Lecture 23 Natural Convection PPT

Lecture 23 Natural Convection PPT - 1 MECE 4364 Heat...

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MECE 4364 Heat Transfer Prof. Dong Liu Department of Mechanical Engineering University of Houston 1 Lecture 23 – Nov 09, 2010 Lecture 23 Free (Natural) Convection 2
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Lecture 23 Free Convection: Overview ± Free Convection (or Natural Convection) ± fluid motion induced by buoyancy forces ± buoyancy forces arise when there are density gradients in a fluid and a body force proportional to density ± Density Gradient ± due to temperature gradient ± Body Force ± gravity (function of mass) thermally driven flow Basic Principle : heavy fluid falls and light fluid rises creating vortices 3 Lecture 23 Overview ± Internal vs. External ± free convection can be generated in a duct or enclosure (internal) ± along a free surface (external) ± in both internal & external cases, free convection can interact with forced convection (mixed convection) ± Free Boundary Flow ± occur in an extensive quiescent fluid ( i.e. , infinite, motionless fluid) ² no forced convection ± induces a boundary layer on a heated or cooled surface (T s T ) ± can generate plumes and buoyant jets 4
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Lecture 23 Dimensionless Parameters ± Pertinent Dimensionless Parameters ± Grashoff Number ± Recall Reynolds number for forced convection: ± Rayleigh Number As Grashoff # increases : buoyancy overcomes friction and induces flow Gr L = g β T s T () L 3 ν 2 ~ buoyancy force viscous force g gravitational constant thermal expansion coefficient (fluid property) L characteristic length 1 T [K -1 ] ideal gas Ra L = Gr L Pr = g T s T ( ) L 3 να = μ ρ kinematic viscosity of fluid Re L = VL ~ inertial force viscous force comparable to Peclet number (Pe) for forced convection 5 Lecture 23 Mixed Convection ± Mixed Convection ± a condition where both free and forced convection effects are comparable ± free convection can assist , oppose , or act orthogonally to forced convection ± When is mixed convection significant? ± an assessment of scales is conducted through a comparison of free and forced non-dimensional parameters ± Affect on heat transfer ± forced and free convection DO NOT combine linearly buoyancy force inertial force ~ Gr L Re L 2 >> 1 O (1) << 1 free convection dominates mixed convection condition forced convection dominates Nu L = f Re L , Gr L ,Pr ( ) Nu L = f Re L Nu L = fG r L Nu L n = Nu L , forced n ± Nu L , free n n = 3 assisting/opposing n = 7 2 or 4 transverse + Î assisting/transverse - Î opposing 6
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Lecture 23 Boundary Layers ± Boundary Layer development on a vertical plate ± heated plate: ascending flow with maximum velocity occurring in the boundary layer and zero velocity at the plate and in the free stream ± cooled plate: descending flow ± Boundary Layer Equations u x + v y = 0 ˆ x direction : u u x + v u y = ν 2 u y 2 + g β T T () ρ c p u T x + v T y = k 2 T y 2 + μ u y 2 buoyancy body force due to gravity Notes: 1. this formulation applied the
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This note was uploaded on 01/27/2011 for the course MECE 4364 taught by Professor Lipinglui during the Winter '10 term at University of Houston.

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Lecture 23 Natural Convection PPT - 1 MECE 4364 Heat...

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