Analysis and Simulations of Nanofluid Flow and Heat Transfer in a Porous Pipe
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The study of ﬂuid ﬂow and heat transfer through a cylindrical pipe and channel with porous boundaries are important research area due to its wide range of applications in engineering and industrial processes. Some practical applications include problems dealing with transpiration cooling, gaseous diffusion in order to produce fuel for nuclear reactors, controlling boundary layer ﬂow over aircraft wings by injection or suction of ﬂuid out of or into the wing, lubrication of porous bearings, petroleum technology, ground water hydrology, seepage of water in river beds, puriﬁcation and ﬁltration pr ocesses. A nanoﬂuid is the suspension of nanoparticles in a base ﬂuid. Nanoﬂuids are promising for heat transfer enhancement due to their high thermal conductivity. For practical applications of nanoﬂuids research in nanoﬂuids convection are important. Owing to their enhanced properties, nanoﬂuids can be used in a plethora of technical and biomedical applications such as nanoﬂuid coolant which include electronics cooling, vehicle cooling, transformer cooling, computers cooling and other electronic devices cooling. Other applications are medical applications which include magnetic drug targeting, cancer therapy and safer surgery by cooling. This study considered the detailed analysis of laminar flow behavior and heat transfer using this innovative ﬂuid as working ﬂuid through a pipe and channel with porous boundaries for both steady and unsteady scenarios. We considered water-based nanoﬂuids where copper and alumina were used as nanoparticles. The appropriate mathematical models for the problems were derived from the laws of conservation of mass, momentum and energy balance. The governing nonlinear Partial Differential Equations (PDE) and boundary conditions were converted into nonlinear Ordinary Differential Equations (ODE) using appropriate similarity transformations for the case of steady state formulated model and method of lines when unsteady situation was considered. These equations were solved analytically by regular perturbation methods with series improvement technique and numerically using an efﬁcient Runge-Kutta-Fehlberg integration technique coupled with shooting scheme and multidimensional Newton-Raphson root ﬁnding technique. In chapter 1, the key concepts and derivations related to ﬂuid ﬂow, the statement of the problem, the objectives of the study, Signiﬁcance of the study and the methodology are given. In chapter 2, the heat transfer characteristics of Berman ﬂow of water-based nanoﬂuids in a porous channel with Navier slip, viscous dissipation and convective cooling is investigated. Chapter 3 the combined effect of variable viscosity, Brownian motion, thermophoresis and convective cooling i on unsteady ﬂow of nanoﬂuid in a cylindrical pipe with permeable wall are analysed. In chapter 4 we investigates the effects of buoyancy force and variable viscosity on unsteady ﬂow and heat transfer of water-based nanoﬂuid containing Copper and Alumina as nanoparticles. Analysis of unsteady water-based nanoﬂuid ﬂow in a permeable cylindrical pipe through saturated porous medium with the effect of buoyancy-driven force, variable viscosity and Navier slip are examined. Theusefulresultsforthevelocity,temperature,nanoparticlesconcentrationproﬁles, pressure gradient, skinfriction and Nusseltnumber were obtained and discussed quantitatively. Theeffectsofimportantgoverningﬂowparametersontheentireﬂowstructurewereexamined. The conclusion remarks are carried out in chapter 6.