Heat Transfer Calculator

Compute heat transfer rates, thermal resistance, and visualize temperature gradients for three fundamental modes of heat transfer. Includes reference tables, real-world examples, and detailed theory.

SI units: k [W/(m·K)], A [m²], T [°C or K], L [m]. Temperature difference in K equals difference in °C.
Copper bar: k=401, A=0.01, T₁=150, T₂=50, L=0.1 Glass window: k=0.8, A=2.0, T₁=25, T₂=-5, L=0.006 Wood wall: k=0.15, A=10, T₁=30, T₂=10, L=0.2
h [W/(m²·K)], A [m²], T [°C or K].
Air natural: h=10, A=2, Tₛ=60, T∞=20 Water forced: h=500, A=0.5, Tₛ=90, T∞=30 Boiling water: h=3000, A=0.1, Tₛ=110, T∞=100
Radiation requires absolute temperature in Kelvin (K = °C + 273.15).
ε [dimensionless], A [m²], T [Kelvin].
Blackbody: ε=1, A=0.5, T₁=800, T₂=300 Polished copper: ε=0.05, A=0.2, T₁=600, T₂=350 Black paint: ε=0.95, A=2, T₁=400, T₂=280
Thermal resistance R = L / (k·A) [K/W]. Heat transfer Q = ΔT / R.
Brick wall: k=0.7, A=12, L=0.25, ΔT=20 Fiberglass: k=0.04, A=8, L=0.15, ΔT=30 Steel plate: k=50, A=0.5, L=0.01, ΔT=100
Privacy-first: All calculations run locally in your browser. No data is sent to any server.
Hot side Cold side Temperature gradient Heat flow direction

Fundamentals of Heat Transfer

Heat transfer is the thermal energy in transit due to a temperature difference. The three fundamental modes — conduction, convection, and radiation — govern energy exchange in everything from electronic cooling to planetary climate. This calculator implements the core governing equations with interactive visualization, enabling engineers, students, and researchers to explore thermal systems quantitatively.

The Fourier rate equation (conduction): Q = −k · A · (dT/dx)

Newton's law of cooling (convection): Q = h · A · (Ts − T∞)

Stefan–Boltzmann law (radiation): Q = ε · σ · A · (T₁4 − T₂4)

where σ = 5.670374419 × 10−8 W/(m²·K⁴)

Why Use an Interactive Heat Transfer Calculator?

  • Engineering Design: Size heat exchangers, insulation, and cooling systems.
  • Educational Aid: Visualize the effect of each parameter on heat transfer rates.
  • Energy Efficiency: Evaluate building envelope performance and reduce energy consumption.
  • Research & Development: Rapidly prototype thermal management strategies.

Detailed Mathematical Derivation

Conduction follows Fourier's law: the heat flux is proportional to the temperature gradient. For a plane wall of thickness L and cross-sectional area A, with thermal conductivity k assumed constant, the steady-state heat transfer rate is:

Q = k · A · (T₁ − T₂) / L

The thermal resistance is R = L / (k · A), so that Q = ΔT / R. This electrical–thermal analogy is powerful for analyzing composite walls and series/parallel configurations.

Convection occurs at a solid–fluid interface. The local heat flux is governed by Newton's law: q″ = h · (Ts − T∞). The convective heat transfer coefficient h depends on fluid properties, flow regime, and geometry. It can range from ~5 W/(m²·K) for natural convection in air to over 10,000 W/(m²·K) for boiling water.

Radiation is the emission of electromagnetic waves from a surface due to its temperature. The net radiative exchange between two blackbodies is proportional to the difference of the fourth powers of absolute temperatures. For real surfaces, emissivity ε (0–1) accounts for the surface's efficiency as a thermal radiator.

Material Properties Reference Table

Material k (W/(m·K)) Typical Use Emissivity ε (approx.)
Copper 401 Heat exchangers, electrical conductors 0.03 – 0.05 (polished)
Aluminum 237 Fins, automotive radiators 0.04 – 0.08 (polished)
Steel (carbon) 50 Structural components, pipes 0.70 – 0.80 (oxidized)
Glass 0.8 Windows, solar collectors 0.90 – 0.95
Brick 0.7 Building walls 0.85 – 0.90
Wood (oak) 0.15 Furniture, flooring 0.85 – 0.90
Fiberglass insulation 0.04 Thermal insulation in buildings —
Air (still) 0.026 Natural convection, insulation —
Water (liquid) 0.60 Heat transfer fluids —

Typical Convection Coefficients

Scenario h (W/(m²·K)) Example
Natural convection – air 2 – 25 Room heating, electronics cooling
Forced convection – air 25 – 250 Fan cooling, HVAC ducts
Forced convection – water 100 – 1000 Water-cooled heat exchangers
Boiling water 1000 – 10,000 Boilers, kettle
Condensing steam 5000 – 15,000 Condensers, power plants
Case Study: Energy-Efficient Building Envelope

An architect is designing a multi‑layer wall for a passive house. The wall consists of: 20 mm plaster (k=0.5), 150 mm fiberglass insulation (k=0.04), and 100 mm brick (k=0.7). Using the thermal resistance calculator, the total R‑value is computed: Rtotal = (0.02/0.5) + (0.15/0.04) + (0.10/0.7) = 0.04 + 3.75 + 0.143 ≈ 3.93 K/W. For a temperature difference of 25°C and wall area of 30 m², the heat loss is: Q = 25 / 3.93 ≈ 6.36 W per m² of wall area, or about 191 W for the entire wall. This analysis demonstrates the dominant role of insulation thickness in reducing energy consumption.

Common Misconceptions

  • "Heat rises" – Warm air rises due to buoyancy, but heat itself (thermal energy) moves via conduction, convection, or radiation in all directions.
  • "Cold flows into a space" – Thermal energy flows from hot to cold; "cold" is the absence of heat.
  • "Black surfaces absorb more heat" – Black surfaces have higher absorptivity (and emissivity), which affects radiative exchange. But a black surface also emits more radiation.
  • "Higher k always means better" – For insulation, low k is desirable; for heat spreaders, high k is needed.

Real‑World Engineering Applications

  • Aerospace: Thermal protection systems for re‑entry vehicles.
  • Automotive: Radiator and engine cooling design.
  • Electronics: Heat sinks, thermal interface materials, and PCB thermal management.
  • Renewable Energy: Solar thermal collectors, concentrated solar power.
  • HVAC: Heating, ventilation, and air conditioning system sizing.
  • Cryogenics: Insulation for liquid nitrogen and helium storage.

Rooted in classical thermodynamics – This tool is built upon the foundational works of Fourier, Newton, and Stefan–Boltzmann, with modern engineering practices from Incropera & DeWitt's "Fundamentals of Heat and Mass Transfer" (8th ed., Wiley). All algorithms have been verified against standard textbook examples. Reviewed by the GetZenQuery tech team, last updated July 2026.

Frequently Asked Questions

Temperature is a measure of the average kinetic energy of molecules in a substance. Heat (thermal energy) is the total energy transferred between systems due to a temperature difference. Heat is energy in transit; temperature is a state property.

For temperature differences (ΔT), using Kelvin or Celsius gives the same numerical value because the scale intervals are identical. For absolute temperatures (e.g., in the Stefan–Boltzmann law for radiation), you must use Kelvin (K = °C + 273.15).

Effective insulation materials have k < 0.1 W/(m·K). Examples include fiberglass (0.04), expanded polystyrene (0.03–0.04), and aerogel (0.015). The lower the k, the better the insulating performance.

This calculator assumes steady‑state conditions (temperatures do not change with time). For transient problems, additional parameters like thermal diffusivity (α = k/(ρ·cp)) and time are needed. We may add a transient module in a future update.

The Stefan–Boltzmann constant (σ = 5.670374419×10⁻⁸ W/(m²·K⁴)) is a fundamental physical constant that relates the total energy radiated by a blackbody to its absolute temperature. It appears in the radiation law and is crucial for astrophysics, climate science, and thermal engineering.

Recommended resources:
References: Incropera & DeWitt (Wiley) · NIST thermophysical properties · Wikipedia: Heat transfer