Convection heat transfer

YMCA University of Science & Technology, FaridabadDepartment of Mechanical Engineering

Dr.Vikram Singh

Convection: Processes and Properties Free Convection:-1) Circulation of bulk fluid motion is caused by changes in fluid density

resulting from temperature gradients between the solid surface and the mainmass of fluid. The stagnant layer of fluid in the immediate vicinity of the hotbody gets thermal energy by conduction.

2) The energy thus transferred serves to increase the temperature and internalenergy of fluid particles. Because of temperature rise, these particles becomeless dense and hence lighter than the surrounding fluid particles. The lighterfluid particles move upwards to a region of low temperature where they mixwith and transfer a part of their energy to the cold particles. Simultaneouslythe cool heavier particles descend downwards to fill the space vacated by thewarm fluid articles.

3) The circulation pattern, upward movement of the warm fluid and downwardmovement of cool fluid, is called convection currents. These currents aresetup naturally due to gravity alone and are responsible for heat convection.

YMCA Institute of EngineeringDepartment of Mechanical EngineeringDr. Vikram Singh

Forced Convection:-1) Flow of fluid is caused by a pump, a fan or by the

atmospheric winds. These mechanical devices provide adefinite circuit for the circulating currents and thatspeeds up the heat transfer rate.

Examples of forced convection are cooling of internal combustion engines, air conditioning installations and nuclear reactors, condenser

tubes and other heat exchange equipment.

Introduction


Dr.Vikram Singh

Forced ConvectionFlow of fluid is caused by a pump, a fan or by theatmospheric winds. These mechanical devices provide adefinite circuit for the circulating currents and thatspeeds up the heat transfer rate.

Examples of forced convection are cooling of internal combustion engines, air conditioning installations and nuclear reactors, condenser

tubes and other heat exchange equipment.


Dr.Vikram Singh

LAMINAR AND TURBULENT FLOWLaminar flow : The fluid particles move in flat or curved un-

mixing layers or streams and follow a smooth continuous path. The paths of fluid movement are well-defined and the fluid particles retain their relative positions at successive cross-sections of the

flow passage. There is no transverse displacement of fluid particles; the particles remain in an orderly sequence in each layer. Soldiers on a parade provide a somewhat crude analogy to laminar flow.


Dr.Vikram Singh

Turbulent flow : The motion of fluid particles is irregular, and itproceeds along erratic and unpredictable paths. The stream linesare interwined and they change in position from instant to instant.Fluctuating transverse velocity components are superimposed onthe main flow, and the velocity of individual fluid elementsfluctuate both along the direction of flow and perpendicular to it.Obviously a turbulent flow is eddying and sinuous rather thanrectilinear in character. The turbulent flow resembles a crowd ofcommuters in a rail road station during the rush hour.

µρVdRe =

mean flow velocity V; density of fluid ρ;dynamic viscosity of the fluid µcharacteristic dimension of the flow passage, for example the diameter d of the pipe


Dr.Vikram Singh

For fluid flow through a pipe, low Reynolds number upto 2300 is indicative of laminar flow. From Re = 2300 to 6000, the laminar flow begins a transition to turbulent flow. Usually the flow is completely turbulent at Re = 6000.

•In many flow situations, the duct is not circular but is rectangular,trapezoidal or even an annulus formed by a tube within anothertube.

•In that case, the characteristics dimension d in the relationRe = Vdρ/µ is the equivalent (hydraulic) diameter which is definedas four time the cross-sectional flow area divided by the wettedperimeter.


Dr.Vikram Singh


Dr.Vikram Singh

NEWTON-RIKHMAN LAW : CONVECTION RATE EQUATION

Q=hA(ts -tf); The unit of h are W/m2-deg, and it is referred to as convective heat transfer

coefficient units of h is

The value of film coefficient is dependent upon :surface conditions : roughness and cleanliness geometry and orientation of the surface : plate, tube and cylinder placed vertically or horizontallythermo-physical properties of the fluid : density, viscosity/specific heat, coefficient of expansion and thermal conductivitynature of fluid flow : laminar or turbulent boundary layer configuration prevailing thermal conditions


Dr.Vikram Singh

Typical values of convective coefficients

Free convection Forced convectionAir 3-7 Air & superheated

steam30-300 W/m2K

Gases 2-20 Oil 60- 3000

liquids 30-300 Water 300- 10,000


Dr.Vikram Singh

Consider a heated wall surface at temperature ts over which a fluid is flowingwith undisturbed velocity U∞ and temperature t∞.The particles of fluid in intimate contact with the plate tend to adhere to it, anda region of variable velocity builds up between the plate surface and the freefluid stream as indicated .


Dr.Vikram Singh

Rate equationThe fluid velocity decreases as it approaches the solid surface, reaching to zero (noslip condition) in the fluid layer immediately next to the surface. This thin layer ofstagnated fluid has been called the hydrodynamic boundary layer. The quantity of heattransferred is highly dependent upon the fluid motion within this boundary layer,being determined chiefly by the thickness of the layer.

The boundary layer thickness δ is arbitrarily defined as the distance y fromthe plate surface at which the velocity approaches 99% of free stream velocity.Likewise a region of fluid motion near the plate in which temperaturegradients exist is the thermal boundary layer and its thickness δt is defined asthe value of transverse distance y from the plate surface at which

99.0≈−−

∞tttt

s

s


Dr.Vikram Singh

Types of ConvectionAt the plate surface, there is no fluid motion and the energy transport can occur only by conduction. From energy balance, this heat transport must equal the heat transferred by convection into the rest of the fluid. Thus

)(0

∞=

−=

∂∂

−= tthAytkAQ s

y

If temperature field of the fluid varies only in the direction of the coordinate normal to the plate surface, then

0)( =∞

−

−=ys dy

dttt

kh


Dr.Vikram Singh

{ }0

0

0

)/()/()(

/)()/(

)(

=

∞

∞

=

=∞

−−=

−

−=

−

−=

y

ss

s

y

ys

lydttttd

lttdydt

khl

dydt

ttkh

The dimensionless parameter hl/k is called Nusselt number. Apparently theNusselt number may be interpreted as the ratio of temperature gradient atthe surface to an overall or reference temperature gradient. The parameter

{ }0)/(

)/()(

=

∞

−−

y

ss

lydttttd The parameter represents the dimensionless slope

of the temperature distribution curve at the surface.

The Nusselt number is a convenient measure of the convective heat transfer coefficient. For a given value ofNusselt number, the convective surface coefficient h is directly proportional to thermal conductivity k of the fluid,and inversely proportional to the significant length l.


Dr.Vikram Singh

Significance of Dimensionless numberReynolds number is indicative of the relative importance of inertial and viscouseffects in a fluid motion.

At low Reynolds number, the viscous effects dominate and the fluid motion is laminar.

At high Reynolds number, the inertial effects lead to turbulent flow and the associatedturbulence level dominates the momentum and energy flux.

Reynolds number constitutes an important criterion of kinematic and dynamic similarity inforced convection heat transfer.

µρ

µρ Vl

VllVRe ===

22

forceviscousforceinteria


Dr.Vikram Singh

Grashof Number

Gr indicates the relative strength of the buoyant to viscous forces.

From its mathematical formulation

2

2

223

23

2

23

force)(viscousforceinteriaforcebuoyant

)()(

)(

×=

×∇=

∇=

∇=

VllVTgl

Tgl

TglGr

µρβρ

µρβρ

µβρ

Grashof number has a role in free convection similar to that played by Reynoldsnumber in forced convection. Free convection is usually suppressed at sufficientlysmall Gr, begins at some critical value of Gr (depending upon the arrangement) andthen becomes more and more effective as Gr increases


Dr.Vikram Singh

Prandtl Number Pr is indicative of the relative ability of the fluid to diffusemomentum and internal energy by molecular mechanisms. From its mathematicalformulation,

Apparently Pr is the ratio of the kinematic viscosity to thermal diffusivity of the fluid.

The kinematic viscosity indicates the momentum transport by molecular friction and thermaldiffusivity represents the heat energy transport through conduction.

Obviously Pr provides a measure of the relative effectiveness of momentum and energy transportby diffusion.

For highly viscous oils, Pr is quite large (100 to 10,000) and that indicates rapid diffusion ofmomentum by viscous action compared to the diffusion of energy.

Prandtl number for gases is near unity and accordingly the momentum and energy transfer bydiffusion are comparable. In contrast, the liquid metals have Pr - 0.003 to 0.01 and that indicatesmore rapid diffusion of energy compared to the momentum diffusion rate.


Dr.Vikram Singh

Stanton Number-St is the ratio of heat transfer coefficient to theflow of heat per unit temperature rise due- to the velocity of the fluid.

Peclet Number Pe is the ratio of heat flow rate by convection to flow rate by

conduction under a unit temperature gradient and through thickness


Dr.Vikram Singh

YMCA Institute of EngineeringDepartment of Mechanical Engineering

Empirical correlations for Free & Forced Convection

Bulk temperature: It denotes the equilibrium temperature that would result if the fluid at a cross-section was thoroughly mixed in an adiabatic container. The bulk temp in heat exchanger tube is arithmetic mean of inlet and outlet temperatures.

Mean film temperature: It is the arithmetic mean of the surface temperature and undisturbed temperature of the fluid which flows past it.

Dr.Vikram Singh

YMCA Institute of EngineeringDepartment of Mechanical Engineering

Local and Average Convective Coefficient

Dr. Vikram Singh


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Convection heat transfer