MECH-414 Momentum & Energy Transport ANALYSIS OF FLOW IN PIPES AND OVER SURFACES 1. Introduction The Navier-Stokes equations govern the motion of a Newtonian fluid; see page 214, Fluid Mechanics Text
The Thermal Boundary Layer The thermal boundary layer is the thin region of wall-adjacent viscous flow in which temperature gradients exist. Consider Ts = Constant. Then, the thickness of the thermal
1
Free Convection (or, Natural Convection) No externally forced flow Buoyancy (density differences) cause flow to occur < 0 , i.e., T . T
Need temperature gradient, in a gravity field.
T1
T1
flow
T2
Non-dimensionalization of Momentum Equation
u u 2u u +v = g (T T ) + 2 x y y
Introduce non-dimensional quantities with superscript *:
u = u * U o ; x = x * L ; y = y* L T = T + T* (Ts T )
Note that al
Boundary-Layer Thickness,
This is a very thin layer in the immediate neighborhood of the body where the fluid viscosity exerts an essential influence, in the sense that the shearing stresses are impo
Notes on Boundary Layers, Integral Approach, etc.
o Flat Plate self-similar governing differential equation:
2f + ff = 0, where f ( x ) ~ ( x, y ) , = ( x, y ) .
o Pipe flow - fully developed governin
Film Condensation on a vertical wall
g Ts T T
Ts T Tsat T
Ts < Tsat < T
T
Ts < T
l
u
Without Phase Change With Phase Change
u,v,T ul ,vl ,Tl
Governing Differential Equations and Boundary Conditions Mo
Chapter 10 Summary of Concepts
1. Pool Boiling pg. 596 The liquid is quiescent, and its motion near the surface is due to free convection and due to mixing induced by bubble growth and detachment. For
February 1, 2006 What is the Hydrodynamic Boundary Layer? The hydrodynamic Boundary Layer on a flat plate is a thin region adjacent to the surface (boundary) within which viscous effects are confined.
Self-Similarity
A flow is said to be self similar if the prevailing velocity profiles at various streamwise stations x can be made congruent, through the use of appropriately defined independent and d
Boundary-Layer Theory
Simplified Navier-Stokes Equations for a very Thin Layer of Flow Adjoining a Solid Boundary
Laminar Boundary Layer Over Flat Plate
2-D Incompressible Flow, x-y coordinates, Navie
Summary of Thermal Considerations for Pipe Flows q s = constant h fd hD Nu D @ k h fd = constant Nu D = constant
Ts = constant h fd = constant Nu D = constant
T . x
dependence on r, x independent of r
SOLUTION FOR THE BOUNDARY LAYER ON A FLAT PLATE
Consider the following scenario. 1. A steady potential flow has constant velocity U in the x direction. 1. An infinitely thin flat plate is placed into
Introduction to Convection: Introduction Flow and Thermal Considerations
Chapter Six and Appendix E Sections 6.1 to 6.9 and E.1 to E.3
Boundary Layer Features Bounda
Boundary Layers: Physical Features
Introduction to Convection: Introduction Flow and Thermal Considerations
Chapter Six and Appendix E Sections 6.1 to 6.9 and E.1 to E.3
Boundary Layer Features Boundary
Boundary Layers: Physical Featur
1
Pool Boiling: Boiling in an otherwise Stationary Liquid
liquid: boiling
Ts > Tsat
q = h (Ts Tsat ) s
(10.3)
= h ( Te )
excess temperature
Boiling Curve
Nucleate Boiling
q = C ( Te ) a [n ] b s
(10.4