Brownian Motion Research Papers - Academia.edu (original) (raw)

An amalgamation of base fluid (usually oil, water, ethylene, glycol, glycerol, etc.) and metallic tiny particles (usually Cu, SiO2, Al2O3, etc.) having diameter less than 100 nm is designated as nanofluid. In last few decades, nanofluids have gained an incredible height owing to their industrial importance and frequent applications in thermal insulations, thermal-power plants, agriculture, purification of oil, sterilization processes, powder technology, automatic transmission of liquids, thermo-siphons, energy preservation, nano-emulsification, nanolubricants, nanofluid detergent, modulators, nuclear reactors and hydrothermal conduction, etc. Bidirectional flows of various fluids impinging over expanding surfaces with the inclusion of nano-sized/tiny particles have a variety of significances in engineering and industrial sectors. The insertion of nano-sized/tiny particles into base liquids enhances the ability of thermal conductivity and usually these are used to overcome the poor thermal enactment of base liquids.
Boundary layer flows impinging over an expanding surface have a prominent role in metal and plastic industries, like: thinning and annealing of wires, manufacturing of rubber and plastic sheets, condensation process along a liquid film, drawing of stretchable sheets and aerodynamic extrusion of plastic films. Moreover, coating of sheets with tiny particles has an indispensable role in the enhancement of heat conveying phenomenon. Thus, we decided to investigate the boundary layer flows with the involvement of tiny particles. It is further inspected that steady bidirectional flow problems are much investigated as compared to the unsteady bidirectional flow problems. In the view of such facts, the core objective of present thesis is to explore bidirectional flow problems of nanofluids affecting over an unsteady elongating obstacle with the features of prescribed heat sources. The present thesis is structured as follows:
Chapter one consists on the literature review and fundamental concepts of liquid mechanics. Mathematical forms of the law of mass, momentum, energy and concentration conservations in Cartesian frame are presented. Boundary layer equations for various liquids (Newtonian, Carreau, Prandtl and Eyring-Powell) in the view of unsteady bidirectional flow are presented, mathematically. Details of nanofluid models and dimensionless numbers are also discussed in this chapter. Basic concept of Keller-Box method for numerical simulations, its advantages and coding procedure through an example from literature are also included in this chapter.
Chapter two explores the unsteady dynamics of a nanomaterial impinging over a bidirectional elongating obstacle with the features of porous medium, magnetic environment and internal heat production/consumption. Random movement and thermodiffusion of tiny/nano-sized particles are also in action. The characteristic of prescribed surface temperature (PST) is also used to maintain the surface temperature. The modeled transport equations are converted into dimensionless forms with the help of similarity transformations before finding the numerical solution via Keller-Box method. Comparison is also constructed with the previously published work and outcomes are in decent acceptance with antecedent published outcomes. The results for reduced Nusselt and Sherwood numbers against parametric values of involved constraints are described through tables. Thermal and concentration fields are discussed and anatomized through several graphical illustrations. The contents of this exploration are published in Special Topics and Reviews in Porous Media: An International Journal 10 (2019) 457-473.
Chapter three discloses bidirectional flow of a nanomaterial with unsteady Cattaneo-Christov double diffusion in the environment of variable thermal conditions. Cattaneo-Christov fluxes are used to investigate the thermal and concentration relaxations. Novel features of random movement and thermo-migration of tiny-sized particles are also retained. Similarity conversions are used to create the system of non-linear ordinary differential equations. The acquired/obtained nonlinear system is computationally tackled by recalling Keller-Box method. Graphical illustrations have been prepared for thermal and concentration setups for distinct choices of impacted constraints. Tables have been formed and deliberated for coefficients of skin friction, temperature gradient and concentration gradient. Obtained outcomes are connected with the formerly available outcomes and found promising agreement. The contents of this investigation are published in Results in Physics 15 (2019) 102581.
Chapter four presents the relationship between unsteady Cattaneo-Christov double diffusion, random movement and thermodiffusion of tiny-sized particles in the existence of convectively heating and zero-mass flux at the bidirectionally stretchable wall. Combination of similarity expressions is implemented to transform the prevailing partial differential equations into ordinary differential equations and then solved, numerically, by using Keller-Box simulation technique. Thermal and concentration phases are discussed with the influences of involved constraints, graphically. The contents of this exploration are recently published in Ain Shams Engineering Journal (2021).
Chapter five describes the unsteady bidirectional flow of magneto-Carreau nanomaterial impacting over an expanding surface with the aspects of thermal radiation and variable thermal conditions. An appropriate set of transforming variables is adopted to metamorphose the transport equations into ordinary differential equations and then simulated via Keller-Box method. Features of the involved constraints for thermal, concentration and velocity phases are graphically addressed. Simulations of effective drag forces, thermal gradient and concentration gradient have been made through tabular arrangements and explained in detail. A marvelous agreement is found by comparing the outcomes with the available reported work for a limited situation. The contents of this assessment are published in Heat Transfer 49 (2020) 3456-3476.
Chapter six frames an unsteady dynamics of a magnetized Eyring-Powell nanofluid impacting over the bidirectional expanding obstacle with the features of prescribed thermal conditions and radiation aspects. Again, transport equations are transmuted into ordinary differential equations with the proper arrangement of similarity variables and then the obtained set of equalities has been solved, numerically. Various tables and plots have been generated to illustrate the rate of heat as well as rate of mass transferences.
Finally, the whole parametric exploration has been validated through a comparison benchmark. The contents of this inspection are published in Case Studies in Thermal Engineering 21 (2020) 100689.
Chapter seven describes the computational study concerning with the unsteady flow of Eyring-Powell magneto nanoliquid over a bidirectionally deformable surface. Transference of activation/Arrhenius energy is used in the improvement of binary-chemical-reaction. Nonlinear significance of thermal radiation is also incorporated in the transport equation of energy. Investigation has been carried out through convective Nield's boundary restrictions. Firstly, useful combination of variables has been implemented to metamorphose the transport equations into ordinary-differential-equations. Later on, Keller-Box approach has been adopted to simulate the physical problem. Physical interpretations of obtained results are also described for temperature and mass concentration distributions through various graphs. Rate of heat transportation has been explained through tabular data for acceptable ranges of involved engineering parameters. Convergence analysis and error estimations of the numerical solution are also presented through various mesh refinement levels of the computational domain. Finally, comparison benchmarks with the restricted cases have been presented for the validation of the results obtained through the present parametric investigation. The contents of this analysis are published in International Journal of Modern Physics C 31 (2020) 2050156.
Chapter eight determines the bidirectional dynamics of Prandtl nanofluid with the aspects of dissipation function, Ohmic hating and magnetic coating. Thermodiffusion and random movement of nano-sized/tiny particles are also explored with the help of Buongiorno model. Prescribed heat/mass flux conditions have been imposed at the stretchable obstacle. An appropriate set of scaling variables has been used to metamorphose the transport equalities into dimensionless forms and then simulated via Keller-Box approach. The features of miscellaneous arising constraints on thermal and temperature phase have been addressed through various plots, while tabular arrangements have been used to inspect the rate of heat/mass transferences. The efficiency of the applied method has been predicated by incorporating error analysis. The contents of this study are published in Heat Transfer 49 (2020) 4801-1819.