Heat Transfer Calculator
Calculate heat transfer calculator calculate thermal conductive heat flux Q_dot = k * A * (Delta T / d) using Fourier's Law of Conduction in Watts, kW, BTU/h, and thermal resistance R-value. Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Conductive Heat Transfer Rate (dot{Q} = k · A · Delta T / d)
Enter your physical parameters below to compute verified heat transfer metrics.
Calculation Results
Calculated using verified physical methodology: Fourier's Law of Heat Conduction: \dot{Q} = k \cdot A \cdot \\Delta T / d
\text{Thermal Resistance (Metric R-Value): } R_{\text{metric}} = \d / k
Quick Summary
The Heat Transfer Calculator evaluates steady-state 1D thermal conduction rate ($\dot{Q} = k \cdot A \cdot \\Delta T / d$) using Fourier's Law of Conduction in Watts (W), Kilowatts (kW), Imperial BTU/h, and metric R-value thermal resistance.
Formula Explanation
Fourier's Law of Heat Conduction: \dot{Q} = k \cdot A \cdot \\Delta T / d
\text{Thermal Resistance (Metric R-Value): } R_{\text{metric}} = \d / k
How It Works
The Heat Transfer Calculator divides temperature difference ($\Delta T$) by thickness ($d$) to get temperature gradient. It multiplies by thermal conductivity ($k$) and area ($A$). It outputs heat transfer rate ($\dot{Q}$) in Watts, kW, Imperial BTU/h, heat flux density ($q = \dot{Q}/A$ in $\text{W/m}^2$), and metric R-value thermal resistance ($R = d/k$).
Step-by-Step Worked Example
Practical Problem: Calculate heat loss rate $\dot{Q}$ through a $d = 0.10\text{ m}$ (10 cm) thick fiberglass insulated wall ($k = 0.04\text{ W/m}\cdot\text{K}$) with surface area $A = 10.0\text{ m}^2$ when temperature difference $\Delta T = 20.0^\circ\text{C}$.
- Step 1: Identify Input Parameters: $k = 0.04\text{ W/(m}\cdot\text{K)}$, $A = 10.0\text{ m}^2$, $\Delta T = 20.0^\circ\text{C}$, $d = 0.10\text{ m}$.
- Step 2: Calculate Temperature Gradient ($\\Delta T / d$): $\text{Gradient} = \frac{20.0^\circ\text{C}}{0.10\text{ m}} = 200.0^\circ\text{C/m}$.
- Step 3: Apply Fourier's Law Formula ($\dot{Q} = k \cdot A \cdot \\Delta T / d$): $\dot{Q} = 0.04 \times 10.0 \times 200.0 = 80.00\text{ Watts (W)}$.
- Step 4: Calculate Metric Thermal Resistance ($R = d / k$) & Imperial BTU/h: Metric R-Value = $\0.10 / 0.04 = 2.50\text{ m}^2\cdot\text{K/W}$ (US R-14.2 insulation equivalent). Imperial BTU/h: $80.0 \times 3.41214 = 272.97\text{ BTU/h}$.
- Step 5: Calculate Heat Flux Density ($q = \dot{Q} / A$): $q = \80.0 / 10.0 = 8.00\text{ Watts per square meter (W/m}^2)$.
Real-World Calculation Examples
Scenario 1: Insulated Fiberglass Wall (10cm thick)
Parameters: $k = 0.04\text{ W/m}\cdot\text{K}$, $A = 10\text{ m}^2$, $\Delta T = 20^\circ\text{C}$, $d = 0.10\text{ m}$
Result: $\dot{Q} = 80.00\text{ W}$ ($272.97\text{ BTU/h}$, $8.0\text{ W/m}^2$, R-2.5 metric). Insulated home wall.
Scenario 2: Single-Pane Glass Window (4mm thick)
Parameters: $k = 0.80\text{ W/m}\cdot\text{K}$, $A = 2\text{ m}^2$, $\Delta T = 20^\circ\text{C}$, $d = 0.004\text{ m}$
Result: $\dot{Q} = 8,000.00\text{ W}$ (8.00 kW, 27,297 BTU/h). Uninsulated glass window heat loss.
Scenario 3: Copper Heat Pipe CPU Cooler (2mm thick)
Parameters: $k = 400.0\text{ W/m}\cdot\text{K}$, $A = 0.005\text{ m}^2$ ($50\text{ cm}^2$), $\Delta T = 10^\circ\text{C}$, $d = 0.002\text{ m}$
Result: $\dot{Q} = 10,000.00\text{ W}$ (10.00 kW, $2,000,000\text{ W/m}^2$ flux). High-performance CPU copper cooler.
Scenario 4: Concrete Foundation Wall (20cm thick)
Parameters: $k = 1.30\text{ W/m}\cdot\text{K}$, $A = 20\text{ m}^2$, $\Delta T = 15^\circ\text{C}$, $d = 0.20\text{ m}$
Result: $\dot{Q} = 1,950.00\text{ W}$ (1.95 kW, 6,654 BTU/h). Concrete basement wall conduction.
Key Benefits of Using This Calculator
Fourier's Law Conduction Engine
Calculates steady-state 1D thermal heat conduction rate ($\dot{Q} = kA\Delta T / d$) across solid materials.
R-Value & Heat Flux Solver
Computes metric thermal resistance ($R = d/k$) and heat flux density ($q = \dot{Q}/A$).
Multi-Unit Readouts
Outputs heat transfer rate in Watts (W), Kilowatts (kW), Imperial $\text{BTU/h}$, and $\text{kcal/h}$.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is heat transfer rate?
Heat transfer rate (Q_dot) is the amount of thermal energy transferred per unit time across a boundary or medium measured in Watts (1 Watt = 1 Joule per second).
What is Fourier's Law of Heat Conduction?
Fourier's Law states that heat transfer rate through conduction is proportional to thermal conductivity k and area A, and inversely proportional to material thickness d (Q_dot = k * A * Delta T / d).
What is thermal conductivity k?
Thermal conductivity (k) is an intensive material property measuring ability to conduct heat in W/(m*K) (e.g. Copper = 400 W/m*K, Glass = 0.8 W/m*K, Fiberglass = 0.04 W/m*K).
What are the three modes of heat transfer?
1. CONDUCTION (molecular collision in solids); 2. CONVECTION (fluid motion transfer); 3. RADIATION (electromagnetic photon emission).
What is thermal resistance R-value?
Metric R-value = d / k (m²*K/W) measures resistance to heat flow; US R-value = Metric R-value * 5.678 (ft²*°F*h/BTU).
What is heat flux q?
Heat flux q = Q_dot / A (W/m²) is the rate of heat flow per unit area.
How converts Watts to BTU per hour (BTU/h)?
Multiply Watts by 3.41214 (1 W = 3.41214 BTU/h).
Who derived Fourier's Law?
French mathematician Joseph Fourier published the law of heat conduction in 1822.
Why is air an excellent thermal insulator?
Trapped stagnant air has an extremely low thermal conductivity k = ~0.026 W/m*K; fiberglass insulation traps air pockets to prevent convection while leveraging air's low conductivity.
What is overall thermal transmittance U-value?
U-value = 1 / R_total (W/m²*K) measures overall thermal conductance of multi-layer wall assemblies.