# Natural Convection – Example – Problem with Solution

## Example: Natural Convection – Flat Plate

A 10cm high vertical plate is maintained at 261Â°C in 260Â°C compressed water (16MPa). Determine the Nusselt number using the simple correlation for a vertical flat plate.

To calculate the Rayleigh number, we have to know:

• the coefficient of thermal expansion, which is: Î² = 0.0022
• the Prandtl number (for 260Â°C), which is: Pr = 0.87
• the kinematic viscosity (for 260Â°C), which is Î½ = 0.13 x 10-6 (note that, this value is significantly lower than that for 20Â°C)

The resulting Rayleigh number is:

The resulting Nusselt number, which represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer is:

Â
References:
Heat Transfer:
1. Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley & Sons, Incorporated, 2011. ISBN: 9781118137253.
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3. U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow.Â DOE Fundamentals Handbook,Â VolumeÂ 2Â ofÂ 3.Â MayÂ 2016.

Nuclear and Reactor Physics:

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