Thermal Boundary Layer and Momentum Boundary Layer
Boundary
layers are an important concept in fluid mechanics, and they play a crucial
role in many engineering applications. When a fluid flows over a solid surface,
two types of boundary layers are formed: thermal and hydrodynamic. These
boundary layers are characterized by distinct features, and understanding them
is crucial for various engineering applications, including heat transfer,
aerodynamics, and fluid mechanics.
Thermal Boundary Layer
The
thermal boundary layer is a thin layer of fluid that forms near a solid
surface, where heat transfer takes place between the solid surface and the
fluid. When a fluid flows over a surface that has a different temperature than
the fluid, heat is transferred from the surface to the fluid or vice versa. The
thermal boundary layer is formed due to the temperature difference between the
solid surface and the fluid.
In
a fluid that is in motion, molecules in the fluid that are in contact with the
solid surface experience a transfer of energy due to the temperature difference
between the surface and the fluid. As a result, the molecules in the fluid near
the surface begin to move faster, creating a thin layer of fluid called the
thermal boundary layer. The thickness of the thermal boundary layer increases
as the distance from the surface increases.
The
thermal boundary layer is characterized by a temperature gradient, which is the
rate at which temperature changes with respect to distance from the solid
surface. The temperature gradient is steepest at the solid surface and
gradually decreases as the distance from the surface increases. As a result,
the fluid temperature is approximately equal to the surface temperature at the
solid surface, and the fluid temperature gradually approaches the bulk fluid
temperature as the distance from the surface increases.
The
thickness of the thermal boundary layer depends on several factors, including
the fluid velocity, fluid properties, surface temperature, and surface roughness.
In general, the thermal boundary layer thickness increases with increasing
fluid velocity, fluid viscosity, and surface temperature, while it decreases
with increasing surface roughness.
The
thickness of the thermal boundary layer can be calculated using the following
equation:
δT=
0.664⋅x/Rex 1/2 Pr1/3
where;
δT
is the thermal boundary layer thickness,
x
is the distance from the leading edge of the surface,
Rex
is the Reynolds number based on the distance x,
and
Pr is the Prandtl number of the fluid.
Consider
the flow of a fluid at a uniform temperature of T∞ over an isothermal flat
plate at temperature Ts. The fluid particles in the layer adjacent to the
surface will reach thermal equilibrium with the plate and assume the surface
temperature Ts. These fluid particles will then exchange energy with the
particles in the adjoining-fluid layer, and so on. As a result, a temperature
profile will develop in the flow field that ranges from Tsat the surface to T∞
sufficiently far from the surface.
Figure 1. Graphical representation of Thermal boundary layer on a flat plate
The
thickness of the thermal boundary layer δt at any location along the surface is
defined as the distance from the surface at which the temperature difference
T−Ts equals 0.99(T∞−Ts).
Momentum/Hydrodynamic Boundary Layer
The
hydrodynamic boundary layer is a thin layer of fluid that forms near a solid
surface, where the velocity of the fluid changes due to the presence of the
solid surface. This phenomenon is of great importance in fluid dynamics and
plays a crucial role in many engineering applications, such as aerodynamics,
hydrodynamics, and heat transfer.
When
a fluid flows over a solid surface, the fluid molecules in contact with the
surface are brought to a stop due to the friction between the fluid and the
surface. This creates a velocity gradient, which results in the formation of
the hydrodynamic boundary layer. The thickness of the hydrodynamic boundary
layer increases as the distance from the surface increases.
The
hydrodynamic boundary layer is characterized by a velocity gradient, which is
the rate at which velocity changes with respect to distance from the solid
surface. The velocity gradient is steepest at the solid surface and gradually
decreases as the distance from the surface increases. As a result, the fluid
velocity is approximately equal to the surface velocity at the solid surface,
and the fluid velocity gradually approaches the bulk fluid velocity as the
distance from the surface increases.
The
thickness of the hydrodynamic boundary layer depends on several factors,
including the fluid velocity, fluid properties, surface roughness, and Reynolds
number. In general, the hydrodynamic boundary layer thickness increases with
increasing fluid velocity, fluid viscosity, and surface roughness, while it
decreases with increasing Reynolds number.
The
Reynolds number is a dimensionless number that is used to predict the onset of
turbulent flow in a fluid. It is defined as the ratio of inertial forces to
viscous forces and is given by the following equation:
Re
= ρVL/ μ
where;
Re
is the Reynolds number,
ρ
is the density of the fluid,
V
is the velocity of the fluid,
L
is the characteristic length scale,
and
μ is the viscosity of the fluid.
The
characteristic length scale depends on the geometry of the problem and is
defined differently for different flow configurations. For example, for flow
over a flat plate, the characteristic length scale is the distance from the
leading edge of the plate.
Figure
2. Graphical representation of Momentum boundary layer
In
Figure 2, air is flowing from left hand side to right hand side. Initially, air
comes with uniform velocity of ‘U∞’(free stream velocity). As we know that due
to stick slip phenomena, the velocity of fluid layer immediately adjacent to
plate surface becomes zero. Then, due to viscosity of the fluid, the velocity
of second layer of fluid also decreases from it's free stream velocity, like
wise the velocity of adjacent fluid layers also begin to decrease from ‘U∞’
but, at one point it will reach near to free stream velocity (U = .99U∞). The
hydrodynamic boundary layer is a line, which is drawn using U= .99 U∞ along the
fluid flow direction.
Difference between Thermal
Boundary Layer and Momentum Boundary Layer
|
Property |
Momentum Boundary Layer |
Thermal Boundary Layer |
|
Governing Equation |
Navier-Stokes Equations |
Energy Equation |
|
Physical Quantity |
Velocity |
Temperature |
|
Primary Cause of Formation |
Viscous Shear Stress |
Thermal Conduction |
|
Flow Characteristic |
Irrotational |
Temperature Gradient |
|
Thickness |
Increases with Increasing Reynolds Number |
Decreases with Increasing Heat Flux |
|
Boundary Condition |
Zero Velocity at the Surface |
Zero Heat Flux at the Surface |
|
Flow Stability |
Laminar or Turbulent |
Laminar or Turbulent |
|
Transition to Turbulent |
Higher Reynolds Number |
Higher Rayleigh Number |
|
Dimensionless Parameters |
Reynolds Number (Re) |
Prandtl Number (Pr), Rayleigh Number (Ra) |
Applications
The thermal and hydrodynamic boundary layers are important in various engineering applications. For example, in heat transfer applications, the thermal boundary layer thickness is important in determining the rate of heat transfer from a solid surface to a fluid. The thickness of the thermal boundary layer can be reduced by increasing the fluid velocity, which can increase the rate of heat transfer.
In aerodynamics applications, the hydrodynamic boundary
layer thickness is important in determining the drag force experienced by an
object in a fluid flow. The thickness of the hydrodynamic boundary layer can be
reduced by smoothing the surface of the object, which can reduce the drag
force.
Conclusion
In conclusion, the boundary layer is an important region in fluid mechanics that occurs near a solid surface in contact with a fluid. Two important types of boundary layers are the momentum boundary layer and thermal boundary layer.
The momentum boundary layer arises due to the transfer of momentum from the fluid to the surface, which leads to the formation of a shear stress at the surface. The thickness of the momentum boundary layer increases with increasing Reynolds number and may transition from laminar to turbulent flow. This boundary layer has important applications in aerodynamics, heat transfer, and drag reduction.
On the other hand, the thermal boundary layer is formed due to the transfer of heat from the surface to the fluid. It arises due to the presence of a temperature gradient near the surface, and the thickness of the thermal boundary layer decreases with increasing heat flux. This boundary layer is important in many industrial processes, such as cooling of electronic devices, heating and cooling of buildings, and heat exchangers.
Both the momentum and thermal boundary layers are governed by different equations and physical quantities, and their properties differ in several ways. Understanding the behavior and characteristics of these boundary layers is essential for many practical applications, such as the design of heat transfer systems and aerodynamic surfaces.
In summary, the study of boundary layers has important
applications in various fields of engineering and science, and further research
in this area is essential to develop more efficient and effective technologies.
Comments
Post a Comment