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Chapter 7 Natural (Free) Convection

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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 governing natural convection phenomena. The chapter covers the governing equations for natural convection, including the Boussinesq approximation, which simplifies the Navier-Stokes equations. It explains the role of Grashof number and Rayleigh number in characterizing the strength of natural convection in different scenarios. In addition to theoretical aspects, the document explores various geometries and configurations where natural convection is prominent, such as vertical and inclined surfaces, enclosures, and heat sinks. It provides insights into heat transfer correlations and empirical correlations used for practical engineering calculations. The chapter also highlights the significance of natural convection in engineering applications, including cooling of electronic devices, solar energy utilization, and building ventilation. It discusses strategies for enhancing or suppressing natural convection for specific engineering needs. Moreover, the document covers experimental techniques and numerical simulations used to investigate and validate natural convection behaviors. It also explores advanced topics such as transient and turbulent natural convection, offering a comprehensive understanding of this complex phenomenon. Researchers, engineers, and students will find this chapter a valuable resource for comprehending the principles and applications of natural convection, enabling them to address challenges and optimize designs across various industries and scientific fields.

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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





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