Free_Convection

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

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 = .
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 10

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online