In this thesis Mathematical models for Gyrotactic bioconvection are developed for diferent uids using variable surfaces. The surfaces includes Vertical Wavy surface , vertical isothermal surface and a stretching surface. The Fluids under consideration are Nano uid , dusty nano uid , Oldroyed-B uid and Maxwell uid. Some important physical quantities such as Magneto hydrodynamics , thermal radiation are included for experimental and physical analysis. Some salient physical quantities such as heat transfer and mass transfer are included for engineering process. In Chapter 01 some basic terms of , governing equations , dimensionless numbers and the methodologies which are used in later chapters are presented. Introduction , history and applications of the work is given in Chapter 02. In Chapter 03 analysis of a nano uid bioconvection ow with heat and mass transfer of a water-based nano uid containing gyrotactic microorganisms over a vertical wavy surface is investigated. The coupled nonlinear set of equations comprised of velocity, temperature, nanoparticle concentration and density of microorganisms is solved numerically by using implicit nite di erence method. Flow characteristics are obtained in terms of skin friction coe cient, Nusselt number, Sherwood number and density number of microorganisms coe cient and are presented graphically by varying several controlling parameters. Interesting observations are recorded for the parameters: Nr, Lb and Rb. It is observed that the amplitude of the wavy surface has pronounced in uence on the rates of heat and mass transfer, skin friction coe cient and density number of the microorganisms coe cient and all these quantities get augmented as the amplitude increases. The aim of present chapter 04 is to establish the detailed numerical results for bio- convection boundary-layer ow of two-phase dusty nano uid. The dusty uid contains gyrotactic microorganisms along an isothermally heated vertical wall. The physical mechanisms responsible for the slip velocity between the dusty uid and nanoparticles, such as thermophoresis and Brownian motion, are included in this study. The in uence of the dusty nano uid on heat transfer and ow characteristics are investigated in this chapter. The governing equations for two-phase model are non-dimensionalized and then solved numerically via two-pointnite di erence method together with the tri- diagonal solver. Results are presented graphically for wall skin friction coe cient, rate of heat transfer, velocity and temperature pro les and streamlines and isotherms. To ensure the accuracy, the computational results are compared with available data and are found in good agreement. The key observation from present analysis is that the mass concentration parameter, D , extensively promotes the rate of heat transfer, Qw, whereas, the wall skin friction coe cient,w, is reduced by loading the dust parameters in water based dusty nano uid. Chapter 05 discusses the three-dimensional ow the gyrotactic bioconvection of an Oldroyd-B nano uid over a stretching surface. Theory of microorganisms is utilized to stabilize the suspended nanoparticles through bioconvection induced by the e ects of buoyancy forces. Analytic solution for the governing nonlinear equations is obtained by using homotopy analysis method (HAM). The e ects of involved parameters on ve- locity, temperature, nanoparticles concentration and density of motile microorganisms are discussed graphically. The local Nusselt, Sherwood and motile micro-organisms numbers are also analyzed graphically. Several known results have been pointed out as the particular cases of the present analysis. It is found that the non-Newtonian uid parameters i.e. relaxation time parameter1 and retardation time parameter2 have opposite e ects on the velocity pro le. The velocity of the uid and boundary layer thickness decreases for increasing relaxation time while it decreases for increasing retardation time e ects. In Chapter 06 the three-dimensional ow of Maxwell nano uid containing gyro- tactic micro-organisms over a stretching surface. The e ects of magneticeld and heat source/sink are also considered. Theory of microorganisms is utilized to stabilize the suspended nanoparticles through bioconvection induced by the e ects of buoyancy forces. Analytic solution for the governing nonlinear equations is obtained by using ho- motopy analysis method (HAM). The e ects of Deborah number, Hartmann number, mixed convection parameter, buoyancy ratio parameter, bioconvection Rayeigh num- ber, stretcing ratio parameter, brownian di usion and thermophoresis di usion param- eters, Prandtl number, Schmidth number, bioconvection Lewis number, bioconvection Peclet number and the micro-organisms concentration di erence parameter on veloc- ity, temperature, nanoparticle concentration and density of motile microorganisms are discussed graphically. The local Nusselt, Sherwood and motile micro-organisms num- bers are also analyzed graphically. Several known results have been pointed out as the particular cases of the present analysis.
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