Ist Doctoral committee MeetingPresentation of Research Proposal

byN.Siva Kumar

Ph.D., Scholar (External Part Time)

Research SupervisorDr. B. RUSHIKUMAR

Fluid Dynamics Division, SAS, VIT University

Date: 26/04/2013 Venue: TT513

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Title Of The Research Work

Scope and Objective

Introduction - Literature survey

Method of Solutions - Methodology

Plan of Work

References

Title of the Proposed Research Work

FLOW IN POROUS MEDIA

Studies On Heat and Mass Transfer in Magneto Hydrodynamics Flows

The study of Heat transfer addresses the transport of energy

due to conduction, convection and radiation in almost all areas

of science and engineering.

Mass transfer specifically refers to the relative motion of

species in a mixture due to concentration gradients. In many

industrial and scientific applications, heat transfer processes occur

simultaneously with mass transfer processes.

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Scope and Objective

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Many processes and phenomena in science,

engineering and technology involve motion of electrically

conducting fluids in the presence of a magnetic field. MHD

flows occur commonly in astrophysical, geophysical, and

industrial environments and also have engineering applications

like MHD power generator, MHD pumps, MHD lubrication and

propulsion. The unique feature of this work is concerned with

finding numerical solutions for MHD flow in a variety of flow

domains and in incompressible electrically conducting fluids.

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Objective

Hence the main objective of the present thesis work is to

solve the problems related to Heat and Mass transfer in MHD flows

with different flow geometries embedded in porous medium, using

advanced Mathematical tools and also using the MATLAB software.

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Introduction - Literature survey

In general, the governing fluid flow equations are

in the form of PDEs.In this connection, the Control of heat and mass

transfer processes by means of external force effects is one of the

most important problems in modern applied physics. We are

interested to the study of the magnetic field effect as it bears on

transfer phenomena: heat and mass transfer. Simultaneous heat and

mass transfer from different geometries embedded in porous medium

has many Engineering and Geophysical applications such as cooling

of nuclear reactors and underground energy transport.

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The developments in MHD are the natural phenomena of an

important and relatively recent shift in the properties of

liberalization, globalization and industrialization in India. During the

latter half of twentieth century, MHD has been simulated by

questions arising in practical problems. During the last five decades,

MHD is extensively diversified for overall development. The main

motivation for such developments is the greater importance that has

been given to self sufficiency in energy sector and industrial

development. The acute shortage of energy the depletion of fossil

fuels and the severity of ecology problems that are being faced in

the country provided extensive scope for research in this area.

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Literature survey A.S.Idowu,M.S.Dada and A.Jimoh(2013) has studied for Dissipative Fluid

Flow Past A moving Vertical Porous plate with Variable Suction.

Arman Hasanpour,Mojtaba Parvizi Omran and Hamid Reza

Ashorynejad(2013) has studied Over the Movable Permeable Plumb surface.

K. Sarada & B. Shanker (2013) has investigated in Free Convection Flow

Over an Infinite Vertical Porous Plate with Heat Absorption.

S. Renuka, *N. Kishan and J. Anand Rao (2009) has studied in Convective

Mass Transfer Flow Past an Infinite,Vertical Porous Plate with Variable Suction

and Soret Effect

G. Sreedhar Sarma, D. Sreenivasu, K. Govardhan, K. Ramakrishna Prasad

(2013) has studied and how to solve numerically vertical surfaces in porous

media considering Soret and Dufour effects

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Mohamed Y. Abou-zeid (2009) has analysed the Flow of Carreau Fluid with

Diffusion and Chemical Reaction through a Non Darcy Porous Medium

K. Sarada & B. Shanker (2013) has investigated in Free Convection Flow Over

an Infinite Vertical Porous Plate with Heat Absorption

S. Renuka, *N. Kishan and J. Anand Rao (2009) has studied in Convective Mass

Transfer Flow Past an Infinite,Vertical Porous Plate with Variable Suction and

Soret Effect

G. Sreedhar Sarma, D. Sreenivasu, K. Govardhan, K. Ramakrishna Prasad (2013)

has studied and how to solve numerically vertical surfaces in porous media

considering Soret and Dufour effects

Mohamed Y. Abou-zeid (2009) has analysed the Flow of Carreau Fluid with

Diffusion and Chemical Reaction through a Non Darcy Porous Medium

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Method of Solutions - Methodology

In this analysis, the mathematical modeling involves highly

non-linear coupled partial differential equations which govern the physical system

applications. In this thesis, we solve these non-linear partial differential equations

first with similarity transformation. By this treatment, the non-linear coupled

partial differential equations converted into non-linear coupled ordinary

differential equations.

There are numerous methods are available in the literature to find the

solution for these non-linear coupled ordinary differential equations. Here, we may

apply an analytical method or numerical techniques to obtain solution for given

physical system.

An analytical solution is obtained by using double regular

perturbation technique to solve the non-linear ordinary differential

equations using the non-dimensional parameter which are involved

in the physical system.

We may also apply to solve these coupled non-

linear ordinary differential equations using finite difference or

finite element method or Shooting technique which uses Range-

Kutta or Range-Kutta-Gill or Range-Kutta-Fehlberg with Newton-

Raphson method. Computations are carried out using Matlab or

Maple or Mathematica or C software.

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Plan Of Work

In this work we want to study the heat and mass transfer in

MHD flows. Some of these problems involve thermal energy and

concentration of species like storage system thermal insulation,

solar collector, geothermal engineering, pollutant dispersal in

aquifer and the storage of nuclear wastes in deep geological

repositories and so on. Using suitable boundary conditions to

determine the nature of fluid flow, heat and mass transfer rate in a

variety fluids and fluid saturated porous materials.

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Our work covers many aspects of fluid flow like electrically

conducting fluid flow and flow through and past a porous media. This

process involves

Heat transfer (conduction, convection, radiation)

Mass transfer (diffusion, evaporation, condensation,

absorption)

Fluid dynamics (single-phase and multiphase flow, flow in

porous media)

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In this connection, the problems proposed to study

here have been considered with a view to possible applications,

particularly in Biology and Medicine.

Some of the problems we are interested to study are

Thermodynamics Analysis of Transfer Phenomena in

Electric and Magnetic Fields

Heat Transfer in a Laminar MHD-Flow

Free MHD Convection

Convective Mass Transfer in Magnetic Field

Heat and Mass Transfer in Magnetizable Fluids

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Previous work done:

A course work completed on Research Methodology in

sciences from july-2013 to december-2013.

Presented a paper on MHD transient free convection and

chemically reactive flow past a porous vertical plate with

radiation and temperature gradient dependent heat source in

slip flow regime in National conference at SV

University ,Tirupati 29-01-2014.

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References

B. Rushi kumar and R. Sivaraj, "MHD viscoelastic fluid non-Darcy flow over a

vertical cone and a plate", International Communications in Heat and Mass

Transfer 40(2013) pp 1-6

Anjali Devi, S. P. and M. Kayalvizhi, 2010. Analytical solution of MHD flow

with radiation over a stretching sheet embedded in a porous medium, Int. J. of

Appl. Math and Mech., Vol. 6, No. 7, pp. 82 – 106.

Hossain, M.A. and Begum, R.A., The effects of mass transfer on the unsteady

free-convection flow past an accelerated vertical porous plate with variable

suction, strophys. Space Sci., 145, 115 (1985).

Nield, D.A., and Bejan, A., (1998) Convection in porous media, 2 nd edition,

Springer-Verlag,Berlin.

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D.A.Nield and A.Bejan, Convection in PorousMedia. NewYork, Springer-

verlag.2006.

InghamD.,popI, Transport phenamina in porous media, I pergaman,

oxford,1998.

Ingam D.PopI, Transport phenomina in porous mediaII,pergman ,oxford,2002.

Singh A.K. The MHD Free-Convection and Mass Transfer Flow with Hall

Current, Viscous Dissipation, Joule

Heating and Thermal Diffusion is Studied. – Indian Journal of Pure and

Applied Physics, 2003, Vol.41, Pp.24-35.

Soundalgekar, V.M. and Ganesan, P., Transient free convective flow past a

semi-infinite vertical plate with mass transfer, Reg. J. Energy Heat and Mass

Transfer, 2, No.1, 83 (1980).

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Srihari, K., Anand Rao, J. and Kishan, N. MHD free convection flow of

anincompressible viscous dissipative fluid in an infinite vertical oscillating plate

with constant heat flux, Jl. Energy, Heat and Mass Transfer, vol 28, pp. 19-

28,2006.

V.Srihari babu and G.V.Ramana reddy, Adv.App.science Research, 2011,

(4):138-146

Satya sagar Saxena and G.K.Dubey, Adv.App.science Research, 2011, (5):115-

129.

Satya sagar Saxena and G.K.Dubey, Adv.App.science Research,

2011,2(4):259-278. Carnahan, H., Luther, H. A., and Wilkes, J.O., (1969).Applied Numerical

Methoda, John Willey, newYork.

Nield, D. A. and Bejan, A., (1998). Convection in Porous media, Second edition,

Springer, New York.

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