Heat Flow Calculator

Material & Dimensions

Material (Thermal Conductivity, $k$)

Custom Conductivity ($k$) Units: BTU/(hr·ft·°F) by default

Cross-Sectional Area ($A$) (ft²)

Thickness ($L$) (ft)

Temperature Difference ($\Delta T$)

Hot Side Temperature ($T_{hot}$) (°F)

Cold Side Temperature ($T_{cold}$) (°F)

Resulting Heat Flow Rate

Temperature Difference ($\Delta T$)

Heat Flow Rate ($Q_{rate}$)

Calculates 1D steady-state heat conduction rate using Fourier’s Law: $Q_{rate} = \frac{k A \Delta T}{L}$. Results are in BTU/hr, assuming inputs are in feet, sq. ft., and °F.

What Is Heat Flow?

Heat flow (or heat transfer rate) measures how much thermal energy moves through a material over time.
It’s influenced by three main factors:

Thermal conductivity (k) – how well the material conducts heat
Cross-sectional area (A) – the area through which heat travels
Thickness (L) – how far the heat must travel
Temperature difference (ΔT) – the difference between the hot and cold sides

The greater the conductivity and temperature difference, the higher the rate of heat flow.
Conversely, thicker materials or poor conductors (like insulation) reduce heat transfer.

The Formula Behind the Heat Flow Calculator

The calculator is based on Fourier’s Law of Heat Conduction:

[
Q_{rate} = \frac{k \times A \times \Delta T}{L}
]

Where:

Qrate = Heat flow rate (BTU/hr)
k = Thermal conductivity of the material (BTU/hr·ft·°F)
A = Cross-sectional area (ft²)
ΔT = Temperature difference between hot and cold sides (°F)
L = Material thickness (ft)

This formula assumes steady-state, one-dimensional heat transfer, meaning the temperature gradient stays constant and heat moves in one direction.

How to Use the Heat Flow Calculator

This calculator is designed to be simple yet powerful. Follow these steps:

Step 1: Select a Material

Choose from common materials with predefined thermal conductivity (k) values:

Aluminum (~220)
Copper (~401)
Steel (~15)
Concrete (~0.3)
Fiberglass Insulation (~0.024)
Water (~0.34)

You can also enter a custom k-value if you’re testing a specific material.

Step 2: Enter Material Dimensions

Area (A) – in square feet
Thickness (L) – in feet

These define the physical size and shape of the section through which heat travels.

Step 3: Input Temperatures

Hot side temperature (Thot)
Cold side temperature (Tcold)

The calculator automatically finds the temperature difference (ΔT = Thot – Tcold).

Step 4: Click “Calculate”

Instantly get the heat flow rate (Qₙ) in BTU/hr.
If your inputs are invalid (like negative or missing numbers), the calculator will display a clear error message so you can correct it.

Example Calculation

Let’s see an example for better understanding.

Parameter	Symbol	Value
Thermal Conductivity	k	220 BTU/hr·ft·°F (Aluminum)
Area	A	1 ft²
Thickness	L	0.5 ft
Hot Temperature	Thot	150°F
Cold Temperature	Tcold	70°F

Step 1: Find ΔT
ΔT = 150 – 70 = 80°F

Step 2: Apply Fourier’s Law
Qₙ = (k × A × ΔT) / L
Qₙ = (220 × 1 × 80) / 0.5 = 35,200 BTU/hr

Result: The aluminum section conducts 35,200 BTU/hr of heat through its surface.

Real-World Applications

The Heat Flow Calculator is a practical tool for anyone working with thermal systems. Common uses include:

Building and HVAC design – Evaluate wall, floor, or insulation performance.
Mechanical and process engineering – Analyze conduction in pipes or machine components.
Energy efficiency studies – Estimate heat loss through materials.
Thermal management design – Size cooling or heating components.
Educational use – Teach and visualize Fourier’s Law in classrooms or labs.

Common Thermal Conductivity Values

Material	Thermal Conductivity (BTU/hr·ft·°F)	Description
Copper	~401	Excellent conductor (used in heat exchangers)
Aluminum	~220	Lightweight metal with high conductivity
Steel	~15	Moderate conductor (used in structures)
Concrete	~0.3	Low conductivity (used in construction)
Water (liquid)	~0.34	Medium conductor for fluids
Fiberglass	~0.024	Excellent insulator

These numbers show why materials like fiberglass are used for insulation — they resist heat flow far better than metals.

Important Notes

Always use consistent units: feet, square feet, and °F.
The calculator assumes steady-state conduction — no transient heat storage.
Results are in BTU/hr (British Thermal Units per hour).
ΔT must be positive (Thot > Tcold).

If the hot side is cooler or equal to the cold side, heat flow will be zero.

Why This Calculator Is Useful

The Heat Flow Calculator helps you:

Save time on manual calculations
Avoid formula mistakes
Quickly compare different materials
Design more energy-efficient systems
Understand real-world heat transfer behavior

It’s not just a calculator — it’s a visual learning tool that connects theory with real-world data.

Formula Summary

[
Q_{rate} = \frac{k \times A \times (T_{hot} - T_{cold})}{L}
]

Where:

(k) → Thermal conductivity (BTU/hr·ft·°F)
(A) → Cross-sectional area (ft²)
(L) → Thickness (ft)
(T_{hot}), (T_{cold}) → Hot and cold surface temperatures (°F)

Key Takeaway

The Heat Flow Calculator simplifies thermal analysis — helping you understand how quickly heat moves through materials. Whether you’re optimizing insulation, designing an HVAC system, or studying heat transfer, it gives you instant, accurate, and intuitive results.