1.6 Mechanisms of Heat Transfer

Heat transfer is all about how energy moves from hot to cold. It's crucial for understanding everything from keeping your coffee warm to cooling your computer. There are three main ways heat moves: conduction, convection, and radiation.

Each method has its own quirks and formulas. Conduction happens through direct contact, convection involves fluid movement, and radiation uses electromagnetic waves. Understanding these helps us tackle real-world heat problems in buildings, cooking, and electronics.

Mechanisms of Heat Transfer

Mechanisms of heat transfer

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• Conduction involves heat transfer through direct contact between particles of matter, occurring in solids, liquids, and gases as heat flows from higher to lower temperature regions, with the rate depending on temperature gradient, material properties (thermal conductivity), cross-sectional area, and distance
• Convection transfers heat by the movement of fluids (liquids or gases), combining effects of conduction and fluid motion, with two types: natural convection driven by buoyancy forces from temperature differences (hot air rising) and forced convection induced by external means (fans, pumps), and the rate depends on fluid properties (density, viscosity, thermal conductivity), velocity, surface area, and temperature difference between the surface and fluid
• Radiation transfers heat through electromagnetic waves without requiring a medium (can occur in a vacuum), emitted and absorbed by all objects, with the rate proportional to the fourth power of absolute temperature ($T^4$) and depending on surface properties (emissivity, absorptivity), area, and view factor (geometric relationship between emitting and absorbing surfaces)

Formulas for heat transfer rates

• Conduction follows Fourier's law: $q = -kA\frac{dT}{dx}$, where $q$ is heat transfer rate (W), $k$ is thermal conductivity (W/m·K), $A$ is cross-sectional area (m²), and $\frac{dT}{dx}$ is temperature gradient (K/m), simplifying for steady-state conduction through a plane wall to $q = \frac{kA(T_1 - T_2)}{L}$, with $T_1$ and $T_2$ as surface temperatures (K) and $L$ as wall thickness (m)
  • The heat flux, which is the heat transfer rate per unit area, can be calculated as $q'' = q/A$
• Radiation follows the Stefan-Boltzmann law: $q = \varepsilon\sigma A(T_1^4 - T_2^4)$, where $\varepsilon$ is surface emissivity (0 ≤ $\varepsilon$ ≤ 1), $\sigma$ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴), $A$ is surface area (m²), and $T_1$ and $T_2$ are absolute temperatures (K) of the surface and surroundings

Heat transfer in real-world scenarios

• Insulation in buildings involves conduction through walls, windows, and roofs, convection from air leakage and natural convection within the building, and radiation from solar radiation through windows and heat emission from surfaces
  • The effectiveness of insulation is often characterized by its thermal resistance, which is the reciprocal of thermal conductivity
• Cooking on a stove involves conduction from the heating element to the pot, convection from the pot to the food by the motion of boiling water (pasta) or air (oven), and radiation from the heating element and pot to the surrounding environment
• Heat sinks in electronics involve conduction from the electronic component (CPU) to the heat sink, convection from the heat sink to the surrounding air often enhanced by fans (computer case), and usually negligible radiation from the heat sink to the environment compared to convection
  • The efficiency of heat transfer in this scenario is influenced by the heat transfer coefficient between the heat sink and the surrounding air

Additional heat transfer concepts

• Thermal diffusivity is a material property that measures the rate at which heat diffuses through a material, combining thermal conductivity, density, and specific heat capacity
• The heat transfer coefficient quantifies the heat transfer between a solid surface and a fluid, incorporating the effects of both conduction and convection in a single parameter