HEAT TRANSFER CO EFFICIENT VS HEAT FLOW RATE BY FORCED CONVECTION

DEPARTMENT OF PETROCHEMICAL ENGINEERING
HEAT TRANSFER CO EFFICIENT VS HEAT FLOW RATE
BY FORCED CONVECTION
A PROJECTREPORT
2014-2015
Submitted by
Under the guidance of
, B-TECH
LECTURER OF PETROCHEMICALDEPARTMENT
In partial fulfillmentforthe awardof degree of
DIPLOMA IN PETROCHEMICAL ENGINEERING
NANDHA POLYTECHNIC COLLEGE
ERODE- 638052
PROJECT REPORT 2014-2015

BONAFIDE CERTIFICATE
This is to certificate that this project report on HEAT TRANSFER CO-EFFICIENT
VS HEAT FLOW RATE BY FORCED CONVECTION is the bonafide work of ) who
carried out the project under
Mr., B.Tech Mr., M.Tech,
PROJECTGUIDE HEAD OFTHE DEPARTMENT
DEPT.OF PETROCHEMICALENGG DEPT.OFPETROCHEMICAL ENGG
NANDHA POLYTECHNICCOLLEGE NANDHA POLYTECHNIC COLLEGE
ERODE-52 ERODE-52
NANDHA POLYTECHNIC COLLEGE
ERODE-638052
PROJECT REPORT2014-2015
HEAT TRANSFER CO-EFFICIENT VS HEAT FLOW RATE

Certifiedthatthisis bonafidereport of project
Work done by
NAME : …………………………………
REG.NO: …………………………………
During The Year 2014-2015
PROJECT GUIDE H.O.D
Certifiedthatthe candidate wasexaminedinvivavoce examination
Heldon
INTERNAL EXAMINER EXTERNAL EXAMINER

ACKNOWLEDGEMENT
We are happy to present this project report entitled HEAT TRANSFER CO-EFFICIENT VS HEAT
FLOW RATE BY FORCED CONVECTION that undertook as part of programmer in diploma engineering
during the year 2010-2011.
We wishtoacknowledge withgratitude and profuse thanks to our beloved chairman T, B.Com.
And our secretary Thiru.S. B.P.T., who has launched a tremendous atmosphere for our education.
We expressour sincere gratitude and profuse thank to Mr.M., M.E., Ph.D., the principal of our
institution for providing all the necessary facility in the college for the successful completion of our
project.
We wishtoconveyour profuse thankto. Mr., M. Tech., Headof the department,Departmentof
petrochemical engineering for bring out this project.
We hardly thank to our project Guide Mr., M Tech., for his encouragement and guidance
throughout this project.
We express our sincere thanks to Mr. KUMAR, B.E., Senior lecturer, Mr. KUMAR,
B.Tech.AndMISS. B.Tech. Lecturer of petrochemical engineering Department and our friends and
beloved parents served in all aspects to complete our project successfully.

SYNOPSIS:
Heat transfer co-efficient; involve production or absorption of energy in the form of heat.
The laws governing the transfer of heat and the types of apparatus that have their main object the
control of heat flow are great importance by forced convection or phase change between a fluid
& a solid. Modes of heat transfer are conduction, convection, radiation. And it from a warmer
fluid to a cooler fluid, usually through a solid wall separating the fluids.
Typical examples are reducing the temperature of a fluid by heat transfer of sensible heat
to a cooler fluid, heat sinks are the heat exchangers used in refrigeration and air conditioning
systems and the radiator (also a heat exchanger) in a car. Heat sinks also help to cool electronic
and optoelectronic devices such as higher power lasers & light emitting diodes. References are
used as cars law, H.S.., and J.C. Jaeger. Conduction of heat in solids; Wiley, 1969 & the
analytical theory of heat transfer by A. Freeman. Dover. 1955. It is used in typical heat exchange
equipment & double pipe heat exchanger. If you have been following along since the beginning
of this lesson, then developing a progressively sophisticated understanding of temperature &
heat.

HEAT TRANSFER CO-EFFICIENT [VS] HEATFLOW RATE
HEAT TRANSFER:
 Heat always moves from a warmer place to a cooler place.
 Hot objects in a cooler room will cool to room temperature.
 Cold objects in a warmer room will heat up to room temperature.
INTRODUCTION:
The several kinds of heat sink assembly commonly used. With the increase in
dissipation from microelectronic devices and the reduction in overall form factors, it become
an essential practice to optimize heat-sink designs with least trade-offs in material and
manufacturing costs. The heat-sink assembly is powerful apparatus for heat removal in
today’s thermal engineering. This apparatus is mainly designed to remove heat effectively
from the equipment to environmental.
The augmentation of heat dissipation in heat sink has attracted the attention of
researchers for several decades. For all types of heat sink assembly, the size of each fin and
the arrangement of fin array play a very important role to promote heat transfer. Kern and
Kraus (1972) studied the optimum design for fin and spine subjected to a constant heat
transfer coefficient. Saski and kishimoto (1986) optimized, with a criterion of fin to channel
thickness ratio of unity, the dimensions of water cooled micro channel at a given pressure
loss.

An analytical method of optimizing forced convection heat sinks was proposed by
knight et al. (1991)(1992) for fully developed flow in closed finned channels. They presented
normalized non-dimensional thermal resistances as a function of the number of channels
again for a fixed pressure drop. Kraus (1988) surveyed the whole progress of extended
surface. During the process for designing fins, material weight and manufacturing
availability are also the important factors to be concerned. Hence, Bar-Cohen andJelinek
(1985) presented a procedure to establish optimum arrays of longitudinal rectangular fins for
the least material optimization.
The optimum ratio of fin thickness to fin length can be found based on the maximum
heat flow per unit width from the fin. Computational techniques were also employed in
investigating the thermal performance of extruded heat sinks. (Metrol, A., 1993; Mansingh,
V. and K. Hassur, 1993) Yeh and Chang (1995) optimized the longitudinal convective fin
arrays that include various profiles. Rectangular, triangular, convex-parabolic and concave-
parabolic profiles were taken into consideration.
For vertical rectangular fins protruding from a vertical rectangular base, leung and
probert (1989) used experimental measurement to find the optimum spacing. Teertstraet al.
(1999) carried out the numerous methods to predict the average heat transfer rate for plate fin
heat sinks used in the design and selection of heat sinks for electronic applications .A
composite solution was developed for the limiting cases of fully developed and developing
flow between isothermal parallel plates and fluid velocity. Poulikakos and Bejan (1982) have
published extensively in the area of optimization according to an entropy minimization
approach. Kou et al. (2003) derived a transcendental equation that includes only three
variables to find the optimum longitudinal fin length and fin number in a heat sink.
In the optimum thermal design of a heat sink for the least material cost there is
usually two approaches forits realistic application. For the first approach, the shape and the
cross- sectional area of fin array and the total volume of the fins in a heat sink are prescribed
to ascertain its optimum fin length accompanied by the total fin number (Kou, et al., 2003).
For the second approach the number of fins and the volume of each fin are fixed to find its
optimal fin length and fin cross-section area for each particular fin shape (Bar- Cohen, A.
and M.Jelinek, 1985; Yeh. R.H. and M. Chang, 1995), where the shape of the longitudinal

fin is limited by theAust. J. Basic & Appl. Sci., 5(12): 1685-1692, 2011.1686rectangular
cross-section and the width or height of the fin is assumed to be a fixed constant, the cross-
section of the longitudinal fin in study can cover square, rectangular, equilateral triangular
and cylindrical fin arraysbecause of the generalized mathematical formulation. Instead of
assuming a fixed width in a rectangular fin, assumes a known ratio of fin thickness to fin
width in advance to match the requirement of the present analysis. In this paper by knowing
the values of Biota number, Bi, heat transfer coefficient, H and shape parameter, the
optimum equation with maximum heat dissipation can be solved to find the optimum
specification of fins in a heat sink.
Finally the performance of heat sink for square, rectangular triangular and cylindrical
fin arrays is demonstrated by thermal resistance, which is the most important factor for a heat
sink in designing an electronic cooling system.
Forced convection wall cavity insulation is conventionally measured and labeled for
thermal performance under specific steady state conditions with solid isothermal bounding
surfaces. This configuration, as a result, does not include air flow through the insulation that
can occur in actual applications.
Walls of low-rise residences, for example, have leakage paths through which air can
move due to small pressure differences between the interior and exterior of a residence. This
movement of air has an effect on the heating and cooling loads of the building. One approach
to the determination of the load added to a building due to air leakage adds the heat load
resulting from air flow to the heat flow through the envelope without forced convection.
The assumption that the
heat flow through insulation without air flow and the heat transfer resulting from air flow can
be added is not valid if the temperature distribution in the wall cavity insulation is affected
by the movement of air through the insulation. If wall cavity insulation is tight in a cavity,
then air leakage will be through the insulation and the temperature profile in the insulation
will be disturbed. Underlined and Johansson have provided a theoretical analysis of the
effect of air flow through thermal insulation that predicts heat-flow changes that depend on
the direction of air flow relative to the direction of air movement. Underlined and Johansson
used the terms contra flux insulation and pro flux insulation for the cases where the heat flow

is opposite the air-flow direction or heat flow is in the same direction as the air flow. The
purpose of the present research is to measure the effective thermal resistance of wall cavity
insulation with an imposed air flow through the insulation.
RE = ∆T/(Qnet/0.3414)
Where Qnet is the heat loss or gain from the conditioned space. The RE defined by is a
system value that depends on the air-flow.
DESCRIPTION OF APPARATUS:
The important relationship between Reynolds number, prenatal number and Nussle
number in heat exchanger design may be investigated in this self-containedunit. The
experimental set up (see sketch) consists of a tube through which air is sent in by a blower.
The test section consists of a long electrical surface heater on the tube which serves as a
constant heat flux source on the flowing medium. The inlet and outlet temperatures of the
flowing medium are measured by thermocouples and also the temperatures at several
locations along the surface heater from which an average temperature can be obtained. An
orifice meter in the tube is used to measure the airflow rate with a ‘U’ tube water manometer.
An ammeter and a voltmeter is provided to measure the power input to the heater. A power
regulator is provided to vary the power input to heater.Amulti point digital temperature
indicator is provided to measure the above thermocouples input. A valve is provided to
regulate the flow rate of air.
MODES OF HEAT TRANSFER:
 Conduction
 Convection
 Radiation
CONDUCTION:
 Transfer of thermal energy by direct contact – energy is transferred from
molecule to molecule when they collide.

 Best in solids, less in liquids, even less in gases.
 Good conductors transfer heat rapidly because their particles have greater
freedom to collide more often.
 Example: metals (esp. Cu, and Al)
 Poor conductors (insulators) transfer heat slowly.
 Example: Styrofoam, wood, glass, air.
CONVECTION:
 Transfer of thermal energy by currents in fluids (gases and liquids).
 Heat is carried by the fluid from a heat source to a heat sink.
TYPES OF CONVECTION:
THEORY:
 Natural Convection: Heat transfer through circulation of fluid due solely to
gravity.
 Forced Convection: Heat transfer through circulation of fluid due to forced
fluid movement (fan, pump, etc.)
NATURAL CONVECTION:
Convection Cell – driven by differences in density
 Fluid absorbs heat from a Heat Source (by conduction or radiation).
 Rises because it expands becoming less dense and therefore buoyant.
 As it rises it displaces the cooler fluid above it.
 The warm fluid begins to give up its heat to the surroundings (Heat Sink)
 The cooler fluid is denser and sinks continuing to force the warmer fluid up.

 This cooler fluid is now in contact with the Heat Source and absorbs energy,
expands and begins to rise. (The cycle continues…).
 Example: sea breeze/land breeze.
FORCED CONVECTION:
 The same heat exchange process as in the previous slide occurs, but the
current is driven by some external force like a fan or pump rather than just by
buoyancy.
 Example: Convection Oven or water pumped through the heating pipes in a
house.
RADIATION:
 Transfer of thermal energy by electromagnetic waves.
 All objects at temperatures above absolute zero radiate heat.
 Amount depends on object’s temperature, surface area, & color.
 Dark objects absorb and radiate radiant energy better than light ones,
Reflective objects don’t easily absorb or radiate energy.
 Examples: solar energy reaches earth across empty space, holding your hand
Near a hot object you feel the radiant energy.
HEAT SINK CATEGORIES:
One way to categorize heat sinks is by the cooling mechanism employed to remove
heat from the heat sinks. It can be largely divided into five categories: Passive Heat Sinks are
used in either natural convection or in applications where heat dissipation does not rely on
designated supply of air flows. Semi-Active Heat Sinks leverage off existing fans in the
system. Active Heat Sinks employ designated fans for its own use such as fan heat sinks in
either impingement or vertical flows. This type of heat sinks usually involves mechanically

moving component and its reliability depends on heavily on the reliability of the moving
parts.
Liquid Cooled Cold Plates typically employ tubes in –block designs or pumped water, oil, or
other liquids. Phase Change Recalculating System includes two-phase system that employ a
set of boiler and condenser in a passive self-driven mechanism. Heat pipe system incorporate
either no wicks in a gravity fed arrangement or wicks that do not require gravity feeds. This
category also includes solid –to- liquid systems but those are usually used to moderate
transient temperature gradient rather than for the purpose of dissipating heat.
Heat Sink Types: Heat sinks can be classified in terms of manufacturing methods and their
final form shapes.
There are common types of heat sink categories.
1. STAMPINGS:
Copper or aluminum sheet metals are stamped into desired shapes. They are used in
traditional air-cooling of electronic components and offer a low cost solution to low density
thermal problems. Suitable for a high volume production and advanced tooling with high
speed stamping would lower costs. Additional laborsaving options, such as taps, clips and
interface materials, can be factory applied to help reduce the board assembly costs.
2. EXTRUSIONS:
Allow the formation of elaborate two-dimensional shapes capable of dissipating large
wattage loads. They may be cut machined and incorporating serrated fins improves the
performance by approximately10 to 20 % at the expense of extrusion rate. Extrusion limits,
such as the fin height-to-gap aspect ratio, minimum fin thickness-to-height and maximum
base to fin thickness usually dictate the flexibility in design options. As the aspect ratio
increases, the extrusion tolerance needs to be compromised.
3. BONDED / FABRICATED FINS:
Most air cooled heat sinks are convection limited and the overall thermal
performance of an air cooled heat sink can often be improved significantly if more surface

area exposed to their stream can be provided even at the expense of conduction paths. This
process allow for a much greater fin height-to-gap aspect ratio of 20 to 40 %, greatly
increasing the cooling capacity without increasing volume requirements.
4. CASTINGS:
Sand, lost core and die casting processes are available with or without vacuum
assistance, in aluminum or copper-bronze. This technology is used in high density pin which
provide maximum performance when using impingement cooling.
5. FOLDED FIN:
Corrugated sheet metal in either aluminum or copper increases surface area and
hence the volumetric performance. The heat sink is then attached to either a base plate or
directly to the heating surface via epoxying or brazing. It is not suitable for high profile heat
sinks due to the availability and from the fin efficiency point of view. However it allows to
obtain high performance heat sinks in applications where it is impractical or impossible to
use extrusions or bonded fins.
HEAT TRANSFER COEFFICIENT:
To calculate the coefficient α we need the relative easy access able values of the temperature
and the volume flow:
The transferred heat (Q) in a exchanger:
Q = α x A x (T2 - T1) x Δt
with: α = heat transfer coefficient, A = heat transfer surface, (T2 -T1)= temperature
difference, Δt = examined time frame
The transferred heat (Q) of one of the liquids:
Q = cp x dm x (T2 - T1) x Δt

With: cp = heat capacity of the fluid, dm= volume flow of the fluid, (T2 - T1) =
temperature difference, Δt = examined time frame equalizing the both heat transfers as well
as the average temperatures ΔTm.
(T_Hot_In -T_Coldt_Out) - (T_Hot _Out- T_Coldt_In)
∆Tm =
ln(T_Hot_In - T_Coldt_Out/T-Hot_Out - T_Coldt_In)
Results in the heat transfer coefficient (α):
α = cp x dm x (T2 - T1)
A x ΔTm
For the control (development of heat transfer coefficient) are no absolute values required, so
it is possible to set A as constant (=1), and assuming always the same liquid cp and hence the
same density ρ and set both as well as constant (=1). Doing like this we will get the
"qualitative" Heat transfer coefficientαm.
me = 1 x dv x (T2 - T1) / 1 x ΔTm
dv x (T2 - T1)S
αm =
ΔTm

Using: T2, T1 the inlet and outlet temperature of the fluids and the
volume flow.
The heat loss is also taken as constant.
DIAGRAM:
SPECIFICATION:
Pipe diameter (Do): 33 mm
Pipe diameter (Di): 28 mm.
Length of test section (L): 400 mm.
Blower: 35 No. FHP motor.
Orifice Diameter (d): 14 mm.
Dimmer stat: 0 to 2 amp, 230 volt, AC.
Temperature indicator: Digital type and range 0 - 200 °c.

Voltmeter: 0 -100 /200v.
Ammeter: 0 – 2 amp.
Heater: Nichrome wire heater wound on
Test Pipe (Band Type) 400 watt.
TOTAL HEAT TRANSFER:
The total rate at which heat is lost from the cylinder in this experiment will be:
The total heat transfer correlates to the sum of convection and radiation.
NATURAL CONVECTION – NEWTON’S LAW OF COOLING:
 qc is the rate of heat transfer by convection.
 hc is the convective heat transfer coefficient.
 a is the surface area available.
 ts is the average surface temperature.
 ta is the ambient temperature.
ENERGY BALANCE:
rctotal qqq  
)( asccfcnc TTAhqqq 

In this experiment a cylinder is heated electrically so the amount of energy supplied
to the cylinder can be calculated using the equation:
NUSSELT NUMBER RELATIONS:
For natural convection, Nu depends on the Rayleigh number, Ra. The Rayleigh
number can be written in terms of the Grashof and Prandtl numbers, Gr and Pr.
Grashof and Prandtl numbers are given by
.
RELEVANT FLUID PROPERTIES:
 g gravitational acceleration ( 9.81 m/s ).
 β volume expansion coefficient, ( 1/ Tfilm )( K-1 ).
 v kinematic viscosity ( μ / ρ )( m2 /s ).
 cp specific heat ( J/kg ·K ).
 ρ density ( kg / m3 ).
FORCED CONVECTION HEAT TRANSFER COEFFICIENT CALCULATION:
INTRODUCTION – NEWTON’S LAW OF COOLING:
Forced convection heat transfer coefficients can be conveniently
calculated with Excel spreadsheets. This type of calculation is typically based on a
correlation of dimensionless numbers, usually Nusselt number in terms of Reynolds number
PrRa Gr 
2
3
)(
v
DTTg
Gr a


k
Cpv 

Pr

and Prandtl number. Forced convection occurs with a fluid moving past a solid surface when
the fluid and the solid are at different temperatures. Newton’s Law of Cooling [Q = hA (Ts -
Tf) ] is a simple expression for the rate for convective heat transfer. The parameters in
Newton’s Law of Cooling are:
 Q is the rate of forced convection heat transfer (Btu/hr – U.S. or W – S.I.).
 Tsis the solid temperature (oF – U.S. or oC – S.I.).
 Tf is the fluid temperature (oF – U.S. or oC – S.I.).
 A is the area of the surface that is in contact with the fluid (ft2 – U.S. or m2 –
S.I.).
 h is the convective heat transfer coefficient (Btu/hr-ft2-oF – U.S. or W/m2-K –
S.I.).
DIMENSIONLESS NUMBERS – NUSSELT, REYNOLDS AND PRANDTL:
Determining a good estimate for the heat transfer coefficient, h, is often the most
difficult part of forced convection heat transfer calculations. The process for estimating the
heat transfer coefficient for a particular forced convection application is often through a
correlation for Nusselt number (Nu) in terms of Reynolds number (Re) and Prandtl number
(Pr). These three dimensionless numbers are defined in the box below, along with the
definitions of the parameters that appear in them.

NUSSELT NUMBER CORRELATIONS FOR TURBULENT FLOW INSIDE A PIPE:
The DittusBoelter equation, which has been around since 1930 (ref #1) has two forms as
follows:
Nuo = 0.023 Re0.8Pr0.4 , for ‘heating’ (temperature of wall > temperature of fluid), and
Nuo = 0.026 Re0.8Pr0.3 , for ‘cooling’ (temperature of wall < temperature of fluid).
Subject to: 0.7 <Pr<120 ; 10,000 < Re < 160,000; L/D > 10 ( L/D > 50 according to
some authors). It is a rather simple equation to use, but has a fairly narrow range of
acceptable values for Re and Pr.
Another correlation (from ref #2) is shown in the box at the right. The range of
values for Re and Pr for this correlation are also shown. This correlation can be used for a
wider range of values of Re and Pr.
A third correlation is shown in the box at the left below. This correlation, described
by Pethukov (ref #3) is only a minor variation of the second correlation shown at the right.
This third correlation works for an even wider range of values for Re and Pr.
Excel spreadsheets can be used to conveniently calculate forced convection heat
transfer coefficients from correlations like these or others for configurations like laminar
pipe flow, flow inside a circular annulus, flow outside a cylinder, flow past a bank of tubes,
or flow in a noncircular cylinder, because the equations can be programmed into the
spreadsheet using Excel formulas.

HEAT TRANSFER COEFFICIENT:
The heat transfer coefficient, in thermodynamics and in mechanical and chemical
engineering, is used in calculating the heat transfer, typically by convection or phase change
between a fluid and a solid:
Where,
q = heat flow in input or lost heat flow, J/s = W
h = heat transfer coefficient, W/(m2K)
A = heat transfer surface area, m2
ΔT = difference in temperature between the solid surface and surrounding fluid area,
K
From the above equation, the heat transfer coefficient is the proportionality
coefficient between the heat flux, that is heat flow per unit area, q/A, and the thermodynamic
driving force for the flow of heat (i.e., the temperature difference, ΔT).
The heat transfer coefficient has SI units in watts per squared meter -kelvin:
W/(m2K).Heat transfer coefficient is the inverse of thermal insulance. This is used for
building materials (R-value) and for clothing insulation.

There are numerous methods for calculating the heat transfer coefficient in different
heat transfer modes, different fluids, flow regimes, and under different thermohydraulic
conditions.
DERIVATION OF CONVECTIVE HEAT TRANSFER COEFFICIENT:
An understanding of convection boundary layers is necessary to understanding
convective heat transfer between a surface and a fluid flowing past it. A thermal boundary
layer develops if the fluid free stream temperature and the surface temperatures differ. A
temperature profile exists due to the energy exchange resulting from this temperature
difference.
Thermal Boundary Layer
The heat transfer rate can then be written as,

And because heat transfer at the surface is by conduction,
These two terms are equal; thus
Rearranging,
Making it dimensionless by multiplying by representative length L,
The right hand side is now the ratio of the temperature gradient at the surface to the
reference temperature gradient. While the left hand side is similar to the Biot modulus. This
becomes the ratio of conductive thermal resistance to the convective thermal resistance of the
fluid, otherwise known as the Nusselt number, Nu.
.
CONVECTIVE HEAT TRANSFER CORRELATIONS:

Although convective heat transfer can be derived analytically through dimensional
analysis, exact analysis of the boundary layer, approximate integral analysis of the boundary
layer and analogies between energy and momentum transfer, these analytic approaches may
not offer practical solutions to all problems when there are no mathematical models
applicable. As such, many correlations were developed by various authors to estimate the
convective heat transfer coefficient in various cases including natural convection, forced
convection for internal flow and forced convection for external flow. These empirical
correlations are presented for their particular geometry and flow conditions. As the fluid
properties are temperature dependent, they are evaluated at thefilmtemperatureTf, which is
the average of the surface Ts and the surrounding bulk temperature, .
.
NATURAL CONVECTION:
EXTERNAL FLOW, VERTICAL PLANE:
Churchill and Chu correlation for natural convection adjacent to vertical planes.NuL
applies to all fluids for both laminar and turbulent flows. L is the characteristic length with
respect to the direction of gravity, and RaL is the Rayleigh Number with respect to this
length.
For laminar flows in the range of RaL< 109, the following equation can be further improved.

EXTERNAL FLOW, VERTICAL CYLINDERS:
For cylinders with their axes vertical, the expressions for plane surfaces can be used
provided the curvature effect is not too significant. This represents the limit where boundary
layer thickness is small relative to cylinder diameter D. The correlations for vertical plane
walls can be used when
.
EXTERNAL FLOW, HORIZONTAL PLATES:
W.H. McAdams suggested the following correlations. The induced buoyancy will be
different depending upon whether the hot surface is facing up or down. For a hot surface
facing up or a cold surface facing down,
.
.
For a hot surface facing down or a cold surface facing up,
.

The length is the ratio of the plate surface area to perimeter. If the plane surface is inclined at
an angle θ, the equations for vertical plane by Churchill and Chu may be used for θ up to 60o.
When boundary layer flow is laminar, the gravitational constant g is replaced with g cosθ for
calculating the Ra in the equation for laminar flow.
EXTERNAL FLOW, HORIZONTAL CYLINDER:
For cylinders of sufficient length and negligible end effects, Churchill and Chu has the
following correlation for 10 − 5<RaD< 1012
.
EXTERNAL FLOW, SPHERES:
For spheres, T. Yuge has the following correlation. For Pr≃1 and
.
FORCED CONVECTION:
INTERNAL FLOW, LAMINAR FLOW:
Sieder and Tate has the following correlation for laminar flow in tubes where D is
the internal diameter, μ_b is the fluid viscosity at the bulk mean temperature, μ_w is the
viscosity at the tube wall surface temperature.
.
INTERNAL FLOW, TURBULENT FLOW:

The Dittus-Boelter correlation (1930) is a common and particularly simple
correlation useful for many applications. This correlation is applicable when forced
convection is the only mode of heat transfer; i.e., there is no boiling, condensation,
significant radiation, etc. The accuracy of this correlation is anticipated to be ±15%.
For a fluid flowing in a straight circular pipe with a Reynolds number between 10
000 and 120 000 (in the turbulent pipe flow range), when the fluid's Prandtl number is
between 0.7 and 120, for a location far from the pipe entrance (more than 10 pipe diameters;
more than 50 diameters according to many authors[2]) or other flow disturbances, and when
the pipe surface is hydraulically smooth, the heat transfer coefficient between the bulk of the
fluid and the pipe surface can be expressed as:
Where,
KW - thermal conductivity of the bulk fluid.
DH - Di - Hydraulic diameter.
Nu - Nusselt number.
(Dittus-Boelter correlation).
Pr - Prandtl number.
Re - Reynolds number.
n = 0.4 for heating (wall hotter than the bulk fluid) and 0.33 for cooling (wall cooler
than the bulk fluid).
The fluid properties necessary for the application of this equation are evaluated at the
bulk temperature thus avoiding iteration.
FORCED CONVECTION, EXTERNAL FLOW:

In analyzing the heat transfer associated with the flow past the exterior surface of a
solid, the situation is complicated by phenomena such as boundary layer separation. Various
authors have correlated charts and graphs for different geometries and flow conditions. For
Flow parallel to a Plane Surface, where x is the distance from the edge and L is the height of
the boundary layer, a mean Nusselt number can be calculated using the Colburn analogy.
.
THOM CORRELATION:
There exist simple fluid-specific correlations for heat transfer coefficient in boiling.
The Thom correlation is for flow boiling of water (subcooled or saturated at pressures up to
about 20 MPa) under conditions where the nucleate boiling contribution predominates over
forced convection. This correlation is useful for rough estimation of expected temperature
difference given the heat flux.
Where:
ΔTsat is the wall temperature elevation above the saturation temperature, K
qis the heat flux, MW/m2
P is the pressure of water, MPa
Note that this empirical correlation is specific to the units given.
HEAT TRANSFER COEFFICIENT OF PIPE WALL:
The resistance to the flow of heat by the material of pipe wall can be expressed as a
"heat transfer coefficient of the pipe wall". However, one needs to select if the heat flux is
based on the pipe inner or the outer diameter.

Selecting to base the heat flux on the pipe inner diameter, and assuming that the pipe
wall thickness is small in comparison with the pipe inner diameter, then the heat transfer
coefficient for the pipe wall can be calculated as if the wall were not curved:
Wherethe effective thermal conductivity of the wall material and x isthe wall thickness.
If the above assumption does not hold, then the wall heat transfer coefficient can be
calculated using the following expression:
Wheredi and do are the inner and outer diameters of the pipe, respectively.
The thermal conductivity of the tube material usually depends on temperature; the mean
thermal conductivity is often used.
COMBINING HEAT TRANSFER COEFFICIENTS:
For two or more heat transfer processes acting in parallel, heat transfer coefficients simply
add:
For two or more heat transfer processes connected in series, heat transfer coefficients add
inversely:
For example, consider a pipe with a fluid flowing inside. The rate of heat transfer between
the bulk of the fluid inside the pipe and the pipe external surface is:

Where,
q = heat transfer rate (W)
h = heat transfer coefficient (W/(m2·K))
t = wall thickness (m)
k = wall thermal conductivity (W/m·K)
A = area (m2)
ΔT = difference in temperature.
OVERALL HEAT TRANSFER COEFFICIENT:
The overall heat transfer coefficientU is a measure of the overall ability of a series of
conductive and convective barriers to transfer heat. It is commonly applied to the calculation
of heat transfer in heat exchangers, but can be applied equally well to other problems.
For the case of a heat exchanger, U can be used to determine the total heat transfer
between the two streams in the heat exchanger by the following relationship:
q = UAΔTLM
where
q = heat transfer rate (W)
U = overall heat transfer coefficient (W/(m²·K))
A = heat transfer surface area (m2)
ΔTLM = log mean temperature difference (K)

The overall heat transfer coefficient takes into account the individual heat transfer
coefficients of each stream and the resistance of the pipe material. It can be calculated as the
reciprocal of the sum of a series of thermal resistances (but more complex relationships exist,
for example when heat transfer takes place by different routes in parallel):
Where,
R = Resistance(s) to heat flow in pipe wall (K/W)
Other parameters are as above.
The heat transfer coefficient is the heat transferred per unit area per kelvin. Thus area
is included in the equation as it represents the area over which the transfer of heat takes
place. The areas for each flow will be different as they represent the contact area for each
fluid side.
The thermal resistance due to the pipe wall is calculated by the following
relationship:
Where,
x = the wall thickness (m)
k = the thermal conductivity of the material (W/(m·K))
A = the total area of the heat exchanger (m2)
This represents the heat transfer by conduction in the pipe.

The thermal conductivity is a characteristic of the particular material. Values of
thermal conductivities for various materials are listed in the list of thermal conductivities.
As mentioned earlier in the article the convection heat transfer coefficient for each
stream depends on the type of fluid, flow properties and temperature properties.
Some typical heat transfer coefficients include:
 Air - h = 10 to 100 W/(m2K).
 Water - h = 500 to 10,000 W/(m2K).
THERMAL RESISTANCE DUE TO FOULING DEPOSITS:
Surface coatings can build on heat transfer surfaces during heat exchanger operation
due to fouling. These add extra thermal resistance to the wall and may noticeably decrease
the overall heat transfer coefficient and thus performance. (Fouling can also cause other
problems.)
The additional thermal resistance due to fouling can be found by comparing the
overall heat transfer coefficient determined from laboratory readings with calculations based
on theoretical correlations. They can also be evaluated from the development of the overall
heat transfer coefficient with time (assuming the heat exchanger operates under otherwise
identical conditions). This is commonly applied in practice, e.g. the following relationship is
often used:
=
Where,
Uexp = overall heat transfer coefficient based on experimental data for the heat
exchanger in the "fouled" state, .

Upre = overall heat transfer coefficient based on calculated or measured ("clean
heat exchanger") data, .
Rf = thermal resistance due to fouling, .
TURBULANT PIPE FLOW CORELATIONS:
There are several correlations available for calculation of the convective heat transfer
coefficient for turbulent flow of a fluid in a pipe, with the fluid and pipe at different
temperatures. The temperature of the pipe may be either hotter or colder than the fluid or in
other words, the fluid may be either heated or cooled by the pipe.
Classic Correlations: A
classic correlation for the convection heat transfer for turbulent flow in a pipe is the Dittus-
Boelter equation (ref #3), which was published in1930, as:
Nu = 0.0243 Re
0.8
Pr
0.4
for heating of the fluid (Twall>Tfluid)
Nu = 0.0265 Re
0.8
Pr
0.3
for cooling of the fluid (Twall<Tfluid)
In subsequent years, the equations have been revised somewhat and the equation, Nu
= 0.023 Re0.8
Pr0.4
, has come to be known as the Dittus-Boelter equation, with anode that the
exponent on Pr should be 0.3 if the fluid is being cooled. See Wither ton (Ref #4) for
discussion of this change in the equation that has come to be known as theDittus-Boelter
equation.
Solution: Values for the density, viscosity, specific heat, and thermal conductivity of water
are needed at the fluid bulk temperature (85o
F) and the viscosity is also needed at the wall
temperature (120o
F). Tables and/or graphs of fluid properties are available in many fluid
mechanics, thermodynamics, and heat transfer textbooks and handbooks. They can also be
obtained from various websites through a search for “viscosity of water,” “thermal
conductivity of air,” etc.

For water at 85o
F: density = 1.93 slugs/ft.3
, viscosity = 1.64 x 10-5
lb.-sec/ft2
(slug/ft-sec),
Specific heat = 32.2 Btu/slug-o
F, and thermal conductivity = 0.33 Btu/hr-ft-o
F.
Calculation of Re and Pr: The Reynolds’s number (Re) and Prandtl number (Pr) are needed
for
Both equations:
ReD = DV / = (2/12) (1.8) (1.93)/( 1.64 x 10-5
) = 35,305
Pr = Cp/k = 3600(1.64 x 10-5
) (32.2)/ (0.33) = 5.8
(The 3600 factor is needed to convert sec to hr)
Dittus-Boelter equation: Nu = 0.023 Re0.8
Pr0.4
= 0.023(35305)0.8
(5.8)0.4
= 201
Calculate the heat transfer coefficient, h, from the definition of Nu (Nu = hD/k)
h = (Nu) (k)/D = 201*0.33/ (2/12) = 399 Btu/hr-ft2
-o
F
Sieder-Tate equation: Nu = 0.023 Re0.8
Pr1/3
( b/ w) 0.14
For this equation, the viscosity of the water at the wall temperature (120o
F) is also
w =1.16 x 10-5
lb-sec/ft2
(slug/ft-sec)
Thus: Nu = 0.023(35305)0.8
(5.8)1/3
(1.64 x 10-5
/1.16 x 10-5
)0.14 = 188
Calculate the heat transfer coefficient, h, from the definition of Nu (Nu = hD/k)
h=(Nu)(k)/D= 188*0.33/(2/12) = 372 Btu/hr-ft2
-o
F
More Recent Correlations – In 1970 Petukhov (ref #6) presented the following equation,
which somewhat more complicated, but provides greater accuracy than Dittus-
Boelter&Sieder-Tate equations. The f in the following equations is the friction factor. The
equation given here is from for 3000 < Re < 5 x 10
6
, with smooth pipe (independent

Correction for Variations in Fluid Properties – Lienhardt&Lienhardt (ref #2) give
Following update of the Sieder-Tate viscosity factor to correct for variations in fluid
Properties.
After calculating Nuo at the fluid bulk temperature, using either the
Petukhovcorrelationor the Gnielinsky correlation, that value of Nusselt number
should be corrected for fluid property variations with one of the following equations:
For liquids b/ w< 12.5:
NuD = Nuo ( b/ w)n
, with n = 0.11 for fluid heating and n = 0.25 for fluid
cooling
For gases with absolute temperature ratio: 0.27 < Tb/Tw< 2.7
NuD = Nuo (Tb/Tw) n
, with n = 0.47 for fluid heating and n = 0 for fluid
cooling

Example #3: Calculate the convective heat transfer coefficient using the
PetukhovandGnielinsky correlations, for the same conditions as Example #1 (water at an
average bulk temperature of 85o
F through a 2 inch diameter pipe that is at 120o
F, with the
water velocity in the pipe being 1.8 ft/sec.
Solution: As calculated in Example #2: Re = 35,305 and Pr = 5.8. Substituting into the
equation for f:
f = (0.790 ln (35,305) – 1.64)-2
= 0.02273
Substituting values for f, ReD and Pr into either the Petukhov correlation or the
Gnielinskycorrelation gives Nuo = 236. (Both give the same result in this case.)
Fluid property variation factor: b/ w = 1.64/1.16 = 1.41, thus
NuD = Nuo ( b/ w) 0.11 = (236) (1.410.11) = 245
h = (Nu) (k)/D = 245*0.33/ (2/12) = 485 Btu/hr-ft2
-o
F
This value of h is about 20% higher than the Dittus-Boelter estimate and about
30%higher than the Sieder-Tate estimate. The heat transfer coefficient spreadsheet that came
with this course is set up to calculate the forced convection coefficient for turbulent pipe
flow using the Gielinskycorrelation on the “turbo. Pipe flow” tab in the section following
that in which Dittus-Boelter and Sieder-Tate calculations are made. The calculations in
Example #3 can be confirmed with the spreadsheet and the heat transfer coefficient for other
turbulent pipe flow cases can be calculated using the Gielinsky correlation.
LAMINAR PIPE FLOW CORELATIONS:
Convection heat transfer associated with laminar flow in a circular tube (Re < 2300)
is less common than with turbulent flow. The correlations are rather simple, however, with
the Nusselt number being constant for fully developed flow. The L/D ratio for the entrance
length required to reach fully developed flow is larger for laminar flow than for turbulent
flow, however, so practical situation with entrance region flow are possible. Two correlations

for use in the entrance region are included in this discussion.
Fully Developed Flow - Both of the first two references at the end of this course givethe
following expressions for the Nusselt number in fully developed laminar flow in a
Pipe (i.e. L >> Le):
For uniform wall heat flux: NuD = 4.36
For uniform wall temperature: NuD = 3.66
The entrance length for pipe flow (Le) is the portion of the pipe in which the
velocityProfile is changing. The velocity profile remains the same, however, throughout the
fullydeveloped flow portion of the pipe, as illustrated in the diagram below.
For laminar flow, the entrance length can be estimated from the equation:
Le/D = 0.06 ReD
Laminar Entry Region Flow –Incropera et al (ref #1) gives the following twocorrelations
or use in estimating convection heat transfer coefficients for laminar entryregion flow.
Laminar Entry Region Correlation #1 (L < Le):

Example #4: Estimate the convection heat transfer coefficient for water flowing through a 2inch
diameter pipe at a velocity of 0.1 ft/sec. The average bulk temperature of the water is 85
o
F and
the pipe wall temperature is constant at 120
o
F. Estimate the heat transfer coefficient for a) the
case where L >> Le (fully developed flow) and b) L < Lv.

Solution: The properties of water at 85
o
F that were used in Example #2 and #3 can be
used here (density = 1.93 slugs/ft
3
, viscosity = 1.64 x 10
-5
lb-sec/ft
2
(slug/ft-sec), specific heat
= 32.2Btu/slug-
o
F, and thermal conductivity = 0.33 Btu/hr-ft-
o
F.) The viscosity of water at
120
o
F is 1.16 x 10
-5
lb-sec/ft
2
(slug/ft-sec).
The Prandtl number will be the same as in Example #2: Pr = 5.8
The Reynolds number can be calculated as:
ReD
-5
) = 1961
For fully developed flow ( L>> Le ) with uniform wall temperature:
Thus, NuD = 3.66
H = (Nu) (k)/D = 3.66*0.33/(2/12)
= 7.2 Btu/hr-ft
2
-
o
F
For laminar entry region flow (L < Le), correlation #1 should be used here, because Pr>
From that correlation: NuD = 12.0
Thus: h = (Nu) (k)/D = 12.0*0.33/ (2/12)
= 23.8 Btu/hr-ft
2
-
o
F
These calculations can also be conveniently made with the course spreadsheet,
asshown in the screenshot on the next page. This tab on the spreadsheet has provisionfor
entering the following input parameters: the pipe diameter, D; the pipe length, L; the
entrance length, Le; the average velocity of the fluid in the pipe, V; the average bulk fluid
temperature, Tb; and the following fluid properties at the average bulk fluid temperature:
Density, viscosity, specific heat, and thermal conductivity. The spreadsheet then makes
some unit conversions, calculates the Reynolds number and Prandtl number, and then
calculates the Nusselt number and heat transfer coefficient using each of the Correlations
discussed above in this section.

NATURAL CONVECTION HEAT TRANSFER CONFIGURATIONS:
Natural convection heat transfer takes place when a fluid is in contact with a solid
surface that is at a different temperature than the fluid and fluid motion is not caused by an
external driving force such as a pump or blower. With natural convection, fluid motion is
caused by fluid density differences due to temperature variation within the fluid. The natural
convection solid surface configurations for which heat transfer coefficient correlations will
be presented and discussed in this course are:
Heat transfer from a vertical surface
Heat transfer from a horizontal surface
Heat transfer from an inclined flat surface
Heat transfer from a horizontal cylinder
Heat transfer from a sphere
USE OF S.I. UNITS IN HEAT TRANSFER COEFFICIENT
CALCULATIONS:
The correlations presented for all of the forced convection and natural
convectionconfigurations are in terms of dimensionless numbers (Reynolds, Prandtl, Nusselt,
Grashof, and Rayleigh numbers), so the equations in those correlations remain the same for
any set of units. Whatever set of units is being used, you need to be sure, however, that the
units on the parameters used to calculate any of those dimensionless numbers are consistent,
so that the units all “cancel out” and the number is indeed dimensionless.
Example #13: If a convection heat transfer coefficient is to be determined from a
calculatedvalue of Nusselt number together with known fluid thermal conductivity, k, in
W/m-K and characteristic length, D, in m, what will be the units of the heat transfer
coefficient?

Solution: The definition of Nusselt number (Nu = hD/k) can be rearranged to: h = Nu k/D.
Since Nu is dimensionless, the units of h will be the units of k divided by the units of
D, or simply: units of h = (W/m-K)/m =W/m
2
-K.
Example #14: Use the Dittus-Boelter correlation to estimate the convective heat transfer
coefficient in kJ/hr-m
2
-k, for flow of water at 30
o
C, with velocity equal 0.55 m/s, through a
50mm diameter pipe which has a surface temperature of 50
o
C.
Solution:The needed properties of water at 30
o
C are: density = 995 kg/m
3
,
viscosity=0.000785 N-s/m
2
, specific heat = 4.19 kJ/kg-K, thermal conductivity = 0.58 W/m-
K.
HEAT EXCHANGER:
A heat exchanger is a piece of equipment built for efficient heat transfer from one
medium to another. The media may be separated by a solid wall, so that they never mix, or they
may be in direct contact. They are widely used in space heating, refrigeration, air conditioning,
power plants, chemical plants, petrochemical plants, petroleum refineries, natural gas processing,
and sewage treatment. The classic example of a heat exchanger is found in an internal
combustion engine in which a circulating fluid known as engine coolant flows through radiator
coils and air flows past the coils, which cools the coolant and heats the incoming air.
Types of heat exchangers:

Shell and tube heat exchanger:
Shell and tube heat exchangers consist of a series of tubes. One set of these tubes contains the
fluid that must be either heated or cooled. The second fluid runs over the tubes that are being
heated or cooled so that it can either provide the heat or absorb the heat required. A set of tubes
is called the tube bundle and can be made up of several types of tubes: plain, longitudinally
finned, etc. Shell and tube heat exchangers are typically used for high-pressure applications (with
pressures greater than 30 bar and temperatures greater than 260 °C) This is because the shell and
tube heat exchangers are robust due to their shape.
There are several thermal design features that are to be taken into account when designing the
tubes in the shell and tube heat exchangers. These include:
 Tube diameter: Using a small tube diameter makes the heat exchanger both economical
and compact. However, it is more likely for the heat exchanger to foul up faster and the
small size makes mechanical cleaning of the fouling difficult. To prevail over the fouling
and cleaning problems, larger tube diameters can be used. Thus to determine the tube
diameter, the available space, cost and the fouling nature of the fluids must be
considered.
 Tube thickness: The thickness of the wall of the tubes is usually determined to ensure:
o There is enough room for corrosion
o That flow-induced vibration has resistance
o Axial strength
o Availability of spare parts
o Hoop strength (to withstand internal tube pressure)
o Buckling strength (to withstand overpressure in the shell)
 Tube length: heat exchangers are usually cheaper when they have a smaller shell
diameter and a long tube length. Thus, typically there is an aim to make the heat
exchanger as long as physically possible whilst not exceeding production capabilities.

However, there are many limitations for this, including the space available at the site
where it is going to be used and the need to ensure that there are tubes available in
lengths that are twice the required length (so that the tubes can be withdrawn and
replaced). Also, it has to be remembered that long, thin tubes are difficult to take out and
replace.
 Tube pitch: when designing the tubes, it is practical to ensure that the tube pitch (i.e., the
center -center distance of adjoining tubes) is not less than 1.25 times the tubes' outside
diameter. A larger tube pitch leads to a larger overall shell diameter which leads to a
more expensive heat exchanger.
 Tube corrugation: this type of tubes, mainly used for the inner tubes, increases the
turbulence of the fluids and the effect is very important in the heat transfer giving a better
performance.
 Tube Layout: refers to how tubes are positioned within the shell. There are four main
types of tube layout, which are, triangular (30°), rotated triangular (60°), square (90°) and
rotated square (45°). The triangular patterns are employed to give greater heat transfer as
they force the fluid to flow in a more turbulent fashion around the piping. Square patterns
are employed where high fouling is experienced and cleaning is more regular.
 Baffle Design: baffles are used in shell and tube heat exchangers to direct fluid across the
tube bundle. They run perpendicularly to the shell and hold the bundle, preventing the
tubes from sagging over a long length. They can also prevent the tubes from vibrating.
The most common type of baffle is the segmental baffle. The semicircular segmental
baffles are oriented at 180 degrees to the adjacent baffles forcing the fluid to flow upward
and downwards between the tube bundles. Baffle spacing is of large thermodynamic
concern when designing shell and tube heat exchangers. Baffles must be spaced with
consideration for the conversion of pressure drop and heat transfer. For thermo economic
optimization it is suggested that the baffles be spaced no closer than 20% of the shell’s
inner diameter. Having baffles spaced too closely causes a greater pressure drop because
of flow redirection. Consequently having the baffles spaced too far apart means that there
may be cooler spots in the corners between baffles. It is also important to ensure the

baffles are spaced close enough that the tubes do not sag. The other main type of baffle is
the disc and donut baffle which consists of two concentric baffles, the outer wider baffle
looks like a donut, whilst the inner baffle is shaped as a disk. This type of baffle forces
the fluid to pass around each side of the disk then through the donut baffle generating a
different type of fluid flow.
Conceptual diagram of a plate and frame heat exchanger.
A single plate heat exchanger

An interchangeable plate heat exchanger applied to the system of a swimming pool
Plate heat exchanger:
Another type of heat exchanger is the plate heat exchanger. One is composed of multiple,
thin, slightly separated plates that have very large surface areas and fluid flow passages for heat
transfer. This stacked-plate arrangement can be more effective, in a given space, than the shell
and tube heat exchanger. Advances in gasket and brazing technology have made the plate-type
heat exchanger increasingly practical. In HVAC applications, large heat exchangers of this type
are called plate-and-frame; when used in open loops, these heat exchangers are normally of the
gasket type to allow periodic disassembly, cleaning, and inspection. There are many types of
permanently bonded plate heat exchangers, such as dip-brazed and vacuum-brazed plate
varieties, and they are often specified for closed-loop applications such as refrigeration. Plate
heat exchangers also differ in the types of plates that are used, and in the configurations of those
plates. Some plates may be stamped with "chevron" or other patterns, where others may have
machined fins and/or grooves.
Plate & shell heat exchanger:
A third type of heat exchanger is plate & shell heat exchanger which combines plate heat
exchanger and shell & tube heat exchanger technologies. In the heart of the heat exchanger there
are a fully welded circular plate pack which is made by pressing and cutting round plates and
welding them together. Nozzles are added which carry flow in and out of the plate pack (the
'Plate side' flow path).The fully welded plate pack is assembled into an outer shell which creates
a second flow path ( the 'Shell side'). Plate and shell technology offers high heat transfer, high
pressure, and high operating temperature, compact size, low fouling and close approach
temperature. In particular, it does completely without gaskets, which provides security against
leakage at high pressures and temperatures.

Adiabatic wheel heat exchanger:
A fourth type of heat exchanger uses an intermediate fluid or solid store to hold heat,
which is then moved to the other side of the heat exchanger to be released. Two examples of this
are adiabatic wheels, which consist of a large wheel with fine threads rotating through the hot
and cold fluids, and fluid heat exchangers.
Phase-change heat exchangers:
Typical kettle reboiler used for industrial distillation towers
Typical water-cooled surface condenser

In addition to heating up or cooling down fluids in just a single phase, heat exchangers
can be used either to heat a liquid to evaporate (or boil) it or used as condensers to cool a
vaporand condense it to a liquid. In chemical plants and refineries, reboilers used to heat
incoming feed for distillation towers are often heat exchangers.
Distillation set-ups typically use condensers to condense distillate vapors back into liquid.
Power plants which have steam-driven turbines commonly use heat exchangers to boil
water into steam. Heat exchangers or similar units for producing steam from water are often
called boilers or steam generators.
In the nuclear power plants called pressurized water reactors, special large heat
exchangers which pass heat from the primary (reactor plant) system to the secondary (steam
plant) system, producing steam from water in the process, are called steam generators. All fossil-
fueled and nuclear power plants using steam-driven turbines have surface condensers to convert
the exhaust steam from the turbines into condensate (water) for re-use.
To conserve energy and cooling capacity in chemical and other plants, regenerative heat
exchangers can be used to transfer heat from one stream that needs to be cooled to another
stream that needs to be heated, such as distillate cooling and reboiler feed pre-heating.
This term can also refer to heat exchangers that contain a material within their structure that has
a change of phase. This is usually a solid to liquid phase due to the small volume difference
between these states. This change of phase effectively acts as a buffer because it occurs at a
constant temperature but still allows for the heat exchanger to accept additionalheat. One
example where this has been investigated is for use in high power aircraft electronics.

Direct contact heat exchangers:
Direct contact heat exchangers involve heat transfer between hot and cold streams of two
phases in the absence of a separating wall. Thus such heat exchangers can be classified as:
 Gas – liquid
 Immiscible liquid – liquid
 Solid-liquid or solid – gas
Most direct contact heat exchangers fall under the Gas- Liquid category, where heat is
transferred between a gas and liquid in the form of drops, films or sprays.
Such types of heat exchangers are used predominantly in air conditioning, humidification,
hot water heating,water and condensing plants.

Forced Convection Heat Transfer Coefficient Correlations:
Inputs
Average fluid temperature Tb = 85 °F
Pipe Diameter D = 2 inch
Average Velocity V = 1.8 Ft/sec
Fluid Density ρ = 1.93kg/ft³
Fluid Viscosity µ = 0.0000164lb-sec/ft²
Fluid Specific Heat Cр = 1 Btu/lb°F
Fluid Thermal Conductivity K = 0.33 Btu/hr-ft-°F
Pipe Length L = 15 Ft
Average Wall Temperature T = 120 °F
Fluid Viscosity At Temp µ = 1.164E-05 Lb-sec/ft

Calculations:
Reynolds number, Re = 35.05
Prandtl number Pr = 5.8
Correlation, DittusBoelter Nu = 201
Twall>Tfluid
h = 399 Btu/hr-ft²-°F
Twall<Tfluid Nu = 169
h = 335Btu/hr-ft²-°F
Correlation, Sieder Tate
Nu = 188
h = 372 Btu/hr-ft²-°F
OBSERVATION:
Pipe outside diameter=2.8mm
Pipe internal diameter=25mm
Orifice internal diameter =14mm
Density of water =1000kg/m2
Density of air =1.0121 kg/m2

TABULATION:
S.no Manometer
Reading
Voltmeter
Reading
Ammeter
reading
Temp in ˚c
T1 ˚c T2˚c T3˚c T4˚c T5˚c T6˚c
1 5 120 1 44 59 61 66 71 35
2 5 120 1 44 62 68 70 84 43
3 5 120 1 44 69 66 80 85 44
4 5 120 1 44 72 73 86 93 46
5 5 120 1 44 78 75 87 96 46
6 5 120 1 44 86 72 99 98 46

PROCEDURE:
 Switch on the mains.
 Switch on the blower.
 Adjust the regulator to any desired power input to heater.
 Adjust the position of the valve to any desired flow rate of air.
 Wait till steady state temperature is reached.
 Note manometer readings h1 and h2.
 Note temperatures along the tube. Note air inlet and outlet temperatures
 Note volt meter and ammeter reading.
 Adjust the position of the valve and vary the flow rate of air and repeat
The experiment.
 For various valve openings and for various power inputs and readings
May be taken to repeat the experiments. The readings are tabulated
The heat input Q = h A L M T D = m cp (temp. of tube – temp. of air)
M = mass of air. Cp = specific heat of air.
LMTD= (AvgTemp Of tube – outlet air temp) – (Avg. temp of tube – inlet air
temp.)
H= heat transfer co-efficient. A = area of heat transfer = T1d1
From the above the heat transfer co-efficient ‘h’ can be calculated. These
experimentally determined values may be compared with theoretical values.
Calculate the velocity of the air in the tube using orifice meter / water
manometer.

The volume of air flowing through the tube (Q) = (cd2
1
2
2√2gh0 ) / (√a1
2 – a2
2 ) m3 /
sec.
ho= heat of air causing the flow.
= (h1 – h2) ℮w/℮a
h1and h2 are manometer reading in meters.
a 1= area of the tube.
a2 = area of the orifice.
Hence the velocity of the air in the tube V = Q / a1 m/sec heat transfer rate and flow
rates are expressed in dimension less form of Nusselt number and Reynolds number
which are defined as
Nu = h D/k Re = Dvp/ υ
D = Dia. Of the pipe
V = Velocity of air
K = Thermal conductivity of air.
The heat transfer co-efficient can also be calculated from Dittus-Boelter
correlation.
Nu = 0.023 Re0.8 Pr 0.4
Where Pr is the Prandtl number for which air can be taken as 0.7. The Prandtl
number represents the fluid properties. The results may be represented as a plot of Nu
exp/ Nu corr. Vs Re which should be a horizontal line.

RESULT:
Thus the experiment was studied, graph and tabulation was drawn.
PHOTOGRAPHY OF HEAT TRANSFER CO-EFFICIENT VS HEATFLOW

RATE BY FORCED CONVECTION
CONCLUSION:

A major part of most convection heat transfer calculations is determination of a value
for the heat transfer coefficient. The equations for forced convection coefficients are
typically in the form of a correlation for Nusselt number in terms of Reynolds
numberandPrandtlnumber, while natural convection correlations give Nusselt number in
termsofPrandtl number andeitherGrashof number or Rayleigh number. This courseincludes
correlations for five different forced convection configurations and five differentnatural
convection configurations. A spreadsheet included with the course can be used to calculate
heat transfer coefficients for either laminar or turbulent flow through pipes.

REFERENCES:
 Inprocera, f.p., dewitt, s.p., bergman, t.l., &lavine, a.s., fundamentals of Heat
And mass transfer, 6
th
ed,hoboken, nj, wiley, 2007.
 Lienhard, j.h, iv &lienhard, j.h. V, a heat transfer textbook,4
th
ed,Cambridge,
ma, phlogiston press, 2011. (A free electronic textbook)
 Dittus, p.w. &boelter, l.m., univ. Calif. Pub. Eng., vol. 1, no. 13, pp 443-461
(reprinted in int. Comm. Heat mass transfer, vol. 12, pp 3-22., 1985.
 Winterton, r.h.s., where did the dittus and boelter equation come from,int.
J.ZZHeat mass transfer,vol 41, nos 4-5, pp 809-810, 1998.
 E.n. Sieder&g.e. Tate. Heat transfer and pressure drop of liquids in tubes.
Ind. Eng. Chem., 28:1429, 1936.
 Petukhov, b.s., heat transfer and friction in turbulent pipe flow with variable
Properties.Int.f. Irvine, jr and j.p. Hartnett, editors, advances in heattransfer,
vol. 6, pp 504-506, academic press, inc, new York, 1970.

HEAT TRANSFER CO EFFICIENT VS HEAT FLOW RATE BY FORCED CONVECTION

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to HEAT TRANSFER CO EFFICIENT VS HEAT FLOW RATE BY FORCED CONVECTION

Similar to HEAT TRANSFER CO EFFICIENT VS HEAT FLOW RATE BY FORCED CONVECTION (20)

Recently uploaded

Recently uploaded (20)

HEAT TRANSFER CO EFFICIENT VS HEAT FLOW RATE BY FORCED CONVECTION