Heat Transfer Calculator

What are the three modes of heat transfer?

Heat transfer occurs by three mechanisms: conduction (through solid material), convection (between a surface and a moving fluid), and radiation (electromagnetic emission without a medium). Each mode is governed by a different law and depends on different material and geometric properties.

Conduction follows Fourier's law: Q = k×A×ΔT/L, where k is thermal conductivity. Convection follows Newton's law of cooling: Q = h×A×ΔT, where h is the convection coefficient. Radiation follows the Stefan-Boltzmann law: Q = ε×σ×A×(T₁⁴−T₂⁴), where ε is emissivity and σ is the Stefan-Boltzmann constant.

In chemical process equipment — heat exchangers, reactors, furnaces, and insulated piping — all three modes often operate simultaneously. Understanding their relative contributions is essential for efficient equipment design, energy optimization, and temperature control.

Formula: Conduction: Q = k × A × ΔT / L Convection: Q = h × A × ΔT Radiation: Q = ε × σ × A × (T₁⁴ - T₂⁴) σ = 5.67 × 10⁻⁸ W/(m²·K⁴)

Example Calculation

Conduction through a 50 mm thick steel wall (k = 50 W/m·K), area = 2 m², ΔT = 100°C: Q = 50 × 2 × 100 / 0.05 = 200,000 W = 200 kW. Thermal resistance = L/(k×A) = 0.05/(50×2) = 0.0005 K/W.

When to Use This Calculator

• Estimating heat loss through insulated pipe walls or vessel walls to size insulation thickness
• Comparing heat transfer rates across different modes to identify the dominant mechanism in your system
• Sizing heat exchangers by calculating the required surface area for a given duty and temperature difference
• Evaluating whether radiation shielding is needed for high-temperature equipment to protect nearby instrumentation or personnel

Common Mistakes to Avoid

• Using Celsius instead of Kelvin for radiation calculations — the Stefan-Boltzmann law requires absolute temperature (K), and using °C gives drastically wrong results
• Assuming a single convection coefficient for all conditions — h varies from ~5 W/m²K for natural convection in air to ~10,000 W/m²K for forced convection of water; using the wrong order of magnitude invalidates the result
• Neglecting contact resistance between surfaces — bolted or pressed joints can have thermal resistance equivalent to several millimeters of steel, significantly reducing heat transfer
• Forgetting that thermal conductivity of insulation materials increases with temperature — fiberglass insulation at 300°C conducts 2-3× more heat than at 50°C

How to Interpret Results

• If thermal resistance is dominated by one layer (e.g., insulation R is 10× the steel wall R), improving that layer yields the biggest efficiency gain
• A very high heat flux density (>100 kW/m²) may indicate risk of local boiling, thermal stress, or material degradation — verify that the surface temperature stays within limits
• For radiation results, check whether the emissivity value reflects the actual surface condition — polished metal (ε ≈ 0.05) and oxidized metal (ε ≈ 0.8) differ by 16×

Related Standards & References

• ASTM C177 — Standard test method for steady-state heat flux measurements by the guarded-hot-plate apparatus: defines how thermal conductivity values of insulation materials are measured and reported
• ASME PTC 4 — Fired steam generators: performance test code for heat transfer efficiency calculations in boilers and industrial heaters
• ISO 6946 — Building components and building elements — thermal resistance and transmittance: U-value calculation applicable to composite walls and insulated pipe lagging
• Incropera & DeWitt — 'Fundamentals of Heat and Mass Transfer' (8th ed., Wiley): standard reference for Dittus-Boelter, Churchill-Bernstein, and Stefan-Boltzmann correlations

Frequently Asked Questions

What is thermal resistance and how is it used?

Thermal resistance (R = ΔT/Q) is analogous to electrical resistance. For conduction, R = L/(k×A). For convection, R = 1/(h×A). When multiple layers or modes are in series, total resistance is the sum of individual resistances. This makes it easy to analyze composite walls, insulated pipes, and heat exchangers by adding resistances.

When does radiation become important relative to conduction and convection?

Radiation becomes significant above about 300°C and dominant above 600-800°C because it scales with T⁴. In furnaces, kilns, and high-temperature reactors, radiation is the primary heat transfer mode. At ambient temperatures, radiation is typically a small fraction of total heat transfer unless the surface is in a vacuum (no convection) or well-insulated (minimal conduction).

How do I combine multiple heat transfer modes in a single calculation?

For series paths (e.g., convection → wall conduction → convection), use the thermal resistance analogy: total R = R_conv1 + R_cond + R_conv2, then Q = ΔT_total / R_total. For parallel paths (e.g., radiation + convection from the same surface), add the heat rates: Q_total = Q_radiation + Q_convection. The overall heat transfer coefficient U combines all resistances: 1/UA = Σ(1/hA) + Σ(L/kA).