Heat Transfer: Conduction

• Conduction, convection, and radiation are the three primary ways heat is transferred.
• Heat transfer is critical in many applications, including engineering, climate science, and everyday life.

Conduction

• Conduction is the transfer of heat through a material by direct molecular contact.
• It occurs when a temperature gradient exists within a body.
• Heat flows from the region of higher temperature to the region of lower temperature.
• It requires physical contact between objects.
• It occurs in solids, liquids, and gases, but is most effective in solids due to their denser molecular structure.
• The rate of heat transfer by conduction is governed by Fourier's Law.
• Fourier's Law states that the heat flux is proportional to the temperature gradient and the thermal conductivity of the material.
• Thermal conductivity (k) is a measure of a material's ability to conduct heat.
• Materials with high thermal conductivity (e.g., metals) conduct heat readily.
• Materials with low thermal conductivity (e.g., insulators) resist heat transfer.
• The formula for heat transfer by conduction is Q = k * A * (ΔT/d), where:
  • Q is the rate of heat transfer.
  • k is the thermal conductivity of the material.
  • A is the cross-sectional area through which heat is transferred.
  • ΔT is the temperature difference across the material.
  • d is the thickness of the material.
• Applications of conduction include:
  • Heating a metal spoon in hot soup.
  • Heat transfer through the wall of a building.
  • Cooling of electronic components using heat sinks.

Convection

• Convection is the transfer of heat by the movement of fluids (liquids or gases).
• It involves the combined effects of conduction and fluid motion.
• There are two types of convection: natural (or free) and forced.
• Natural convection occurs when fluid motion is caused by buoyancy forces due to density differences resulting from temperature variations.
• Hotter fluids are less dense and rise, while cooler fluids are denser and sink, creating convection currents.
• Forced convection occurs when fluid motion is induced by an external source, such as a fan or pump.
• The rate of heat transfer by convection is governed by Newton's Law of Cooling.
• Newton's Law of Cooling states that the heat flux is proportional to the temperature difference between the surface and the fluid.
• The formula for heat transfer by convection is Q = h * A * (Ts - Tf), where:
  • Q is the rate of heat transfer.
  • h is the convection heat transfer coefficient.
  • A is the surface area in contact with the fluid.
  • Ts is the surface temperature.
  • Tf is the fluid temperature.
• The convection heat transfer coefficient (h) depends on various factors. These include fluid properties, flow velocity, and the geometry of the surface.
• Applications of convection include:
  • Boiling water in a pot.
  • Cooling a computer with a fan.
  • Weather patterns (e.g., sea breezes).
  • Heating and cooling systems in buildings.

Radiation

• Radiation is the transfer of heat by electromagnetic waves.
• It does not require a medium and can occur through a vacuum.
• All objects with a temperature above absolute zero emit thermal radiation.
• The rate of energy radiated by an object is described by the Stefan-Boltzmann Law.
• Stefan-Boltzmann Law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.
• The formula for heat transfer by radiation is Q = ε * σ * A * (T⁴ - T₀⁴), where:
  • Q is the rate of heat transfer.
  • ε is the emissivity of the object (a value between 0 and 1).
  • σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴).
  • A is the surface area of the object.
  • T is the absolute temperature of the object.
  • T₀ is the absolute temperature of the surroundings.
• Emissivity (ε) is a measure of how effectively an object emits thermal radiation.
• A black body has an emissivity of 1, meaning it is a perfect emitter and absorber of radiation.
• Shiny surfaces have low emissivities and reflect more radiation.
• Applications of radiation include:
  • The sun heating the Earth.
  • Heat from a fireplace.
  • Microwave ovens heating food.
  • Infrared cameras detecting heat signatures.

Combined Heat Transfer

• In many real-world scenarios, heat transfer occurs through a combination of conduction, convection, and radiation.
• For example, a hot cup of coffee loses heat through:
  • Conduction through the cup material.
  • Convection from the cup's surface to the surrounding air.
  • Radiation from the cup's surface to the surroundings.
• Analyzing these combined heat transfer mechanisms is essential for designing efficient thermal systems.
• Engineers often use heat transfer correlations and numerical simulations to predict heat transfer rates accurately.

Factors Affecting Heat Transfer

• Several factors can influence the rate of heat transfer in each mode:
  • Temperature difference: Larger temperature differences lead to higher heat transfer rates.
  • Surface area: Larger surface areas allow for more heat transfer.
  • Material properties: Thermal conductivity, convection heat transfer coefficient, and emissivity play crucial roles.
  • Fluid properties: Density, viscosity, and specific heat of fluids affect convection heat transfer.
  • Geometry: The shape and orientation of objects influence both convection and radiation.
  • Air flow: Increase in airflow increases amount of heat lost