Heat Transfer Calculator
Our thermodynamics & heat calculator computes heat transfer accurately. Enter measurements for results with formulas and error analysis.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Heat Transfer Calculator
Calculator
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Formula: Q = kAΔT/L (conduction) | Q = hAΔT (convection) | Q = εσA(T₁⁴-T₂⁴) (radiation)
Additional inputs: Surface Emissivity (0 to 1).
Worked example — Q = 160W | R_th = 0.1875 °C/W | R-value = 3.75
Formula
Q = kAΔT/L (conduction) | Q = hAΔT (convection) | Q = εσA(T₁⁴-T₂⁴) (radiation)
Heat conduction rate depends on thermal conductivity, area, temperature difference, and thickness (Fourier's Law). Convection depends on the heat transfer coefficient. Radiation follows the Stefan-Boltzmann law with the fourth power of absolute temperature.
Worked Examples
Example 1: Wall Insulation Heat Loss
Problem:Calculate heat loss through a 150mm fiberglass-insulated wall (k = 0.04 W/m·K), area = 20m², with 20°C inside and -10°C outside.
Solution:k = 0.04 W/(m·K), A = 20 m², ΔT = 30°C, L = 0.15m Q = kA(ΔT)/L = 0.04 × 20 × 30 / 0.15 = 160W Thermal Resistance = L/(kA) = 0.15/(0.04×20) = 0.1875 °C/W R-value = L/k = 0.15/0.04 = 3.75 m²·K/W Heat Flux = 160/20 = 8 W/m²
Result:Q = 160W | R_th = 0.1875 °C/W | R-value = 3.75
Example 2: Cooling Electronics with Forced Convection
Problem:A 50W processor has a heatsink with 0.02m² surface area. Air is forced over it with h = 150 W/(m²·K). What is the temperature rise?
Solution:Q = hA(ΔT), so ΔT = Q/(hA) ΔT = 50 / (150 × 0.02) = 16.7°C If ambient = 25°C, heatsink temp = 41.7°C Thermal Resistance = 1/(hA) = 1/(150×0.02) = 0.333 °C/W
Result:ΔT = 16.7°C | T_surface = 41.7°C | R_th = 0.333 °C/W
Frequently Asked Questions
What are the three modes of heat transfer?
Heat transfers through three fundamental mechanisms: (1) Conduction — heat flows through a solid material or between materials in direct contact, driven by a temperature gradient. Rate depends on thermal conductivity, area, temperature difference, and material thickness. (2) Convection — heat transfer between a surface and a moving fluid (liquid or gas). Can be natural (driven by buoyancy) or forced (driven by fans/pumps). Rate depends on the convection coefficient, area, and temperature difference. (3) Radiation — heat transfer via electromagnetic waves (infrared). Does not require a medium and can occur through vacuum. Rate depends on emissivity, temperature, and area.
What is Fourier's Law of conduction?
Fourier's Law states that the rate of heat conduction through a material is proportional to the negative temperature gradient and the cross-sectional area: Q = -kA(dT/dx). For a flat wall with uniform properties: Q = kA(T_hot - T_cold)/L, where Q is heat transfer rate (Watts), k is thermal conductivity (W/m·K), A is cross-sectional area (m²), ΔT is temperature difference (K or °C), and L is thickness (m). Materials with high k (metals) conduct heat well; materials with low k (insulators) resist heat flow. This law is the basis for insulation design and heat exchanger calculations.
What is thermal resistance?
Thermal resistance (R_th) is the opposition to heat flow, analogous to electrical resistance. For conduction: R_th = L/(kA) (°C/W). For convection: R_th = 1/(hA) (°C/W). The heat transfer rate is Q = ΔT/R_th, just like Ohm's law (I = V/R). For series thermal resistances (multiple layers), total R = R1 + R2 + R3... For parallel paths, 1/R_total = 1/R1 + 1/R2... The R-value used in building insulation is the thermal resistance per unit area: R-value = L/k (m²·K/W or ft²·°F·h/BTU).
What is the convection heat transfer coefficient?
The convection heat transfer coefficient (h) quantifies how effectively heat transfers between a surface and a fluid. It depends on fluid properties, flow velocity, geometry, and whether convection is natural or forced. Typical values: Natural convection in air = 5-25 W/(m²·K). Forced convection in air = 25-250 W/(m²·K). Natural convection in water = 100-900 W/(m²·K). Forced convection in water = 250-12,000 W/(m²·K). Boiling water = 3,000-100,000 W/(m²·K). The coefficient is often determined empirically using dimensionless correlations involving Nusselt, Reynolds, and Prandtl numbers.
What is the Stefan-Boltzmann Law?
The Stefan-Boltzmann Law governs thermal radiation: Q = εσA(T_hot⁴ - T_cold⁴), where ε is emissivity (0-1, surface property), σ = 5.67×10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant, A is surface area (m²), and T is absolute temperature in Kelvin. Key points: radiation depends on the fourth power of temperature (doubling temperature increases radiation 16×), all objects above 0K emit radiation, emissivity varies from ~0.02 (polished silver) to ~0.95 (black body paint), and radiation can transfer heat through vacuum (how the Sun heats the Earth).
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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