Heat Transfer Rate Calculator (Conduction, Convection & Radiation

Thermodynamics: The Three Fundamental Modes of Heat Transfer

Thermal energy flows spontaneously from regions of higher temperature to lower temperature across three physical mechanisms:

• Conduction (Fourier's Law): Direct molecular kinetic energy transfer through stationary solids or fluids without bulk motion. Governed by material thermal conductivity k and inverse thermal resistance .

• Convection (Newton's Law of Cooling): Energy transfer between a solid surface and an adjacent moving fluid (liquid or gas), combining microscopic conduction with macroscopic fluid advection. Classified into Natural / Free Convection (buoyancy driven) and Forced Convection (fans, pumps, wind).

• Thermal Radiation (Stefan-Boltzmann Law): Electromagnetic waves emitted by all matter with temperature above absolute zero (0 K). Requires no medium and scales with the fourth power of absolute temperature (T^4), making it the dominant heat transfer mechanism in high-temperature furnaces, space vacuum, and solar radiation.

How to Use This Calculator

Enter your Heat Transfer Mechanism — choose from Combined Total Heat Transfer (Conduction, Convection & Radiation), Fourier Conduction (q = k · A · ΔT / L), Newton's Convection (q = h · A · ΔT), Heat Transfer Surface Area (A in m²) (e.g. 2.5), Hot Source / Surface Temperature (T₁ in °C) (e.g. 120), Cold Sink / Ambient Temperature (T₂ in °C) (e.g. 25), Thermal Conductivity (k in W/(m·K) [Conduction]) (e.g. 0.85 (Brick: 0.85, Steel: 45, Insulation: 0.04)), Material Wall Thickness (L in meters [Conduction]) (e.g. 0.15 (150 mm)), Convective Heat Transfer Coeff (h in W/(m²·K) [Convection]) (e.g. 25 (Free air: 5-25, Forced air: 25-250, Water: 500-10,000)), and Surface Emissivity (ε between 0.0 and 1.0 [Radiation]) (e.g. 0.85 (Blackbody: 1.0, Oxidized metal: 0.8, Polished: 0.05)). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Thermodynamic Heat Transfer Fundamental equations:

Fourier Conduction: q_cond = -k · A · (Δ T) / (L) = (Δ T) / (R_cond), R_cond = (L) / (k A)

Newton Convection: q_conv = h · A · (T_surface - T_∞) = (Δ T) / (R_conv), R_conv = (1) / (h A)

Stefan-Boltzmann Radiation: q_rad = · σ · A · ( T_1^4 - T_2^4 )

Where: σ = 5.670374 × 10^-8 W/(m^2 · K^4), T in Kelvin (K)

Heat Flux: q'' = (q) / (A) (W/m^2)

Worked Example

For example, evaluating an industrial oven wall of area \ with interior surface \ (393.15 K) and ambient surroundings \ (298.15 K), where convection coefficient \, and emissivity Convection loss is . Radiation loss is 0.85 × (5.670374 × 10^-8) × 2.5 × (393.15^4 - 298.15^4) = 0.85 × 5.670374 × 10^-8 × 2.5 × (2.3891 × 10^10 - 7.8996 × 10^9) = 1,926.8 W. Total combined heat loss is \ with heat flux .

Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.