Heat Transfer Calculator

Heat transfer is the movement of thermal energy from a region of higher temperature to one of lower temperature. Three distinct physical mechanisms govern this process: conduction (energy diffusion through a solid or stationary fluid via molecular interactions), convection (energy transport by bulk fluid motion across a surface), and radiation (energy emission as electromagnetic waves, requiring no medium). Understanding which mechanism dominates in a given scenario is essential for accurate thermal analysis.

Conduction follows Fourier's Law: Q = k·A·(T₁ − T₂)/d, where k is thermal conductivity, A is cross-sectional area, the temperature difference drives the flux, and d is the thickness of the material. High-conductivity materials like copper (k ≈ 400 W/m·K) transfer heat far more rapidly than insulating foams (k ≈ 0.03 W/m·K). Convection is described by Newton's Law of Cooling: Q = h·A·(T_s − T∞), where h is the convective coefficient, which ranges from about 2–25 W/m²·K for natural air convection up to 10,000 W/m²·K for boiling liquids. Radiation uses the Stefan-Boltzmann Law: Q = ε·σ·A·(T_s⁴ − T_amb⁴), where ε is emissivity (a surface property between 0 and 1), σ = 5.67 × 10⁻⁸ W/m²·K⁴ is the Stefan-Boltzmann constant, and temperatures must be in Kelvin. Note that radiation scales with the fourth power of absolute temperature, making it dominant at high temperatures.

Practical applications span a vast range of engineering disciplines. Building scientists use conduction calculations to choose wall insulation R-values. Mechanical engineers apply convection analysis to design CPU heat sinks and engine cooling systems. Aerospace engineers model radiative heat transfer for spacecraft thermal control and re-entry vehicle design. Chemical engineers size shell-and-tube heat exchangers using combined conduction and convection analysis. Even simple domestic scenarios — insulating a hot-water pipe or sizing a space heater — rely on these exact principles.

This calculator treats each heat transfer mode independently, assuming one-dimensional, steady-state conditions. In reality, conduction, convection, and radiation often occur simultaneously and must be analyzed as a combined system using thermal resistance networks. The conduction formula assumes uniform material properties (constant k) with no heat generation within the medium. For composite walls or layered materials, the total thermal resistance is the sum of individual layer resistances. The convection coefficient h is treated as a constant input, but in practice h depends on flow regime (laminar vs. turbulent), fluid properties, geometry, and surface orientation — it is typically determined from empirical correlations involving dimensionless numbers such as the Nusselt, Reynolds, and Prandtl numbers. The radiation model assumes a gray surface (ε independent of wavelength) radiating to a large surrounding enclosure; view factors and inter-surface radiation exchange are not accounted for. Temperatures in the radiation formula are converted from °C to Kelvin internally, but users must ensure absolute temperature differences are physically meaningful (T_s > T_amb for positive heat flow). Highly transient systems or problems with phase change (boiling, condensation) require time-dependent or latent-heat analysis beyond this steady-state tool.