Heat transfer mechanisms are the ways energy moves from one place to another due to temperature differences. Conduction, convection, and radiation are the three main types, each with unique characteristics and applications in everyday life and engineering.

Understanding these mechanisms is crucial for designing efficient thermal systems. Factors like temperature gradients, surface area, and material properties play key roles in determining how quickly heat flows, impacting everything from building insulation to industrial processes.

Heat Transfer Mechanisms

Mechanisms of heat transfer

• Conduction
  • Occurs through direct contact between particles of a substance, transferring kinetic energy from more energetic to less energetic particles
  • Takes place in solids, liquids, and gases, with solids being the most effective due to their tightly packed particles (metals, ceramics)
  • Driven by temperature gradients within a material, causing heat to flow from regions of higher temperature to regions of lower temperature
• Convection
  • Transfers heat through the movement of fluids, such as liquids or gases (water, air)
  • Combines the effects of conduction within the fluid and the bulk motion of the fluid itself
  • Can occur naturally due to buoyancy-driven flow (hot air rising) or can be forced by external means (fans, pumps)
• Radiation
  • Transmits heat through electromagnetic waves, such as infrared radiation from the sun or a fire
  • Does not require a medium for transmission, allowing heat transfer through vacuum (space)
  • Depends on factors such as the temperature, surface properties (emissivity, absorptivity), and geometry of the emitting and absorbing bodies

Factors affecting heat transfer

• Temperature gradient
  • Represents the difference in temperature between two points in a system, driving heat transfer from the higher temperature region to the lower temperature region
  • A steeper temperature gradient results in a higher rate of heat transfer (hot coffee cooling faster in a cold room)
• Surface area
  • Determines the size of the area available for heat transfer, with larger surface areas allowing for more effective heat exchange
  • Increasing the surface area, such as by using fins or heat exchangers, enhances the rate of heat transfer (radiators in cars)
• Material properties
  • Thermal conductivity measures a material's ability to conduct heat, with higher values indicating better heat transfer (copper, aluminum)
    • Materials with higher thermal conductivity allow heat to flow through them more easily, leading to faster heat transfer
  • Emissivity describes the ability of a surface to emit thermal radiation relative to a perfect blackbody, with values ranging from 0 to 1
    • Surfaces with higher emissivity are more effective at radiating heat (black paint, oxidized metals)
  • Absorptivity quantifies the ability of a surface to absorb thermal radiation, with values ranging from 0 to 1
    • Surfaces with higher absorptivity are better at absorbing heat from their surroundings (dark-colored objects)

Conduction and Convection Heat Transfer

Fourier's law in conduction

• Fourier's law quantifies heat transfer rates in conduction problems using the equation: $q = -kA\frac{dT}{dx}$
  • $q$: heat transfer rate in watts (W)
  • $k$: thermal conductivity of the material in watts per meter-kelvin (W/m·K)
  • $A$: cross-sectional area perpendicular to the direction of heat flow in square meters (m²)
  • $\frac{dT}{dx}$: temperature gradient in kelvins per meter (K/m)
• Steady-state conduction occurs when the temperature distribution does not change with time (insulated walls)
• One-dimensional conduction refers to heat transfer along a single spatial dimension, such as through a plane wall
• Thermal resistance is the resistance to heat flow, analogous to electrical resistance, and can be calculated for a plane wall using $R = \frac{L}{kA}$, where $L$ is the wall thickness in meters (m)

Convective heat transfer analysis

• Newton's law of cooling describes convective heat transfer using the equation: $q = hA(T_s - T_∞)$
  • $q$: convective heat transfer rate in watts (W)
  • $h$: convective heat transfer coefficient in watts per square meter-kelvin (W/m²·K)
  • $A$: surface area exposed to the fluid in square meters (m²)
  • $T_s$: surface temperature in kelvins (K)
  • $T_∞$: fluid temperature far from the surface in kelvins (K)
• The convective heat transfer coefficient ($h$) depends on various factors:
  • Fluid properties such as density, viscosity, and thermal conductivity
  • Flow characteristics, including velocity and turbulence (laminar vs. turbulent flow)
  • Surface geometry and roughness (flat plates, cylinders, spheres)
• The Nusselt number ($Nu$) is a dimensionless parameter that relates convective heat transfer to conductive heat transfer, calculated using $Nu = \frac{hL}{k}$, where $L$ is a characteristic length in meters (m) and $k$ is the fluid's thermal conductivity in watts per meter-kelvin (W/m·K)

Thermal Radiation

Principles of thermal radiation

• Blackbody radiation
  • A perfect blackbody is an ideal surface that absorbs all incident radiation and emits the maximum possible energy at a given temperature
  • The spectral emissive power of a blackbody is given by Planck's law: $E_{bλ} = \frac{C_1}{\lambda^5[exp(\frac{C_2}{\lambda T})-1]}$
    • $C_1$ and $C_2$: radiation constants (3.742 × 10⁻¹⁶ W·m² and 1.439 × 10⁻² m·K)
    • $\lambda$: wavelength in micrometers (μm)
    • $T$: absolute temperature in kelvins (K)
  • The Stefan-Boltzmann law gives the total emissive power of a blackbody: $E_b = \sigma T^4$
    • $E_b$: total blackbody emissive power in watts per square meter (W/m²)
    • $\sigma$: Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴)
• Emissivity ($ε$)
  • Emissivity is the ratio of a surface's emissive power to that of a blackbody at the same temperature, ranging from 0 to 1
  • A perfect blackbody has an emissivity of 1, while real surfaces have lower values (polished metals ~0.1, non-metals ~0.9)
  • Kirchhoff's law states that for a surface in thermal equilibrium, emissivity equals absorptivity ($ε = α$)
• Absorptivity ($α$)
  • Absorptivity is the fraction of incident radiation absorbed by a surface, ranging from 0 (reflective) to 1 (absorptive)
  • Surfaces with higher absorptivity are more effective at absorbing heat from their surroundings (black surfaces)