1: Heat transfer modes (conduction, convection, radiation)

Heat Transfer Modes (Conduction, Convection, Radiation)

Heat transfer describes the movement of thermal energy due to a temperature difference. Understanding the three fundamental modes – conduction, convection, and radiation – is essential, as they govern thermal processes in diverse systems, from electronics cooling to planetary energy balance. Each mode operates via distinct physical mechanisms.

1. Conduction:

Conduction involves heat transfer through direct molecular interaction within a substance (solid, liquid, or gas) or between substances in direct contact. Energy flows from regions of higher kinetic energy (higher temperature) to regions of lower kinetic energy (lower temperature). In solids, heat is transferred primarily by lattice vibrations (phonons) and, in conductive materials, by free electron movement. In stationary fluids, it occurs via molecular collisions. The rate of conductive heat transfer is governed by Fourier's Law: $q_x = -k A \frac{dT}{dx}$ Where:

• $q_x$ = Heat transfer rate in the x-direction (W)
• $k$ = Thermal conductivity (W/m·K), a material property indicating its ability to conduct heat.
• $A$ = Cross-sectional area perpendicular to heat flow (m²)
• $\frac{dT}{dx}$ = Temperature gradient in the x-direction (K/m)
  The negative sign indicates heat flows down the temperature gradient. Examples include heat flow through a metal rod or a brick wall.

2. Convection:

Convection is the transfer of heat between a solid surface and an adjacent moving fluid (liquid or gas). It combines two mechanisms: (1) conduction through the fluid layer immediately adjacent to the surface (where fluid velocity is effectively zero) and (2) the bulk motion and mixing of the fluid (advection), which carries the heated fluid away. Convection is quantified by Newton's Law of Cooling: $q = h A (T_s - T_\infty)$ Where:

• $q$ = Heat transfer rate (W)
• $h$ = Convective heat transfer coefficient (W/m²·K), dependent on fluid properties, flow velocity, and surface geometry.
• $A$ = Surface area (m²)
• $T_s$ = Surface temperature (K)
• $T_\infty$ = Bulk fluid temperature far from the surface (K)
  Convection is classified as:
• Forced Convection: Fluid motion is driven by external means (e.g., pump, fan).
• Natural (Free) Convection: Fluid motion arises from buoyancy forces due to density variations caused by temperature differences.

3. Radiation:

Thermal radiation is the transfer of energy via electromagnetic waves (primarily infrared). Unlike conduction and convection, it does not require a material medium and can occur through a vacuum. All matter above absolute zero emits thermal radiation due to molecular and atomic activity. The maximum possible radiative emission from an ideal surface (a blackbody) is given by the Stefan-Boltzmann Law: $E_b = \sigma T^4$ Where:

• $E_b$ = Blackbody emissive power (W/m²)
• $\sigma$ = Stefan-Boltzmann constant ($5.67 \times 10^{-8}$ W/m²·K⁴)
• $T$ = Absolute surface temperature (K)
  Real surfaces emit less than a blackbody. Their emission is given by $E = \varepsilon \sigma T^4$ where $\varepsilon$ (emissivity, $0 \leq \varepsilon \leq 1$) is a surface property. Radiation exchange between surfaces depends on their temperatures, emissivities, and geometric configuration (view factors). The sun warming Earth is a classic example of radiative heat transfer.