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Free_Convection

# Free_Convection - 1 Free Convection(or Natural Convection...

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1 1 T 2 T flow 1 T 2 T Sufficiently large to overcome retarding influence of viscous forces. 2 1 T T > Heat transfer occurs by conduction. 2 1 T T < 1 2 T T < 2 T Free Convection (or, Natural Convection) No externally forced flow Buoyancy (density differences) cause flow to occur 0 T ∂ρ < , i.e., T ↑ ρ ↓ . Need temperature gradient , in a gravity field . Natural-Convection Flow bounded by a surface or not bounded by a surface, i.e., free-boundary flows.
2 u(y) T , (u 0) ρ = x y s T T (Heated vertical plate) > Governing Differential Equation (x-Momentum) 2 2 u u 1 p u u v g x y x y + = − + ν ρ ∂ (1) But p g x = −ρ (2) (from evaluating Eq. (1) in quiescent region.) 2 2 u u g u u v ( ) x y y + = ρ − ρ + ν ρ (3) Introduce Volumetric Coefficient of Thermal expansion β . force per unit mass Buoyancy force.

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3 p c 1 T = ∂ρ β = − ρ (4) Hence, 1 (T T ) T T ρ − ρ β = − ⇒ ρ − ρ = + ρβ ρ 2 2 u u u u v g (T T ) x y y + = β + ν (5) , (7) …Momentum Continuity u v 0 x y + = (6) Thermal Energy 2 2 T T T u v
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Free_Convection - 1 Free Convection(or Natural Convection...

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