On steady flows due to a Riga surface

Abstract

Investi gation for fluid flows over a stretching sheet has relevance in processes like polymer industries, wire drawi ng of plastic films, paper production etc. The variation of sheet thickness is useful in civil, mechani ca l and aeronauti ca l engineering. The use of variab le thickness helps to red uce the we ight of structural elements. However it is seen that extensive literature exists for the flow due to flat stretching surface. The flow induced by stretch in g surface with variable surface thickn ess is not attended properl y. Further after the advent of nanofluids, the boundary layer flows caused by a moving surface had drawn the attention of recent researchers. The process of heat treatment is the method by wh ich metals are heated while undergo in g series of specific operations that do not allow the meta ls to reach the molten state. Existence of nanofl uid has generated fUlther interest in this directi on. Nanofl uid is material in which so lid nanoparticles with length sca le of 1- IOOnm are suspended in conventiona l heat transfer base fluid. These nano particles enhance the thermal conductivity and convective heat transfer coeffici ent of base fluid significantly. In 2009, Pantokratoras and Magyari examined the boundary-layer flow of low electrica l conductivity fluid s over a Riga plate i.e., the control device of Ga ilitis and Lielausis which is electromagnetic actuato r consisting of a spanwise aligned array of alternating electrodes and permanent magnets, mounted on a pl ane surface. This set up referred as Riga plate can be app lied to red uce the friction and pressure drag of submarines by preventing boundary layer separation . It has been noticed that earlier investigators have not reported the influence of heat transfer in flow of nanofluid past a Riga plate with variab le thickness. Literature survey also confirms that flows by Riga pl ate is analyzed scarcely. Motivated by the above facts, the present thesis is structured in the followin g fashion . Chapter 1 contains literature survey and laws of conservation of mass, linear momentum and energy. Boundary layer equations of viscous and Casson fluids are presented. Basic idea of homotopy ana lysis method is also included. Chapter 2 discusses the characteristi cs of boundary layer flow of nanofl uid induced by a Ri ga plate with variable thickness. Propel1ies of heat transfer are studied with convective boundary conditions and heat generation/absorption. Nanoparticle flu x is assumed zero at the surface. Appropriate transformations are employed to develop the non-d imensionalized governin g equations. Impacts of ve loc ity, temperature and nanoparticles vo lume fraction distributions are described through graphs corresponding to va rious pertinent parameters. The main results of this problem are published in Journal of Molecular Liquids 222 (2016) 854- 862. Chapter 3 addresses the double stratification effects in the flow by a Ri ga plate with variab le thickness. Nanofluid subject to Brownian motion and thermophoresis is considered. Grinberg-term for wa ll Lorentz force due to Riga plate of vari able thickness is accounted. Moreover the impacts of chemica l reaction, viscous dissipation and therma l radiation are also taken into account fo r the present model. Analysis is developed for the case when no-sl ip conditions of ve locity, thermal and concentration distributions do not hold. A numerica l scheme is employed to solve the non-linear coupled differential equations. Numerical solutions are discussed for all the involved parameters. The results of this chapter are submitted in Result in Physics. Chapter 4 investigates the boundary layer mixed co nvective flow of nanoflu id bounded by a permeable Riga-plate. Nanofluid model consists of Brown ian motion and thermophoresis. Velocity slip condition is imposed. Riga plate has constant temperature and concentration. Shooting technique is fo llowed for the numerical so lution . Nusse lt and Sherwood numbers ii are examined. This wo rk IS published In The European Physical Journal Plus, 131(6), (2016) 1-9 . Chapte,· 5 examines the effects of EMHD in flow of nanofl uid past a porous Riga sheet with gyrotactic microorganism and nanoparticles. Modeling is presented via Grinberg term and a Lorentz force parallel to the wall of a Riga plate. The fluid is weakly electrica lly conducting and the Lorentz force decreases exponentia lly. Using shooting method, the obtained nonlinear coupled ODEs are so lved. [n particular we discussed the behav ior of temperature, ve loc ity, motile microorganism density and nanoparticle concentration. Nusse lt and Sherwood numbers are examined. This ana lysis motivates the recent researchers and it prov ides a pl atform for fLllih er study on nanoflu id flow with gyrotactic m icroorgan ism past a Riga plate. This work is published in Neural Computing and Applications DOl 10.1007/s00521-017-3165-7. Chapter 6 analyses the numerical study of flow due to a Riga plate with binary chemi ca l reaction and activation energy. Heat and mass transfer characteristics in boundary layer fl ow of viscous fluid over a Riga plate are discussed. Flow is induced due to a linear stretchabl e surface. Mass transfer is studied in terms of binary chemica l reaction and activation energy. The mod ified Arrhenius function for activation energy is taken. App ropriate variab les are introduced to nondimensionalize the relevant boundary layer expressions. The resulting model is so lved numeri ca lly through the shooting techniqu e. Main observations of this chapter are submitted in Nuclear Engineering and Technology. Effect of entropy generation in mixed convective flow induced by Ri ga plate is studied in Chapter 7. Main aim of this chapter is to examine entropy generation in fl ow of visco Lls nanofluid by a horizontal Riga pl ate. Oberbeck-Bo ussinesq approx imation has been employed 111 the modeling. Shooting technique IS utilized for numerica l sol uti ons iii deve lopment. Res ults for local Nusse lt and Sherwood numbers are examined in addition to ve loc ity, temperature and concentration. Main observations of th is chapter are published in Entropy, 18(6), (2016) 223-229. Chapter 8 deals with the aiding and opposing mixed convectio n flows of Casson nanofluid by a Riga plate w ith chemica l reaction. The effects of chem ica l reaction and Electromagnetohydrodynamics (EMHD) in flow of Casson nanofluid by porous Riga plate are studi ed. The gove rning fl ow problem consists of linea r momentum, the rma l ene rgy and nanopa rti c le concentration equations. Shooting method (SM) is employed for numeri ca l so lution of resulting nonlinea r coupl ed equati ons. The aiding and opposi ng fl ows are discussed by co nside rin g negative and positive va lues of modifi ed Haliman number. N usse lt and She rwood numbe rs a re numericall y discussed. Compa rative study for resu lts is a lso given. The mate rial of chapter e ight is published in Journal of P,"ocess Mechanical Engineedng DOl: https:lldoi.org/10.1177/09544089177