Mathematical Modelling of Biological Variations due to Application of Nanofluids in Body Fluids

Abstract

A substance capable of flowing is termed as a fluid. Fluids are of two types, namely liquids and gases. The study of fluid's behaviour at rest (termed fluid statics) and in motion (termed fluid dynamics) is combinedly known as fluid mechanics. The fluid produced and circulated within the human body or secreted outside the human body is known as body fluid. Blood, saliva, urine, tears, sweat, and breast milk are a few examples of body fluid. Water is the basis of all body fluids and the human body is composed of about 60% of water.Nano fluid is a colloidal mixture in which a base fluid (water, oil, ethylene glycol, etc.) is mixed with nanometer-sized particles (metals, carbides, oxides or carbon nano tubes). Fluids constituting two nanometer-sized particles are termed hybrid nano fluids. Nano fluids tend to upgrade and stabilize the thermal properties of the fluid which marked a revolution in the field of fluid dynamics. The description of a system using mathematical concepts and language is known as mathematical model and the process of developing a mathematical model is known as mathematical modelling. Mathematical models finds its use in natural sciences, engineering disciplines and social sciences. A mathematical model helps to explain a system and to study the effects of different components and also to make predictions about its behaviour. The thesis entitled Mathematical Modelling of Biological Variations due to Application of Nano fluids in Body Fluids has been arranged into 12 chapters. Chapter 1 introduces the basic concepts, preliminaries and definitions to the reader. An extensive review of related literature has been presented in Chapter 2. Owing to the practical applications (like biomedical imaging, hyperthermia, pharmaceuticals, biosensors, medical instruments, bio-chromatography, microchip pump, thermostatic, biomedical science, targeted drug delivery, and cancer therapy), nine fluid flow problems are modeled and investigated in this thesis. In Chapter 3, the bio convective stagnation point flow involving carbon nano tubes along a lengthening sheet subject to induced magnetic field and multiple stratification effects is investigated. The dynamics of water conveying single-wall viicarbon nano tubes (SWCNTs) and magnetite nano particles on the bio convective stagnation-point ow along a stretching sheet subject to chemical reaction, viscous dissipation, induced magnetic field, and stratification effects is investigated in Chapter 4. Non-spherical nanoparticles have gained popularity for their ability in changing the thermo physical properties of a nano fluid. Chapter 5 elucidates the significance of multiple slip and nanoparticle shape on stagnation point flow of blood-based silver nano fluid considering chemical reaction, induced magnetic field, thermal radiation, nano particle shape and linear heat source. The numerical study on the stratification effects of bio convective electroencephalographic (EMHD) flow past a stretching sheet using water-based CNT has been presented in Chapter 6. The focal concern of Chapter 7 is to numerically scrutinize the consequences of multiple slip, linear radiation and chemically reactive species on MHD convective Carreau nanoliquid flow over an elongating cylinder. Moreover, statistical scrutiny on the impact of Hartmann number, thermal radiation and thermal slip parameter over heat transfer rate employing Response Surface Methodology (RSM) and sensitivity analysis is also performed. The nanomaterial flow of Chapter 8 has been modeled using the modified Buongiorno nano fluid model. The impact of the stratification constraints and magnetic field are also accounted. Further, the influence of magnetic field parameter, thermal stratification parameter, volume fraction of magnetite nanoparticles, and velocity ratio parameter on the heat transfer rate has been scrutinized statistically using a five-level four-factor response surface optimized model. In Chapter 9, the dynamics of the T iO2 − H2 O nano material over a non linearly stretched surface and modeled using modified Buongiorno model is investigated. Experimentally derived correlations of the thermal conductivity and dynamic viscosity of the nano material are utilized.The hydro-magnetic bio convective flow of a nano material over a lengthening surface is investigated in Chapter 10. Realistic nano material modelling is achieved by incorporating passive control of the nano particles at the boundary. The impact of the Newtonian heating and Stefan blowing constraints are also accounted. The sensitivity of heat transport rate is also computed. Chapter 11 numerically elucidates the dynamics of elector-magneto hydrodynamic flow of blood-gold nano material over a non linearly stretching surface utilizing the Casson model. The impact of second-order hydrodynamic-slip, nano particle radius, first-order thermal-slip, inter-particle spacing and non-uniform heat source are also accounted. Lastly, Chapter 12 presents the concluding remarks of the thesis and proposals for future work.