Mathematical Modeling And Simulations For The Problems Arising In Heat Transfer Analysis Of Fluid Flows

Heat transfer is a phenomenon describing the flow of thermal energy because of the temperature differences.This dissertation focuses on the mathematical modeling and numerical simulations of problems arising in heat transfer and related applications.The proposed mathematical models represent nonlinear elliptic partial differential equations as well as a nonlinear system of reaction-diffusion equations.The aim is to mathematically explore the possibilities that enhance the heat transfer phenomenon in various settings.The first application focuses on the mathematical modeling of heat transfer in microchannel in the presence of interfacial electrokinetic effects.The resulting model is a nonlinear elliptic set of partial differential equations.For the numerical simulations,we efficiently implement traditional FDM approach,and for the regularity results,we use the classical energy estimates.The interfacial electrokinetic effects result in an additional source term in the classical momentum equation,consequently affecting the characteristics of the flow and heat transfer.The sinusoidal temperature variation is assumed on sidewalls.The published results are properly obtained for various combinations of physical parameters appearing in the governing equations.This comprehensive study reasonably concludes that in the presence of EDL(electric double layer),the average heat transfer rate modestly reduces along with more considerable values of Reynolds number.It is carefully observed that the heat transfer increases with the modest increase in amplitude ratio and phase angle.The flow behaviour and heat transfer rate inside the microchannel are equally affected by the presence of .Another application of heat transfer presented in this dissertation focuses on the steady-state free convection heat transfer in the existence of an exothermal chemical reaction administered via Arrhenius kinetics inside a right-angled field of triangular form occupied by porous media soaked with magnetized nanofluid.An estimate named Darcy-Boussinesq approximation along with a nanofluid prototype mathematically proposed by Buongiorno has been instigated to model the visible phenomenon representing the fluid flow,heat transfer,and nanoparticle concentration.The governing mathematical equations in a dimensionless arrangement are relating the stream function for circulation of fluid,the energy equation,and nanoparticles volumetric fraction.The modeled governing equations are simulated using the conventional finite difference method.The legitimacy of the numerical technique is proven by relating present results with the former works in both numerical and graphical methods.Streamlines,isotherms,and isoconcentrations are carefully plotted and adequately argued for the various parametric regime.The graphical description illustrates that the average Nusselt and Sherwood numbers represent the decreasing function of the Rayleigh number.The study discovered the accountable impact of model parameters like thermophoresis and Brownian diffusion on the local Sherwood number,while a minimum effect on local Nusselt number is witnessed.For future work and to further explore the potential applications of numerical methods in applied sciences,we will concentrate on numerical solutions for chemotaxis-Navier Stokes system to describe the spontaneous emergence of patterns in populations of oxygen-driven swimming bacteria.The idea will be to use finite element approximations in space and finite differences in time combined with the concept of splitting operator to decouple the computing of the fluid part from the chemotaxis one.In precise conclusion,this doctoral dissertation focuses on the practical applications of heat transfer in the field of non-linear mechanics,particularly fluid mechanics.The necessary conclusions are established on the basis of dimensionless numbers like Nusselt number,Reynolds number,Hartmann number,Frank Kamenetskii,Lewis number and thermophoresis parameters,etc.The graphical descriptions of these dimensionless numbers show the general trend of heat transfer in the microchannel as well as the triangular cavity.The numerical simulations scientifically prove the claim that the electrokinetic effects in microchannels and exothermic chemical reaction inside a triangular cavity both affect the heat transfer phenomenon.The choice of FDM as the numerical method to carefully perform simulations represent the fact that its derivation in terms of divided differences is straightforward,and it appeals to a full spectrum of linear and non-linear PDEs.