Download - CONVECTION : An Activity at Solid Boundary
CONVECTION : An Activity at Solid Boundary
P M V Subbarao
Associate Professor
Mechanical Engineering Department
IIT Delhi
Identify and Compute Gradients at Boundary …..
Heat Transfer in Equilibrium Layer
• The thickness of stagnant layer decides the magnitude of normal temperature gradient at the wall.
• And hence, the thickness of wall fluid layer decides the magnitude of convective heat transfer coefficient.
• Typically, the convective heat transfer coefficient for laminar flow is relatively low compared to the convective heat transfer coefficient for turbulent flow.
• This is due to turbulent flow having a thinner stagnant fluid film layer on the heat transfer surface.
At the wall for fluid layer :
TThAy
TAk wallfluidfluid ,
TT
yT
k
hwall
layerwall
fluid
At Thermodynamic equilibrium
wallwallfluid TT ,
Estimation of Heat Transfer Coefficient
• Estimation of heat transfer coefficient is basically computation of temperature profile.
• A general theoretical and experimental study to understand how the stagnant layer is developed.
• The global geometry of the solid wall and flow conditions will decide the structure of stagnant layer.
• Basic Geometry : Internal Flow or External Flow.
TT
yT
k
hwall
wall
fluid
Internal Flows
• Internal flow can be described as a flow whose boundary layer is eventually constrained as it develops along an adjacent surface.
• The objectives are to determine if:• the flow is fully developed (no variation in the
direction of the flow• laminar or turbulent conditions• the heat transfer
q’’
Ti
Ts(x)
Ti Ts(x)q’’
Hot Wall & Cold Fluid
Cold Wall & Hot Fluid
Temperature Profile in Internal Flow
External Flows
• Any property of flow can have a maximum difference of Solid and free stream properties.
• There will be continuous growth of Solid surface affected region in Main stream direction.
• The extent of this region is very very small when compared to the entire flow domain.
• Free stream flow and thermal properties exit during the entire flow.
CONVECTION BOUNDARY LAYER
P M V Subbarao
Associate Professor
Mechanical Engineering Department
IIT Delhi
A tiny but very effective part of A Fluid Flow……
Introduction
• A boundary layer is a thin region in the fluid adjacent to a surface where velocity, temperature and/or concentration gradients normal to the surface are significant.
• Typically, the flow is predominantly in one direction.• As the fluid moves over a surface, a velocity gradient is
present in a region known as the velocity boundary layer, δ(x).
• Likewise, a temperature gradient forms (T ∞ ≠ Ts) in the thermal boundary layer, δt(x),
• Therefore, examine the boundary layer at the surface (y = 0).
• Flat Plate Boundary Layer is an hypothetical standard for initiation of basic analysis.
Velocity Boundary Layer
Fluid particles in contact with the surface have zero velocity
u(y=0) = 0; no-slip boundary condition
Fluid particles in adjoining layers are retarded
δ(x): velocity boundary layer thickness
At the surface there is no relative motion between fluid and solid.
The local momentum flux (gain or loss) is defied by Newton’s Law of Viscosity :
0
y
wall y
u
Momentum flux of far field stream:
2
2''
uP
The effect of solid boundary : ratio of shear stress at wall/free stream Momentum flux
Thermal Boundary Layer
Fluid particles in contact with the surface attain thermal equilibrium
T(y=0) = Ts
Fluid particles transfer energy to adjoining layers
δt (x): thermal boundary layer thickness
At the surface, there is no fluid motion, heat transfer is only possible dueto heat conduction. Thus, from the local heat flux:
0
''
y
y
Tkq
wall
This is the basic mechanism for heat transfer from solid to liquid or Vice versa.
The heat conducted into the fluid will further propagate into free stream fluid by convection alone.
Use of Newton’s Law of Cooling:
TThq s''
0
''
yys y
TkTThq
Temperature distribution in a boundary layer of a fluid depends on:
pL
s
ckdx
dpxf
TT
TT,:,Re,
*
**
Scale of temperature:
ss TTTT
:,Re,*
**
dz
dpxf
TT
TTL
s
Pr,,Re,
*
**
dx
dpxf L
Prandtl Number: The ratio of momentum diffusion to heat diffusion.
T
m
Pr
Other scales of reference:
Length of plate: L
Free stream velocity : uoo
Potential for diffusion of momentum change (Deficit or excess) created by a solid boundary.
Potential for Diffusion of thermal changes created by a solid boundary.
0
''
y
s y
TkTThq
0*
0 *scaleLength
scale eTemperatur
yyyy
T
0
**
y
sfluids yL
TTkTTh
Pr,,Re,*
**
0*
* dx
dpxf
k
hL
y Lfluidy
This dimensionless temperature gradient at the wall is named asNusselt Number:
resistance Convection
resistance Conduction1
h
kL
k
hLNu fluid
fluid
Pr,,Re,*
**
0*
* dx
dpxf
k
hL
yNu L
fluidy
Local Nusselt Number