Download Engineering Thermodynamics

CONVECTION HEAT TRANSFER
P M V Subbarao
Associate Professor
Mechanical Engineering Department
IIT Delhi
A Controllable Characteristic of fluids……
Introduction
• Convection involves the transfer of heat by the motion and
mixing of "macroscopic" portions of a fluid (that is, the
flow of a fluid past a solid boundary).
• The term natural convection is used if this motion and
mixing is caused by density variations resulting from
temperature differences within the fluid.
• The term forced convection is used if this motion and
mixing is caused by an outside force, such as a pump.
• Heat transfer by convection is more difficult to analyze
than heat transfer by conduction because no single
property of the heat transfer medium, such as thermal
conductivity, can be defined to describe the mechanism.
• Heat transfer by convection varies from situation to
situation (upon the fluid flow conditions), and it is
frequently coupled with the mode of fluid flow.
• In practice, analysis of heat transfer by convection is
treated empirically (by direct observation).
• Convection heat transfer is treated empirically because of
the factors that affect the stagnant film thickness:
• Fluid velocity
• Fluid viscosity
• Heat flux
• Surface roughness
• Type of flow (single-phase/two-phase)
• Convection involves the transfer of heat between a surface at a given
temperature (Ts) and fluid at a bulk temperature (Tb).
• The exact definition of the bulk temperature (Tb) varies depending on
the details of the situation.
• For flow adjacent to a hot or cold surface, Tb is the temperature of the
fluid "far" from the surface.
• For boiling or condensation, Tb is the saturation temperature of the
fluid. For flow in a pipe, Tb is the average temperature measured at a
particular cross-section of the pipe.
• Newton’s law of cooling suggests a basic relationship for heat transfer
by convection:
Q  hATs  Tb 
h is called as Convection Heat Transfer Coefficient, W/m2K
Realization of Newton’s Law Cooling
• A general heat transfer surface may not be isothermal !?!
• Fluid temperature will vary from inlet to exit !?!?!
• The local velocity of flow will also vary from inlet to exit
?!?!
• How to use Newton’s Law in a Real life?
Local Convection Heat Transfer
Consider convection heat transfer as a fluid passes over a
surface of arbitrary shape:
Apply Newton’s law cooling to a local differential element
with length dx.
q  hTs  T 
''
Ts  T
h is called as Local Convection Heat Transfer Coefficient, W/m2K
The total heat transfer rate Q is
Q   q '' dAs  havg AS Tavg
As
Where, havg is the average convection heat transfer coefficient for
the entire surface.
1
As
havg 
where
Tavg
1

As
As
Tavg
 T
s
 T dAs
As
''
q
 dAs
Therefore
havg 
''
q
 dAs
As
 T
s
A
 T dAs
Concept of Solid Fluid Interaction
• Perfectly
smooth surface (ideal surface)
Real surface
U2
U1
U1
U2
U2
U
U
Φ
Φ
Φ
Specular reflection
Diffuse reflection
• The convective heat transfer is defined for a combined solid
and fluid system.
• The fluid packets close to a solid wall attain a zero relative
velocity close to the solid wall : Momentum Boundary Layer.
• The fluid packets close to a solid wall come to thermal
equilibrium with the wall.
• The fluid particles will exchange maximum possible
energy flux with the solid wall.
• A Zero temperature difference exists between wall and
fluid packets at the wall.
• A small layer of fluid particles close the the wall come to
Mechanical, Thermal and Chemical Equilibrium With solid
wall.
• Fundamentally this fluid layer is in Thermodynamic
Equilibrium with the solid wall.
Heat Transfer in Equilibrium Layer
At the wall for fluid layer :
 T 
 k fluid A   hAT fluid, wall  T 
 y 
At Thermodynamic equilibrium
T fluid, wall  Twall
 T 
k fluid  
y 

h
Twall  T 
• 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