CONVECTION : An Activity at Solid Boundary

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CONVECTION An Activity at Solid Boundary

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

Identify and Compute Gradients at Boundary ..
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Heat Transfer in Equilibrium Layer
At the wall for fluid layer
At Thermodynamic equilibrium

• 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.

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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.

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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

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Entrance and developed flows
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Temperature Profile in Internal Flow
Hot Wall Cold Fluid
q
Ts(x)
Ti
Cold Wall Hot Fluid
q
Ti
Ts(x)
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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.

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A continuously Growing Solid affected Region.

• The Boundary Layer

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CONVECTION BOUNDARY LAYER

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

A tiny but very effective part of A Fluid Flow
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De Alembert to Prandtl
Ideal to Real
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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, d(x).
• Likewise, a temperature gradient forms (T 8 ? Ts)
  in the thermal boundary layer, dt(x),
• Therefore, examine the boundary layer at the
  surface (y 0).
• Flat Plate Boundary Layer is an hypothetical
  standard for initiation of basic analysis.

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Velocity Boundary Layer
Fluid particles in contact with the surface have
zero velocity u(y0) 0 no-slip boundary
condition Fluid particles in adjoining layers are
retarded d(x) velocity boundary layer thickness
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At the surface there is no relative motion
between fluid and solid. The local momentum
flux (gain or loss) is defied by Newtons Law of
Viscosity
Momentum flux of far field stream
The effect of solid boundary ratio of shear
stress at wall/free stream Momentum flux
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Coefficient of friction
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Thermal Boundary Layer
Fluid particles in contact with the surface
attain thermal equilibrium T(y0) Ts Fluid
particles transfer energy to adjoining layers dt
(x) thermal boundary layer thickness
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Hot Surface Thermal Boundary Layer
Plate surface is warmer than the fluid (Ts gt T8)
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Cold Surface Thermal Boundary Layer
Plate surface is cooler than the fluid (Ts lt T8)
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At the surface, there is no fluid motion, heat
transfer is only possible due to heat conduction.
Thus, from the local heat flux
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 Newtons Law of Cooling
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Scale of temperature
Temperature distribution in a boundary layer of a
fluid depends on
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n Potential for diffusion of momentum change
(Deficit or excess) created by a solid
boundary. a Potential for Diffusion of
thermal changes created by a solid boundary.
Prandtl Number The ratio of momentum diffusion
to heat diffusion.
Other scales of reference
Length of plate L Free stream velocity uoo
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This dimensionless temperature gradient at the
wall is named as Nusselt Number
Local Nusselt Number
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Average Nusselt Number
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Computation of Dimensionless Temperature Profile

• First Law of Thermodynamics for A CV
• Energy Equation for a CV
• How to select A CV for External Flows ?

Relative sizes of Momentum Thermal Boundary
Layers