Enter the temperature difference (ΔT), heat flux, thickness, and thermal conductivity into the calculator to determine the missing variable.
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Heat Flux To Temperature Difference Formula
The following formula is used to calculate the temperature difference across a flat layer under steady 1‑D conduction (constant thermal conductivity) for a given heat flux and thickness.
\Delta T = \frac{q^{\prime\prime} \cdot L}{k}Variables:
- ΔT is the temperature difference across the material (K or °C)
- q″ is the heat flux (W/m²)
- L is the thickness (m)
- k is the thermal conductivity (W/(m·K))
- A is the area (only needed if converting between heat flux and total heat transfer rate, Q = q″·A)
To calculate the temperature difference, multiply the heat flux by the thickness. Then, divide the result by the thermal conductivity.
| W/m² | BTU/hr-ft² |
|---|---|
| 5 | 1.585 |
| 10 | 3.170 |
| 25 | 7.925 |
| 50 | 15.850 |
| 75 | 23.775 |
| 100 | 31.700 |
| 150 | 47.550 |
| 200 | 63.400 |
| 250 | 79.250 |
| 300 | 95.100 |
| 400 | 126.799 |
| 500 | 158.499 |
| 750 | 237.749 |
| 1000 | 316.998 |
| 1500 | 475.498 |
| 2000 | 633.997 |
| 2500 | 792.496 |
| 3000 | 950.995 |
| 4000 | 1267.993 |
| 5000 | 1584.992 |
| *Per calculator units: 1 BTU/hr-ft² ≈ 3.154590 W/m², so 1 W/m² ≈ 0.316998 BTU/hr-ft². | |
What is Heat Flux?
Heat flux (also called thermal flux) is the rate of heat transfer per unit area. It is a vector quantity, meaning it has both magnitude and direction. Heat flux is typically measured in watts per square meter (W/m²). In conduction, the heat-flux vector points in the direction of decreasing temperature (from higher temperature toward lower temperature).
How to Calculate Heat Flux to Temperature Difference?
The following steps outline how to calculate the temperature difference from heat flux.
- First, determine the heat flux (q″).
- Next, determine the thickness of the material (L).
- Next, determine the thermal conductivity of the material (k).
- If you started with total heat transfer rate (Q) instead of heat flux, calculate heat flux using q″ = Q/A.
- Finally, calculate the temperature difference using ΔT = (q″ · L) / k.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Heat flux (q) = 500 W/m²
Thickness (L) = 0.05 m
Thermal conductivity (k) = 200 W/(m·K)
Area (A) = 2 m² (not needed to compute ΔT from heat flux; only needed if converting between Q and q″)