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Chapter 9: Free Convection. x points downward. (a) If the temperature difference exceeds a critical value, the buoyancy forces are able to overcome the retarding influence of viscous forces, and fluid circulation would occur. The top heavier fluid descends, while the lighter bottom fluid rises.

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## Chapter 9: Free Convection

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**Chapter 9: Free Convection**x points downward (a) If the temperature difference exceeds a critical value, the buoyancy forces are able to overcome the retarding influence of viscous forces, and fluid circulation would occur. The top heavier fluid descends, while the lighter bottom fluid rises. (b) No fluid circulation would occur. Free or natural convection: the flow is induced by buoyancy forces which arise from density differences caused by temperature variations in the fluid. The body force normally involved may be gravitational or centrifugal force. Applications:Thermal manufacturing processes, thermal management of electronics systems, and environmental sciences, where it drives oceanic and atmospheric motions, as well as the related heat and mass transfer processes.**Typical Free Convection**Fig. 9.2 Buoyancy-driven free boundary layer flows in an extensive, quiescent medium. (a) Plume formation above a heated wire. (b) Buoyancy jet associated with a heated discharge.**The governing equations may be similar to those for forced**convection except that the flow is driven by buoyancy force. Consider a laminar boundary flow as shown in Fig. 9.3 with the assumptions that the flow is steady, two-dimensional, and constant properties. However, the exception involves the variation of density in the buoyancy force term, since it is this variation that induces fluid motion. Starting with Eq. (6.28), the x-momentum equation would be Typical Free Convection Fig. 9.3 Buoyancy development on a heated vertical plane. The pressure at x is equal to the pressure outside of the boundary layer at the same x. The outside is static and is controlled by gravitational force.**Introducing the volumetric thermal expansion coefficient:**Governing Equations In formulating correlation for predicting free convection heat transfer coefficient, the Grashof number in place of the Reynolds number associated with the forced convection: which may be interpreted as the ratio of the buoyancy forces to the viscous forces acting on the fluid.

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