NUMERICAL SIMULATION OF HEAT TRANSFER IN

CONCENTRIC CYLINDERS WITH AND WITHOUT FINS

A PROJECT REPORT

Submitted to

Jawaharlal Nehru Technological University Hyderabad

In partial fulfillment of the requirements for the award of B-Tech degree in

MECHANICAL ENGINEERING BY

K.KAUSHIK RAO (02E51A0311) K.RAJI REDDY (02E51A0326)P.SUNDEEP VARMA (02E51A0335)

Under the guidance of

M.GOPI KRISHNA, M.TECH

Asst. Prof. MECHANICAL Dept.

DEPARTMENT OF MECHANICAL ENGINEERINGROYAL COLLEGE OF ENGINEERING

(First among ISO 9001:2001 certified JNTU Colleges) MEDAK, A.P. 2005 - 2006.

DEPARTMENT

OF

MECHANICAL ENGINEERING

CERTIFICATE

This is to certify that the project work entitled

“NUMERICAL SIMULATION OF HEAT TRANSFER

IN CONCENTRIC CYLINDERS WITH AND

WITHOUT FINS” is the result of work done by

K.KAUSHIK RAO (02E51A0311)

K.RAJI REDDY (02E51A0326)

P.SUNDEEP VARMA (02E51A0335)

This has been submitted as partial fulfillment for the

award of BACHELOR’S DEGREE in Mechanical

Engineering from the JNTU for the academic year

2005-2006

Principal Head of the department Internal Guide

Mr.N.MALLAPARAJU A.SHIVA RAMAKRISHNA M.GOPI KRISHNA

ACKNOWLEDGEMENT

A project work of this magnitude is not possible

without the help of several people directly or indirectly. It is with

immense satisfaction that we present our practical experience in

the form of a project report we carried out in Cusp Technologies

Pvt Ltd.

We are grateful to Mr.N.MALLAPARAJU C.E,

M.TECH, MISTE, and DIP.T.T Principal of RCEM for giving us

the permission to carry out our project work at Cusp Technologies

Pvt Ltd.

We take this opportunity to thank Sri.M.GOPI

KRISHNA, Asst. Professor of Mechanical Engineering for his

encouragement he had given us throughout the project work.

We wish to express our sincere and profound

gratitude to Sri.KRISHNA MOHAN, Cusp Technologies Pvt Ltd.

for his valuable guidance, which helped us to complete the project

work successfully.

ABSTRACT

Natural convection in concentric annuli has been the

subject of interest in many researchers due to its various

applications in engineering devices. Application areas include

the energy conversion systems found in some designs of nuclear

reactors, concentrating solar collections and thermal energy

storage devices. We consider two-dimensional steady state

natural convection heat transfer in a horizontal annular gap

between two concentric cylinders in witch the inner cylinder is

hotter than the outer one

This project relates to the numerical simulation of

natural convection heat transfer by solving governing equations

for primitive variables pressure, velocities and temperature.

The objective of this project is to further investigate,

numerically, the effect of internal fins on the flow patterns, the

temperature distribution and the heat transfer between

concentric horizontal cylinders.

Fins are employed to increase the heat transfer area, leading to

an increase in the heat transfer between the cylinders. However,

the presence of internal fins alters the flow patterns, temperature

distribution and Nusselt number of the configuration when

buoyancy effects are not negligible.

INTRODUCTION TO CONVECTION: -

CONVECTION: - It is the mechanism by which the

thermal energy is transferred between a solid surface and a fluid

moving over that surface.

Types of Convection:

Natural Convection.

Forced Convection.

Natural Convection:-It

is the type of Convection, which is caused by the density

differences, which is caused by temperature gradient.

Forced Convection:-It

is the type of Convection, which is caused by some external

agency such as pumps, blowers etc.

Incompressible Flow: -

When Density () is function of Temperature (T) and it is

independent of Pressure (P), then flow is said to be

Incompressible flow.

Compressible Flow: -

When Density () is the function of both Temperature (T) and

Pressure (P), and then flow is said to be compressible flow.

INTRODUCTION TO FINS: -

FINS: -Fins are extended surfaces, which are used to increase

the heat transfer rate from one surface to another surface.

Note: -Most of the fins doesn’t affect the fluid flow around it.

PURPOSE OF FINS IN OUR PROJECT: -

Most of the fins remove

the heat from the source by means of conduction and the fluid

surrounding the fin removes the heat by convection.

In this case the fin is

maintained at constant temperature so there is no conduction

heat transfer take place.

The purpose of the fins

is to increase the heat transfer by convection. The purpose of the

fin is to mainly control the fluid matter.

The fin here is to limits

to increase heat transfer by increasing the heat transfer

coefficient (h), where ‘h’

h=,,,, l

Where = Density (kg/m),

=Coefficient of viscosity ()

Velocity (m/sec),

Thermal conductivity (w/m k),

l=length (m).

INTRODUCTION TO CFD: -

CFD stands for Computational Fluid Dynamics.

CFD was started in the early 1960’s but came into prominence

in 1980.The first major industries using CFD were started in

1990’s.

CFD is predicting what will happen, quantitatively, when

fluids flow, often with the complications of:

Simultaneous flow of heat,

Mass transfer (e.g. perspiration, dissolution),

Phase change (e.g. melting, freezing, boiling),

Chemical reaction (e.g. combustion, rusting),

It is concerned with obtaining numerical solution to fluid flow

problems. The basic difference between CFD and other

conventional methods is that in CFD computers are used for

calculation part. The advent of high-speed and large-memory

computers has enabled CFD to obtain solution to many flow

problems including those that are compressible and

incompressible, laminar or turbulent, chemically reacting or

non-reacting.

CFD is the art of replacing the differential equation governing

the Fluid Flow, with a set of algebraic equations (the process is

called discretization), which in turn can be solved with the aid

of a digital computer to get an approximate solution.

Governing equation solved in CFD

Navier stokes equation

[uu/x) + v (u/y)] = p/x) + u (Uxx + Uyy)

Navier Stokes in X direction.

[uv/x) + v (v/y)] = p/y) + u (Vxx + Vyy)

Navier Stokes in Y direction.

Continuity equation

(ux) + (vy) =0.

Momentum equation

U (x) + V (y) = (Cp) + [xx + yy].

PROCEDURE FOLLOWED IN CFD: -

Solving a particular problem generally involves first discretizing

the physical domain that the flow occurs in, such as the interior

of turbine engine or the radiator system of a car. This

discretization is straightforward for very simple geometries such

as rectangles or circles, but is a difficult problem in CAD for

more complicated objects. Currently automatic “mesh

generators” are simply not adequate, requiring extensive

investment of time on the part of the scientist or engineer. This

leads to problems in human-computer interfaces (HCI) and

CASE tools, as well as fundamental problems in graph theory

since the resulting discretization gives a mesh.

On the discretized mesh the Navier-Stokes equations take

the form of a large system of nonlinear equations; going from

the continuum to the discrete set of equations is a problem that

combines both physics and numerical analysis; for example, it is

important to maintain conservation of mass in the discrete

equations. At each node in the mesh, between 3 and 20 variables

are associated: the pressure, the three velocity components,

density, temperature, etc.

OBJECTIVES OF CFD: -

1. To describe the basic features of computer-based numerical

methods for predicting fluid flows, heat and mass transfer,

which falls under the collective name of Computational Fluid

Dynamics (CFD).

2. To use the methods to perform computer simulations of a

range of thermo fluids problems as an aid to understanding.

3. To gain experience of the use of CFD codes as design tools.

APPLICATIONS OF CFD: -

A. Industrial

1. Aerospace: Aerodynamics

Gas Turbines Rocket

2. Automotive Aerodynamics Engines Turbocharger Intake/Exhaust Heating/Cooling Systems 3. Mechanical

Pumps, compressors Heat exchangers Furnaces Nuclear reactors

4. Chemical

Mixers (multiphase) Chemical reactors Separators Boilers, condensers

5. OthersGlass, steel and textile manufacturing: ship building, food processing, etc.

B. Environmental and Safety

Weather prediction River and tidal flows Wind- and water-borne pollution Fire and smoke spread

Wind loading

C. Physiological

Cardiovascular flows (heart, major vessels)

Flow in lungs and breathing passages

CFD-based predictions are never 100%-reliable, because:

The input data may involve too much guess-work or imprecision;

The scientific knowledge base may be inadequate.

The reliability is greater:

For laminar flows rather than turbulent ones For single-phase flows rather than multi-phase

flows;

For chemically-inert rather than chemically-reactive materials;

For single chemical reactions rather than multiple ones;

For simple fluids rather than those of complex composition.

PROBLEM STATAMENT: -

In this project heat

transfer and fluid flow characteristics are studied numerically in

a concentric cylinders with and with out internal fins at different

Rayleigh numbers and at different orientations.

The Rayleigh numbers

considered in this analysis are

10^3 to 10^6.

WITH OUT FINS: -

WITH FIN (0.25)

WITH FIN (0.50)

WITH FIN (0.75)

ASSUMPTIONS MADE IN THE ANALYSIS : -

The flow is 2-

dimensional (i.e. T=x, y).

The flow is steady (i.e.

time =constant).

The flow is

incompressible (i.e.=(T)).

The flow is laminar

(Reynolds num b/w 2000 to 4000).

The working fluid

considered is ‘Air’.

Boussinesque

approximation: - The variation of density in the convective term

is negligible and it is the function of temperature in the body

force term.

This assumption is valid when temperature difference is below

15%.

U/t + U (U/x) + V (U/y) + (U/z)) =

-P/x + (Uxx+Uyy) + f (x).

The fin is maintained

isothermally.

NUMERICAL APPROACH: -

The basic equations of

fluid flow are solved numerically by using Finite Volume

Method.

INTRODUCTION TO FINITE VOLUME METHOD: -

Divide the domain into

sub domain called Control Volume; each Control Volume will

have a point at which the variable is valuated as grid point. The

Control Volume should not overlap each other.

Integrate governing

equations over the Control Volume.

Approximate the

Integrals by using Piece Wise Linear profile.

Apply the discretisation

equations at all other Control Volumes.

Apply boundary

conditions.

Solve the system of

linear equations.

Note: -

Control Volume: - It is

an imaginary volume in the domain through which fluid flows.

BOUNDARY CONDITION FOR THE PROBLEM: -

PROBLEM PROCEDURE:-

Create the geometry in

the Gambit.

Mesh the geometry in

the Gambit.

Meshing of the geometry is done in order to divide the

geometry into control volumes, so that the required

parameters can be analyzed easily.

Specify boundary types

in Gambit.

In this we divide the geometry into different zones to

specify boundary conditions.

Export the geometry into

Fluent.

After initializing the boundary conditions the geometry is

exported to fluent software.

Solving and analyzing

the results.

In this the governing equations are solved and results are

analyzed.

CONTOURS OF NON-DIMENSIONAL TEMPERATURES:

FOR RAYLEIGHS NUMBER 10^3

WITHOUT FIN

WITHFIN 0.25

WITHFIN 0.50

WITHFIN 0.75

FOR RAYLEIGHS NUMBER 10^4

WITHOUT FIN

WITHFIN 0.25

WITHFIN 0.50

WITHFIN 0.75

FOR RAYLEIGHS NUMBER 10^5

WITH OUT FIN

WITH FIN 0.25

WITHFIN 0.50

WITH FIN 0.75

FOR RAYLEIGHS NUMBER 10^6

WITHOUT FIN

WITH FIN 0.25

WITHFIN 0.50

WITHFIN 0.75

CONTOURS OF STREAM FUNCTION DISTRIBUTION

FOR RAYLEIGHS NUMBER 10^3

WITHOUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN 0.75

FOR RAYLEIGHS NUMBER 10^4

WITH OUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN .75

FOR RAYLEIGHS NUMBER 10^5

WITH OUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN 0.75

FOR RAYLEIGHS NUMBER 10^6

WITH OUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN 0.75

CONTOURS OF NUSSELT NUMBER

FOR RAYLIEGHS NUMBER 10^3

WITH OUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN 0.75

FOR RAYLIEGHS NUMBER 10^4

WITH OUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN 0.75

FOR RAYLIEGHS NUMBER 10^5

WITH OUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN 0.75

FOR RAYLIEGHS NUMBER 10^6

WITH OUT FIN

WITH FIN 0.25

WITH FIN 0.50

WITH FIN 0.75

CONCLUSION: -

We have computed results associated with the problem of

internal fin flow between concentric cylinders. Cylinders with

0.75 fin length presents a heat transfer rate of 10% higher than

cylinders with out fin. The divergent fin generates a more

complex flow than the other ones and is related to the fin

geometry. The Nusselt number is proportional to Ra and the fin

length. Moreover, the increase the in fin Nusselt number with

Rayleigh number is increased as the fin size increases.

SCOPE: -

Till now analysis is conducted for

Two dimensional flows

Laminar flows.

Single phase flows.

Non-reactive flows.

In future there is a scope to analysis for

Three dimensional flows

Turbulence flows.

Multi phase flows.

Reactive flows.

BIBILOGRAPHY: -

RC Sachdeva: Heat and Mass transfer.

Chai JM, Patnakar SV: Laminar Natural convection in internally finned horizontal annuli.

Ho CJ, Lin YH, Chen TC: A numerical study of natural convection in concentric cylinders with fixed boundary conditions.