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

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1 1 T 2 T flow 1 T 2 T Sufficiently large to overcome retarding influence of viscous forces. 21 TT > Heat transfer occurs by conduction. < 12 < 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.
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2 u(y) T, (u 0 ) ∞∞∞ ρ = x y s T T (Heated vertical plate) > Governing Differential Equation (x-Momentum) 2 2 uu 1 p u uv g xy x y ∂∂ += −− + ν ∂∂ρ (1) But p g x = −ρ (2) (from evaluating Eq. (1) in quiescent region.) 2 2 g u () y ρ ρ + ν ρ (3) Introduce Volumetric Coefficient of Thermal expansion β . force per unit mass Buoyancy force.
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3 pc 1 T =  ∂ρ β=−  ρ∂  (4) Hence, 1 (T T ) TT ρ−ρ ⇒ ρ −ρ=+ρβ ρ− 2 2 uu u uvg ( T T ) xy y ∂∂ += β + ν (5) , (7) …Momentum Continuity uv 0 (6) Thermal Energy 2 2 T y α (8) Boundary Conditions: y 0 = : u v 0 = = s = .
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This note was uploaded on 10/13/2010 for the course MECH 414 taught by Professor Ghia during the Winter '06 term at University of Cincinnati.

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

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