Numerical Simulations For Some Boundary Layers Flows Around Stationary or Rotating Surfaces

Abstract

Boundary layer flow around stationary or moving bodies have been given special attention by the researchers. Particularly, rotating flows arise in numerous scientific and engineering applications involving turbomachinery, thermal-power generating systems, rotating machinery, computer storage devices, gas turbine rotors, air cleaning machines etc. In this thesis, the intention is to formulate rotationally symmetric fluid motion over stationary or rotating boundaries. The classical von Kármán and Bödewadt flows have been revisited by using variable fluid properties. Time-dependence in von-Kármán flow has been discussed by considering nanofluid assumption. Moreover, Bödewadt flow of visco-plastic fluid is formulated for the first time here. Numerical computations are performed by collocation method based MATLAB package bvp4c and shooing method. Obtained numerical computations are compared with the existing studies and found in excellent agreement. Chapter 1 enlightens some subtle fluid dynamics concepts and presents comprehensive review about rotationally symmetric flows. Governing equations with variable fluid properties and nanofluid assumptions are also presented. In Chapter 2, the outcomes of variable fluid properties on heat transfer in Bödewadt flow with wall suction is the main focus. Precisely, both variable viscosity and thermal conductivity are assumed to exhibit temperature dependency. Computations are worked out for broad parameter values by a numerical approach. Present results are in perfect agreement with the available literature in a limiting sense. Plots for velocity and temperature are presented and explained. The key points of this chapter have been published in Physica A 534 (2019), Article ID: 122138. In Chapter 3, consequences of Bödewadt slip flow on a convectively heated porous disk in a nanofluid is studied. Aspect of partial slip effect is considered in the mathematical model. Numerical simulations for wide range of pertinent parameters are performed by MATLAB built-in package bvp4c. Present results are in perfect agreement with the available literature in a limiting sense. Effects exhibited by velocity and temperature profiles upon changing embedded parameters, are analyzed graphically. Salient results of the analysis are published in Physica Scripta 94 (2019), Article ID: 095701. In Chapter 4, a model of homogeneous-heterogeneous reactions for Bödewadt flow over a permeable disk containing chemically reactive substances is formulated. xiii Aspect of homogeneous-heterogeneous reactions is considered in the mathematical model. Asymptotic solutions for concentration profile are found. Moreover exact analytical solution for concentration is developed under large wall suction assumption, which strongly supports the numerical results. Contribution of reaction rate on the Bödewadt flow is carefully assessed. The findings of this chapter have been published in Applied Sciences 9 (2019), Article ID: 4046. In Chapter 5, unsteady rotating flow generated by a decelerating rotating disk in nanofluid is focused in this chapter. Disk angular velocity is assumed to slow down with increasing duration. Moreover, in order to have a similar solution, a time dependent wall suction velocity is treated. Asymptotic solutions for large similarity variable and large wall suction are derived and discussed. The key points of this chapter have been published in Arabian Journal for Science and Engineering 45, 1143–1154 (2020). In Chapter 6, flow model of Chapter 5 is reconsidered when fluid exhibits variable fluid properties. Expressions of viscosity and thermal conductivity, earlier employed in Chapter 2, are considered here. Numerical computations are performed with special emphasis on the outcome of variable physical properties on the model. The key points of this chapter have been published in International Communications in Heat and Mass Transfer 116 (2020), Article ID: 104673. Chapter 7 is concerned with the Bödewadt flow of Bingham fluid, which is discussed for the first time in this thesis. Additionally, viscous dissipation term with Bingham fluid assumption is also derived, which is not yet available. Permeable wall assumption is invoked for physically consistent temperature profile, as already explained in Chapters 1-3. Role of fluid yield stress on the Bödewadt flow and resulting heat transfer is discussed through numerical solutions. The findings of this work have been published in Alexandria Engineering Journal 60, 2857-2864 (2021). Chapter 8 is concerned with the rotationally symmetric flow of Reiner-Rivlin fluid, which is discussed for the first time in this thesis. Additionally, viscous dissipation term with Reiner-Rivlin fluid assumption is also derived. Permeable wall assumption is invoked for physically consistent temperature profile, as already explained in Chapters 1-3. Role of Reiner-Rivlin fluid parameter on the von-Kármán and Bödewadt flow and resulting heat transfer is discussed through numerical solutions. The findings of this work have been published in Proc IMechE part C: J