Heat transfer — the movement of thermal energy from higher to lower temperature — occurs through three fundamental mechanisms: conduction (direct molecular contact), convection (fluid motion), and radiation (electromagnetic waves). Engineers must understand and calculate all three to design HVAC systems, insulation, heat exchangers, electronic cooling solutions, and industrial processes. Conduction through a wall follows Fourier's law: Q = kA(T₁-T₂)/d, where k is thermal conductivity, A is area, and d is thickness. Convection at a surface follows Newton's law of cooling: Q = hA(Ts-T∞), where h is the convection coefficient. Radiation follows the Stefan-Boltzmann law: Q = εσA(T⁴₁-T⁴₂). Our heat transfer calculator computes heat flow rates for all three mechanisms, determines insulation R-values and U-factors for building applications, sizes heat exchangers using the LMTD method, and estimates steady-state temperatures in multi-layer wall assemblies.
Conduction through walls and insulation
Thermal conductivity (k) determines how readily a material conducts heat: copper 385 W/m·K, aluminum 205, steel 50, glass 1.0, brick 0.6-1.0, wood 0.12-0.17, fiberglass insulation 0.04, and aerogel 0.013. Lower k means better insulation. For a composite wall, total thermal resistance R_total = Σ(d/k) for each layer. A wall with 1/2-inch drywall (R-0.45), 3.5-inch fiberglass batt (R-13), 1/2-inch plywood (R-0.63), and 1-inch foam board (R-5) has R_total ≈ 19. Heat flow Q = A × ΔT / R_total: for 200 sq ft of wall with 50°F temperature difference, Q = 200 × 50 / 19 = 526 BTU/hr. Increasing insulation from R-13 to R-19 batts reduces heat loss by approximately 25%.
Convection in cooling and HVAC systems
The convection coefficient h depends on fluid type, velocity, geometry, and whether flow is forced or natural. Typical values: natural convection in air 5-25 W/m²·K, forced air (fan) 25-250, water natural convection 100-1,200, water forced convection 500-10,000, and boiling water 2,500-25,000. Electronic heat sinks rely on forced convection — a CPU generating 100W with a heat sink area of 0.01 m² and h = 100 W/m²·K (typical fan-cooled) produces a temperature rise of ΔT = Q/(hA) = 100/(100×0.01) = 100°C above ambient — explaining why high-performance CPUs need large heat sinks, heat pipes, or liquid cooling to maintain acceptable temperatures.
Radiation and thermal equilibrium
All objects emit thermal radiation proportional to T⁴ (absolute temperature in Kelvin). The Stefan-Boltzmann law gives power emitted: Q = εσAT⁴, where ε is emissivity (0 for perfect reflector, 1 for perfect blackbody), σ = 5.67×10⁻⁸ W/m²·K⁴. A human body (surface area ≈ 1.7 m², skin temperature 33°C = 306K, ε ≈ 0.97) radiates approximately Q = 0.97 × 5.67×10⁻⁸ × 1.7 × 306⁴ = 817W. But it also absorbs radiation from surroundings — at room temperature (20°C = 293K), absorbed radiation is about 720W, so net radiation loss is approximately 97W (about 20% of resting metabolic heat output). This is why you feel cold near windows in winter — the cold glass surface (5-10°C) radiates much less back to you than a warm wall, creating a net radiative heat loss that you perceive as a draft even without air movement.