This chapter delves into the fascinating realm of natural (free) convection, a mode of heat and mass transfer driven by density differences in a fluid due to temperature variations. The document provides a comprehensive exploration of the fundamental principles, theories, and mathematical models go...
Forsberg Heat Transfer
Chapter 7
Natural (Free) Convection
Dimensionless Numbers for Natural Convection
In natural (free) convection, fluid flow is caused by
density gradients in the fluid. The flow velocity is
significantly less than for forced convection.
Dimensionless numbers associated with
natural convection are:
The Nusselt number , which contains the convective
hL
coefficient Nu =
k
cp
The Prandtl number Pr =
k
1
,The Grashof number , which contains the acceleration
of gravity g and the volumetric coefficient of thermal
1
expansion . For ideal gases, = , where T is the
T
absolute temperature. For liquids and non-ideal gases,
is tabulated.
g (Ts − T ) L3
Gr =
2
The Rayleigh number
g (Ts − T ) L3 g (Ts − T ) L3
Ra = Gr Pr = Pr =
2
k
where: = = thermal diffusivity
cp
Hydrodynamic Boundary Layer on a
Heated Vertical Surface
2
, Hydrodynamic Boundary Layer on a
Cooled Vertical Surface
For a vertical surface, the characteristic length L
is the height of the surface.
For a vertical surface, the transition from laminar to
turbulent occurs at critical distance xc where the
local Rayleigh number is about 109 .
g (Ts − T ) xc3
Raxc (vertical surface) = 10 9
3
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