Puneet Rana

Numerical solution for mixed convection boundary layer flow of a nanofluid along an inclined plate embedded in a porous medium

The steady mixed convection boundary layer flow of an incompressible nanofluid along a plate inclined at an angle @a in a porous medium is studied. The resulting nonlinear governing equations with associated boundary conditions are solved using an optimized, robust, extensively validated, variational finite-element method (FEM) and a finite-difference method (FDM) with a local non-similar transformation. The Nusselt number is found to decrease with increasing Brownian motion number (Nb) or thermophoresis number (Nt), whereas it increases with increasing angle @a. In addition, the local Sherwood number is found to increase with a rise in Nt, whereas it is reduced with an increase in Nb and angle @a. The effects of Lewis number, buoyancy ratio, and mixed convection parameter on temperature and concentration distributions are also examined in detail. The present study is of immediate interest in next-generation solar film collectors, heat-exchanger technology, material processing exploiting vertical and inclined surfaces, geothermal energy storage, and all those processes which are greatly affected by a heat-enhancement concept.

Finite element simulation of unsteady magneto-hydrodynamic transport phenomena on a stretching sheet in a rotating nanofluid

This study examines theoretically and computationally the transient magneto-hydrodynamic boundary layer flow and heat transfer in an incompressible rotating nanofluid over a stretching continuous sheet, with a transverse magnetic field applied normal to the sheet plane. The three-dimensional conservation equations for mass, momentum, energy and species (nanoparticle) diffusion, are normalized into a system of two-dimensional dimensionless boundary layer equations, using appropriate scaling transformations. The resulting nanofluid transport model incorporates a Brownian motion parameter, thermophoresis parameter, rotation parameter, unsteady parameter, Prandtl number, Hartmann magnetic parameter and Lewis number, and physically realistic boundary conditions at the sheet surface and in the free stream. The nonlinear two-point boundary value problem is solved using a robust, efficient finite element method based on the variational formulation. A detailed evaluation of the effects of the governing physical parameters on the velocity components, temperature and nanoparticle concentration via graphical plots is conducted. Primary velocity is strongly retarded with increasing Hartmann number and there is also a reduction in secondary velocity magnitude. Both temperature and nanoparticle concentration are positively affected by the Hartmann number. Increasing rotational parameter decreases both primary and secondary velocity, and also depresses temperature and nanoparticle concentration. Unsteadiness parameter is generally found to enhance primary velocity and temperatures but exhibits a varied influence on secondary velocity and nanoparticle concentration. The reduced Nusselt number (wall temperature gradient) is observed to be depressed with both Brownian motion and thermophoresis effects, whereas the contrary behaviour is computed for the reduced Sherwood number (wall mass transfer gradient). The reduced Nusselt number and the Sherwood number also show a steady decrease with increasing rotational parameter. The present finite element method solutions have been validated extensively with the previously published results, demonstrating excellent correlation. The study has important applications in the manufacture and electromagnetic control of complex magnetic nanofluid materials of relevance to biomedical, energy systems and aerospace systems technologies.

Finite element modeling of conjugate mixed convection flow of Al2O3–water nanofluid from an inclined slender hollow cylinder

Steady laminar mixed convection flow and heat transfer characteristics of Al2O3–water nanofluid about a vertical slender hollow cylinder are investigated numerically, under the effect of wall conduction. The transformed, non-dimensional, nonlinear governing equations (obtained with the Boussinesq approximation) are solved, using a robust, extensively validated, Galerkin finite element method for spherical-shaped nanoparticles with volume fraction ranging up to 4%, with associated boundary conditions. Nine-node quadrilateral finite elements are employed. Experimental models for thermal conductivity and viscosity incorporating Brownian motion terms have been taken into consideration. The influence of physical parameters, namely wall conduction parameter, Richardson number (buoyancy parameter) and nanoparticle volume fraction, on velocity profile, temperature profile and on Nusselt number is shown graphically. Excellent validation of the present numerical results has been achieved with earlier published results. Both skin friction coefficient and Nusselt number are enhanced with increasing Richardson number. With increasing inclination angle there is a decrease in average Nusselt number. Furthermore, average Nusselt number and interfacial temperature are both reduced with nanoparticle diameter. The flow is accelerated with increasing Richardson number whereas the bulk temperature is found to be suppressed. The study has important applications in thermal enhancement of solar energy systems.

Rayleigh–Bénard Convection in a Nanofluid Layer Using a Thermal Nonequilibrium Model

In this paper, we study the effect of local thermal non-equilibrium on the linear thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two-temperature model has been used for the effect of local thermal non-equilibrium among the particle and fluid phases. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. We observe that for linear instability, the value of Rayleigh number can be increased by a substantial amount on considering a bottom heavy suspension of nano particles. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series method has been used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is also investigated by solving the finite amplitude equations using a numerical method.

Effect of chemical reaction and viscous dissipation on MHD nanofluid flow over a horizontal cylinder: Analytical solution

An analytical study of the MHD boundary layer flow of electrically conducting nanofluid over a horizontal cylinder with the effects of chemical reaction and viscous dissipation is presented. Similarity transformations have been applied to transform the cylindrical form of the governing equations into the system of coupled ordinary differential equations and then homotopy analysis method has been implemented to solve the system. Homotopy analysis method (HAM) does not contain any small or large parameter like perturbation technique and also provides an easiest approach to ensure the convergence of the series of solution. The effects of chemical reaction parameter, magnetic parameter and other important governing parameters with no flux nanoparticles concentration is carried out to describe important physical quantities.

Dual Solutions in MHD Boundary Layer Nanofluid Flow and Heat Transfer with Heat Source/Sink considering Viscous Dissipation

In this present analysis, the numerical investigation of steady, magneto-hydrodynamic boundary-layer nanofluid past a permeable shrinking sheet has been discussed considering Brownian motion and thermophoresis. The effect of viscous dissipation, heat source/sink and suction/injection are taken into account and controlled by the non-dimensional parameters. After using appropriate similarity transformation, the final system of ordinary differential equation is solved numerically by shooting technique. The dual solutions exist for whereas unique solution is obtained at critical values and solution does not exist for for other fixed parameters. The current study shows that the effect of nonlinear parameter, Hartmann number and heat source/sink on skin friction and rate of heat transfer. The results are validated for the limiting cases.

Mixed Convective Heat Transfer Flow of Nanofluid past a Permeable Vertical Flat Plate with Magnetic Effects: A Finite Element Study

Steady, two dimensional mixed convection laminar boundary layer flow of incompressible nanofluid along a permeable vertical semi-infinite flat plate with magnetic field effects has been investigated numerically. The resulting govering equations (obtained from the boussinesq) with associated boundary conditions are solved, using a robust, extensively validated, Galerkin Finite Element Method for different types of spherical shaped metal oxide nanoparticles with two different ratios of the nanolayer thickness to the original particle radius (0.02 or 0.1). The effects of the parameters governing the problems are discussed and shown graphically. The present study is of immediate interest in next-generation solar film collectors, heat exchangers technology, material processing exploiting vertical surfaces and all those processes which are highly affected with heat transfer.

Unsteady electromagnetic radiative nanofluid stagnation-point flow from a stretching sheet with chemically reactive nanoparticles, Stefan blowing effect and entropy generation

This article investigates the combined influence of nonlinear radiation, Stefan blowing and chemical reactions on unsteady electro-magneto-hydrodynamic stagnation-point flow of a nanofluid from a horizontal stretching sheet. Both electrical and magnetic body forces are considered. In addition, the effects of velocity slip, thermal slip and mass slip are considered at the boundaries. An analytical method named as homotopy analysis method is applied to solve the non-dimensional system of nonlinear partial differential equations which are obtained by applying similarity transformations on governing equations. The effects of emerging parameters such as Stefan blowing parameter, electric parameter and magnetic parameter on the important physical quantities are presented graphically. In addition, an entropy generation analysis is provided in this article for thermal optimization. The flow is observed to be accelerated both with increasing magnetic field and electrical field. Entropy generation number is markedly enhanced with greater magnetic field, electrical field and Reynolds number, whereas it is reduced with increasing chemical reaction parameter.

Unsteady MHD nanofluid flow past a stretching sheet with Stefan blowing effect: HAM solution

The present article concerns an analytical investigation of an unsteady MHD stagnation flow of nanofluid over a stretching sheet with the influence of Stefan blowing and temperature dependent heat source. The conservation equations of mass, momentum, energy and nanoparticles concentration are converted into a dimensionless system of partial differential equations. Homotopy analysis method has been applied to solve this system. The influence of leading parameters is shown graphically.The present article concerns an analytical investigation of an unsteady MHD stagnation flow of nanofluid over a stretching sheet with the influence of Stefan blowing and temperature dependent heat source. The conservation equations of mass, momentum, energy and nanoparticles concentration are converted into a dimensionless system of partial differential equations. Homotopy analysis method has been applied to solve this system. The influence of leading parameters is shown graphically.

Influence of g–jitter on the Rayleigh-Bénard convection in nanofluids with internal heat source

In the present framework, a horizontal nanofluid layer with lower surface temperature comparatively higher than other side, under the influence of internal heat generation has been explored with nonlinear terms. The external control of convective transport phenomena is being affected by time-periodic vertical vibrations (gravity modulation). Utilizing Fourier Series approximations, stability analysis has been performed to obtain the Nusselt number (Nu) as a function of various pertinent parameters (especially Pr, Rn, Le, NA, e and Ω). Moreover, the results are discussed with streamlines and isotherms plots.In the present framework, a horizontal nanofluid layer with lower surface temperature comparatively higher than other side, under the influence of internal heat generation has been explored with nonlinear terms. The external control of convective transport phenomena is being affected by time-periodic vertical vibrations (gravity modulation). Utilizing Fourier Series approximations, stability analysis has been performed to obtain the Nusselt number (Nu) as a function of various pertinent parameters (especially Pr, Rn, Le, NA, e and Ω). Moreover, the results are discussed with streamlines and isotherms plots.