Heat Transfer Modes and Laws

Modes of Heat Transfer

• Conduction: Transfer of heat through solids, primarily by the movement of free electrons and vibrations. Solids are good conductors, while gases are poor conductors.
• Convection: Transfer of heat within fluids (liquids and gases) due to the movement of fluid particles. Convection can be free (natural) or forced, depending on the driving force.
• Radiation: Transfer of heat through electromagnetic waves. All objects emit and absorb radiation, and this mode is not dependent on a medium.

Conduction: Fourier's Law

• Fourier's Law describes heat conduction. Heat flux (rate of heat transfer per unit area) is proportional to the temperature gradient.
• The equation is: q = -kA(dT/dx)
  • q: rate of heat transfer
  • k: thermal conductivity of the material
  • A: area normal to heat flow
  • dT/dx: temperature gradient

Convection: Newton's Law of Cooling

• Newton's Law of Cooling describes convective heat transfer. The rate of heat transfer is proportional to the temperature difference between the surface and the surrounding fluid.
• The equation is: q = hA(Ts - Tf)
  • q: rate of heat transfer
  • h: convective heat transfer coefficient
  • A: surface area
  • Ts: surface temperature
  • Tf: fluid temperature

Radiation: Stefan-Boltzmann Law

• The Stefan-Boltzmann Law describes the rate of heat transfer by radiation from a surface. The rate of heat transfer is proportional to the fourth power of the absolute temperature of the surface.
• The equation is: q = εσAT^4
  • q: rate of heat transfer
  • ε: emissivity of the surface
  • σ: Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/m^2K^4)
  • A: surface area
  • T: absolute temperature of the surface

Problems and Applications

• The provided notes include numerous problems related to heat transfer calculation in various scenarios (e.g., slabs, cylinders).
• They demonstrate applying the above formulas to different situations involving conduction, convection, and radiation. The examples cover solving for heat transfer rates (q). This often requires known values of thermal conductivity (k) and convective heat transfer coefficient (h), material properties (like thickness) and temperature differences.

Explore the different modes of heat transfer, including conduction, convection, and radiation. Understand Fourier's Law for conduction and Newton's Law of Cooling for convection. This quiz will test your knowledge of these fundamental heat transfer concepts.