heat transfer is the process of thermal energy moving from a system at a higher temperature to another at a lower temperature.
• This transfer happens through three primary mechanisms: conduction, convection, and radiation.

Conduction

• Conduction is the transfer of heat through a material without any motion of the material itself.
• It occurs when there is a temperature gradient within a substance.
• Heat flows from the hotter to the colder region.
• It is most effective in solids, but can also happen in fluids.
• At a microscopic level, conduction involves the transfer of kinetic energy between adjacent atoms or molecules.
• In solids, especially metals, heat is also conducted by free electrons.
• The rate of heat conduction depends on the material's thermal conductivity (k), the area (A) through which heat is transferred, the temperature difference (ΔT), and the thickness (d) of the material.
• Fourier's Law of Conduction describes this relationship: Q = -kA(ΔT/d), where Q is the heat transfer rate.
• Materials with high thermal conductivity (e.g., metals) conduct heat rapidly, while those with low thermal conductivity (e.g., wood, plastic) are poor conductors and act as insulators.
• Examples include:
  • A metal spoon heating up when placed in a hot cup of coffee.
  • Heat flowing through the wall of a building on a cold day.
  • Touching a metal object that feels colder than a wooden object at the same room temperature due to the metal's higher conductivity drawing heat away from your hand more quickly.

Convection

• Convection is the transfer of heat through the movement of fluids (liquids or gases).
• It occurs when a fluid is heated, becomes less dense, and rises, displacing cooler fluid which then sinks.
• This creates a circulating current that transfers heat.
• There are two types of convection: natural (or free) and forced.
• Natural convection occurs due to density differences caused by temperature variations within the fluid.
• Forced convection occurs when an external force, such as a fan or pump, causes the fluid to move.
• The rate of heat transfer by convection depends on factors like the fluid's velocity, its thermal properties (density, specific heat, viscosity), and the geometry of the surface.
• Newton's Law of Cooling approximates the convective heat transfer: Q = hA(Ts - Tf), where:
  • Q is the heat transfer rate.
  • h is the convective heat transfer coefficient.
  • A is the surface area.
  • Ts is the surface temperature.
  • Tf is the fluid temperature.
• Examples include:
  • Boiling water, where hot water rises from the bottom of the pot and cooler water sinks to take its place.
  • A radiator heating a room, where warm air rises and cool air circulates back to the radiator.
  • The cooling of a computer's CPU by a fan.
  • Sea breezes, where warm air over land rises and cooler air from the sea moves in to replace it.

Radiation

• Radiation is the transfer of heat through electromagnetic waves.
• It does not require a medium and can occur in a vacuum.
• All objects with a temperature above absolute zero emit thermal radiation.
• The amount and type of radiation emitted depend on the object's temperature and surface properties.
• The rate of energy radiated by an object is described by the Stefan-Boltzmann Law: Q = εσAT^4, where:
  • Q is the heat transfer rate.
  • ε is the emissivity of the object (a value between 0 and 1, indicating how effectively it emits radiation).
  • σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4).
  • A is the surface area of the object.
  • T is the absolute temperature of the object in Kelvin.
• Emissivity is a measure of how effectively a surface emits thermal radiation. A black body has an emissivity of 1, meaning it is a perfect emitter and absorber of radiation.
• Objects also absorb radiation.
• The rate at which an object absorbs radiation depends on its absorptivity (which is equal to its emissivity according to Kirchhoff's Law of Thermal Radiation) and the amount of radiation incident on its surface.
• Examples include:
  • The sun warming the Earth.
  • Heat from a fireplace warming a room.
  • A microwave oven heating food.
  • The human body emitting infrared radiation.