Declaration of Authorship We hereby certify that this thesis is our own work and was completed for partial fulfilment of the undergraduate degree in Mechanical Engineering at Bangladesh University of Engineering and

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Declaration of Authorship

We hereby certify that this thesis is our own work and was completed for partial fulfilment of the

undergraduate degree in Mechanical Engineering at Bangladesh University of Engineering and

Technology. We declare that where any or all part of this thesis has previously been submitted

for a degree or any other qualification at this university or any other university, this has been

clearly stated. All the published work of others and all sources of information have been properly

attributed and acknowledged and with the exception of such references, this work is entirely our

own and all authors have contributed equally to the project.

Signed:

Md Imran Khan

Md. Mamun Billah

Mohammed Mizanur Rahman

Abstract

This thesis illustrates a numerical study of steady two dimensional mixed convention heat

transfer phenomena in a rectangular channel with an active flow modification system by means

of a variable speed heat conducting cylinder that is placed at the center of the channel. In the

current study, an isothermal low temperature is maintained on the upper wall while a discrete

isoflux heater is installed on the lower wall. The Prandtl number of air flowing through the

channel is kept fixed at 0.71 while the Reynolds and the Grashof numbers are varied

considerably for four different configurations of the cylinder such as: i) channel with no cylinder,

ii) channel with stationary cylinder, iii) channel with cylinder rotating clockwise and iv) channel

with counter clockwise rotating cylinder. The speed ratio is varied as 0.5, 1.0 and 1.5 for only the

counter-clockwise and clockwise rotational setups. The impact on the flow pattern and

temperature field is evaluated in terms of the distribution of streamlines, isothermal lines while

the impact on the heat transfer phenomena is analyzed in terms of the local and surface averaged

Nusselt numbers. The results point out that the cylinder’s configuration, rotational speed,

Grashof and Reynolds numbers significantly impact the flow pattern, temperature field and the

heat transfer characteristics. Glapke and Afsaw [11] analyzed natural convection in a circular

enclosure with a concentric hexagonal cylinder.

Acknowledgements

All praises be to Allah, the Most Gracious and Most Merciful, for giving us the strength and

knowledge to successfully complete this thesis.

We are extremely grateful and honored to have had the opportunity to work under the

supervision of Dr. Mohammad Nasim Hasan, Associate Professor of Department of Mechanical

Engineering, Bangladesh University of Engineering and Technology whose kindness, patience

and guidance helped us shape our work into what it is today. For his mentorship and for the time

and effort that was put in to make us understand the problem more clearly, we would like to

express our sincerest gratitude and appreciation.

Dedicated to our beloved parents

Table of Contents  Page 
Declaration of Authorship  1 
Abstract  2 
Acknowledgements  3 
Dedication  4 
List of Figures  7 
List of Tables  8 
Nomenclature  9 
Chapter 1  11 
1.1 Convection Heat Transfer  11 
1.1.1 Natural Convection  13 
1.1.2 Forced Convection  14 
1.1.3 Mixed Convection  14 
1.2 Classification of Mixed Convection  15 
1.3 Mixed Convection in Cavity  16 
1.3.1 Closed Cavity Problems  16 
1.3.2 Open Cavity Problems  17 
1.4 Literature  17 
Chapter 2 Mathematical Modelling  19 
2.1 Physical Model  19 
2.2 Assumptions  20 
2.3 Governing Equations  20 
2.4 Dimensional Analysis  21 
2.4.1 Dimensionless Numbers  21 
2.5 Dimensionless Boundary Conditions  22 
Chapter 3 Numerical Methodology  24 
3.1 Advantages of Numerical Analysis  24 
3.2 Solution of Differential Equations  25 
3.3 Finite Element Method  26 
3.3.1 Advantages and Disadvantage of the Finite Element Method  30 
3.4 Galerkin Weighted Residual Method  31 
3.5 Mesh Generation  33 
3.6 Grid Sensitivity Test  35 
3.7 Validation of Isothermal Lines and Streamlines  36 
3.8 Summary  38 
Chapter 4 Results and Discussions  39 
4.1 Effect of Grashof Number and Reynolds Number  40 
4.2 Effect of Cylinder Speed Ratio  49 
4.3 Effect on Heat Transfer Characteristics  58 

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DeclarationofAuthorshipWeherebycertifythatthisthesisisourownworkandwascompletedforpartialfulfilmentoftheundergraduatedegreeinMechanicalEngineeringatBangladeshUniversityofEngineeringandTechnology.Wedeclarethatwhereanyorallpartofthisthesishaspreviouslybeensubmittedforadegreeoranyotherqualificationatth...

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Declaration of Authorship We hereby certify that this thesis is our own work and was completed for partial fulfilment of the undergraduate degree in Mechanical Engineering at Bangladesh University of Engineering and

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