Rayleigh Number formula |
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\( Ra \;=\; \dfrac{ \rho \cdot g \cdot \alpha_c \cdot \Delta T \cdot l^3 }{ \mu \cdot \alpha }\) | ||
Symbol | English | Metric |
\( Ra \) = Rayleigh number | \(dimensionless\) | \(dimensionless\) |
\( \rho \) (Greek symbol rho) = fluid density | \(lbm \;/\;ft^3\) | \(kg \;/\; m^3\) |
\( g \) = gravitational acceleration | \(ft \;/\; sec^2\) | \(m \;/\; s^2\) |
\( \alpha_c \) (Greek symbol alpha) = thermal expansion coefficient | \(in \;/\; in\;F\) | \(mm \;/\; mm\;C\) |
\( \Delta T \) = temperature differential | \(F\) | \(K\) |
\( l \) = length | \(ft\) | \(m\) |
\( \mu \) (Greek symbol mu) = absolute viscosity | \(lbf - sec \;/\; ft^2\) | \( Pa - s \) |
\( \alpha \) (Greek symbol alpha) = thermal diffusivity | \(ft^2 \;/\; sec\) | \(m^2 \;/\; s\) |
Rayleigh number, abbreviated as Ra, a dimensionless number, is used in fluid dynamics and heat transfer to predict the onset of convection in a fluid or gas. It characterizes the relative importance of buoyancy forces due to temperature differences and the dissipative effects of viscosity and diffusivity. It is used particularly in the context of natural convection, which is the process where fluid motion is induced by temperature differences within the fluid itself, without the need for external mechanical forces.
The Rayleigh number indicates whether convection currents will form due to temperature differences. When the Rayleigh number exceeds a certain critical value, it signifies the transition from a steady, laminar flow to an unstable, convective flow regime.
Key Points about Rayleigh Number
The Rayleigh number is a fundamental parameter in understanding the transition between different modes of heat transfer and fluid motion, making it valuable in various scientific and engineering fields.