Calculator Inputs
Plot of Boundary Layer Growth and Heat Transfer
Example Data Table
| Fluid Case | Velocity (m/s) | x (m) | δt (mm) | Pr | havg (W/m²·K) | Qavg (W) |
|---|---|---|---|---|---|---|
| Air over plate | 1.5 | 0.25 | 0.65 | 0.71 | 7.31 | 5.87 |
| Air over plate | 2.5 | 0.4 | 0.77 | 0.71 | 8.43 | 7.62 |
| Air over plate | 4 | 0.6 | 1.21 | 0.71 | 10.48 | 10.9 |
| Water over plate | 0.8 | 0.2 | 0.16 | 6.2 | 1.23 | 187.5 |
Formula Used
This calculator estimates thermal boundary layer thickness for forced convection over a flat plate by combining hydrodynamic layer growth, Reynolds number, Prandtl number, and Nusselt correlations.
For Prandtl number above 1, thermal diffusion is slower than momentum diffusion, so the thermal boundary layer becomes thinner than the velocity boundary layer. For Prandtl number below 1, the opposite trend appears.
How to Use This Calculator
- Enter plate length and the streamwise location where you want local results.
- Provide fluid speed, kinematic viscosity, Prandtl number, and thermal conductivity.
- Enter plate width and temperatures to estimate total heat transfer rate.
- Select automatic regime detection or force laminar or turbulent assumptions.
- Press the calculate button to display results above the form.
- Review the table, plotted trends, and export data using CSV or PDF.
Frequently Asked Questions
1. What does the thermal boundary layer represent?
It is the region next to the surface where fluid temperature changes from wall temperature toward the free stream value. Outside it, the fluid remains nearly unaffected thermally.
2. Why is Prandtl number important here?
Prandtl number compares momentum diffusivity with thermal diffusivity. It strongly affects the relative thickness of the thermal layer and changes the Nusselt number used for heat transfer calculations.
3. When should I use laminar correlations?
Laminar correlations are usually appropriate when the local Reynolds number remains below the classical transition range, often near 5×105 for smooth flat plates with modest disturbances.
4. What if the flow transitions on the plate?
This calculator uses simplified full-laminar or full-turbulent estimates, or automatic switching based on Reynolds number. Mixed transition regions need more detailed models for higher accuracy.
5. Can I use this for curved surfaces?
Not directly. The equations are intended for external flow over a smooth flat plate. Curved bodies, rough walls, and pressure gradients require different correlations.
6. Why does the thermal layer become thinner for large Pr?
Large Prandtl number means heat diffuses more slowly than momentum. Temperature changes stay closer to the wall, so the thermal boundary layer thickness decreases relative to the velocity layer.
7. Is the heat transfer rate exact?
No. It is an engineering estimate based on average convection correlations and uniform property assumptions. Strong property changes, radiation, or nonuniform surfaces can alter real performance.
8. What units should I use?
Use SI units throughout: meters, seconds, square meters per second, watts per meter-kelvin, kilograms per cubic meter, and joules per kilogram-kelvin.