Nanofluid Saturated Porous Medium Research Articles

Natural convection boundary layer flow due to gyrotactic microorganisms about a vertical cone in porous media saturated by a nanofluid

The similarity solution for Darcy free convection about an isothermal vertical cone with fixed apex half angle, pointing downward in a nanofluid saturated porous medium, has been made. It is assumed that the medium contains gyrotactic microorganisms along with nanoparticles and the cone is subjected to concentration of nanoparticles and density of motile microorganisms. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. The governing partial differential equations are converted into nonlinear ordinary differential equations using unique similarity transformations. The effects of the governing parameters on the dimensionless quantities such as velocity, temperature, nanoparticle concentration, density of motile microorganisms, local Nusselt, local Sherwood and local density numbers for both nanoparticles, and motile microorganism density are explored. A comprehensive numerical computation is carried out for various values of the parameters that describe the flow characteristics.

Lie Group Analysis on Brownian Motion and Thermophoresis Effect on Free Convective Boundary-Layer Flow on a Vertical Cylinder Embedded in a Nanofluid-Saturated Porous Medium

Natural convective boundary-layer flow of a nanofluid on a heated vertical cylinder embedded in a nanofluid-saturated porous medium is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Lie groups analysis is used to get the similarity transformations, which transform the governing partial differential equations to a system of ordinary differential equations. Two groups of similarity transformations are obtained. Numerical solutions of the resulting ordinary differential systems are obtained and discussed for various values of the governing parameters.

Investigation of Unsteady Mixed Convection Flow near the Stagnation Point of a Heated Vertical Plate embedded in a Nanofluid-Saturated Porous Medium by Self-Similar Technique

This paper aims to study the problem of unsteady mixed convection in a stagnation flow on a heated vertical surface embedded in a nanofluid-saturated porous medium. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The presence of a solid matrix, which exerts first and second resistance parameters, is considered in this study. The self-similar solutions for the system of equations governing the problem are obtained. The resulting system of ordinary differential equations that govern the flow is solved numerically using fourth-fifth order Runge-Kutta with shooting method. Numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as skin friction, Nusselt number and Sherwood number are produced for different values of the influence parameters.

The thermal entrance region in a porous medium saturated by a nanofluid: analysis of the Brinkman's model

The Darcy-Graetz problem for a channel filled by a nanofluid saturated porous medium is studied. The flow is assumed to be fully developed and described through Brinkman's model. For the model of the nanofluid, both thermophoresis and Brownian diffusion are taken into account. After an adiabatic preparation region, a boundary temperature linearly varying with the longitudinal coordinate is prescribed. A study of the thermal behaviour of the nanofluid is performed by solving numerically the fully-elliptic coupled equations, with reference both to the thermal entrance region and to the fully developed region. With reference to the fully developed region the solution has been obtained analytically, while for the thermal entrance region it has been obtained numerically, by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). The analysis shows that, for physically interesting values of the Peclet number, the concentration field depends very weakly on the temperature distribution, for any given value assumed by the Darcy number. Indeed, since the effects of thermophoresis and Brownian diffusion are negligible, the homogeneous model could be employed effectively.

Effect of suction/injection on free convection along a vertical plate in a nanofluid saturated non-Darcy porous medium with internal heat generation

The effect of internal heat generation on free convection along a vertical plate embedded in a nanofluid saturated non-Darcy porous medium in the presence of suction/injection is analyzed. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms by non-dimensional variables. The resulting equations are solved numerically by an accurate, implicit, iterative finite-difference methodology and the obtained results are compared favorably with previously published work. A parametric study is performed to illustrate influence of the temperature exponent, non-Darcy, suction/injection, Brownian motion and thermophoresis parameters on the profiles of the velocity components, temperature and nanoparticle volume fraction. The numerical data for the heat and nanoparticle mass transfer rates have been tabulated for various parametric conditions.

Nonlinear Thermal Darcy Convection in a Nanofluid Saturated Porous Medium Under Gravity Modulation

Nonlinear Thermal Darcy Convection in a Nanofluid Saturated Porous Medium Under Gravity Modulation

Viscous Dissipation and Newtonian Heating Effects on Free Non-Linear Convection in a Nanofluid Saturated Porous Media

The paper provides an analysis of viscous dissipation and free non-linear convection effects on the two dimen- sional boundary layer flow of a viscous incompressible nanofluid through a vertical convectively heated wall. The nanofluid flow model includes the effects of nanoparticle Brownian motion and thermophoresis. The governing non-similar nonlinear differential equations are solved using a local non-similarity technique. The present nanofluid flow model, which has not yet been reported in the literature, finds applications in heat transfer devices where the density temperature relations are complex and the viscosity of the fluid has a significant effect on the heat transfer rate. It is found that the nonlinearity in the density temperature relationship causes an initial acceleration of the nanofluid while reducing the nanofluid temperature and the heat transfer rate at the surface.

Non-Darcy Natural Convection From a Vertical Cylinder Embedded in a Thermally Stratified and Nanofluid-Saturated Porous Media

In recent years, nanofluids have attracted attention as a new generation of heat transfer fluids in building heating, heat exchangers, plants, and automotive cooling applications because of their excellent thermal performance. Various benefits of the application of nanofluids include improved heat transfer, heat transfer system size reduction, minimal clogging, microchannel cooling, and miniaturization of systems. In this paper, a study of steady, laminar, natural convection boundary-layer flow adjacent to a vertical cylinder embedded in a thermally stratified nanofluid-saturated non-Darcy porous medium is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, and a generalized porous media model, which includes inertia and boundary effects, is employed. The cylinder surface is maintained at a constant nanoparticles volume fraction, and the wall temperature is assumed to vary with the vertical distance according to the power law form. The resulting governing equations are nondimensionalized and transformed into a nonsimilar form and then solved by Keller box method. A comparison is made with the available results in the literature, and our results are in very good agreement with the known results. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity, temperature, and volume fraction, as well as local shear stress and local Nusselt and Sherwood numbers, are presented graphically. The salient features of the results are analyzed and discussed. The results indicate that, when the buoyancy ratio or modified Grashof number increases, all of the local shear stress, local Nusselt number, and the local Sherwood number enhance while the opposite behaviors are predicted when the thermophoresis parameter increases. Moreover, increasing the value of the surface curvature parameter leads to increases in all of the local shear stress and the local Nusselt and Sherwood numbers while the opposite behaviors are obtained when either of the thermal stratification parameter or the boundary effect parameter increases.

Mixed convective boundary layer flow over a vertical cylinder embedded in a porous medium saturated with a nanofluid

Purpose – The purpose of this work is to study the mixed convection boundary layer flow past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. Design/methodology/approach – Solutions of the set of non-similarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method. Findings – It was found that the heat transfer rate decreases and mass transfer rates increase as Lewis number increases. The heat and mass transfer rates increase as the buoyancy ration parameter increases. As the thermophoresis parameter Nt increases, the heat transfer rate decreases where as the mass transfer rate increases. As the Brownian parameter Nb increases, the heat transfer rate decreases. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The heat and mass transfer rates increase as the buoyancy ratio number Nr increases. The Brownian motion and thermophoresis of nanoparticles increases the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross-diffusion terms that arise with a binary fluid. Research limitations/implications – The analysis is valid for steady, mixed convection two-dimensional boundary layer flow in a nanofluid-saturated Darcy porous medium. An extension to non-Darcy porous medium is left as a part of future study. Practical implications – The research is applicable for enhancing heat exchanger effectiveness by employing nanofluids. Originality/value – The study is useful to engineers interested in designing heat exchangers, water and atmospheric pollution.

Influence of Viscous Dissipation on Mixed Convection in a Non-Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid-saturated non-Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far-field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite-difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non-dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21083

Natural Convection in Triangular Enclosures Filled with Nanofluid Saturated Porous Media

This work focuses on the numerical modeling of a steady, laminar natural convection flow in a triangular enclosure partially heated from below and with a cold inclined wall filled with Cu-water nanofluid having variable thermal conductivity and viscosity. The problem is formulated in terms of the vortices stream function formulation and the resulting governing equations are solved numerically using an efficient finite difference method. Various results for the streamline and isotherm contours, as well as the local and average Nusselt numbers, are presented for a wide range of Rayleigh numbers and volume fractions of nanoparticles. Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number as the volume fraction of nanoparticles changes. The placement and length of the heat source along the bottom wall is observed to have significant effects on the behavior of the average Nusselt number.

Influence of Viscous Dissipation on Free Convection in a Non-Darcy Porous Medium Saturated with Nanofluid in the Presence of Magnetic Field

The effects of viscous dissipation and magnetic field on free convection heat and mass transfer along a vertical plate embedded in a nanofluid saturated non-Darcy porous medium have been studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless form by non-similarity variables. The resulting system of equations is then solved numerically by an accurate implicit finite-difference method. The numerical results are compared and found to be in good agreement with previously published results for a special case of the present investigation. The effect of the physical parameters on the flow, heat transfer and nanoparticle concentration characteristics of the model is presented through graphs and the salient features are discussed.

Magnetic effect on thermally stratified nanofluid saturated non-Darcy porous medium under convective boundary condition

The flow, heat and nanoparticle mass transfer characteristics in the free convection from a vertical plate in a thermally linearly stratified nanofluid saturated non-Darcy porous medium under convective boundary condition is investigated. In addition, the magnetic field effect under convective boundary condition is incorporated in the nanofluid model. The transformed non-similar non-linear coupled partial differential equations representing the transport of mass, momentum, thermal energy, and the nanoparticles volume fraction are solved numerically by the Blottner [18] scheme, which is modified to accommodate the effect of the convective boundary condition. The accuracy of the numerical results is validated by a quantitative comparison of the heat transfer rates with previously published results for a special case and the results are found to be in good agreement. It is observed that the thermal transport is significantly affected due to the stratification of the medium and it is more significant with varying values of the parameters related to the nanofluid in the medium as well as the Biot number due to the convective boundary condition. The effects of thermal stratification, non-Darcy, convection and magnetic field parameters on the velocity, temperature, nanoparticle volume fraction, heat and nanoparticle mass transfer rates are illustrated graphically.

Double-Diffusive Free Convection Flow Past an Inclined Plate Embedded in a Non-Darcy Porous Medium Saturated with a Nanofluid

In this investigation, we intend to present the influence of the prominent Soret effect on double-diffusive free convection heat and mass transfer in the boundary layer region of a semi-infinite inclined flat plate in a nanofluid saturated non-Darcy porous medium. The transformed boundary layer ordinary differential equations are solved numerically using the shooting and matching technique. Consideration of the nanofluid and the coupled convective process enhanced the number of non-dimensional parameters considerably thereby increasing the complexity of the present problem. A wide range of parameter values are chosen to bring out the effect of Soret parameter on the free convection process with varying angle of inclinations making the wall geometry from vertical to horizontal plate. The effects of angle of inclination and Soret parameter on the flow, heat and mass transfer coefficients are analyzed. The numerical results obtained for the velocity, temperature, volume fraction, and concentration profiles, local wall temperature, local nanoparticle concentration, and local wall concentration reveal interesting phenomenon, and some of these qualitative results are presented through the plots.

Conjugate heat transfer in a porous cavity filled with nanofluids and heated by a triangular thick wall

The conjugate natural convection–conduction heat transfer in a square domain composed of nanofluids filled porous cavity heated by a triangular solid wall is studied under steady-state conditions. The vertical and horizontal walls of the triangular solid wall are kept isothermal and at the same hot temperature Th. The other boundaries surrounding the porous cavity are kept adiabatic except the right vertical wall where it is kept isothermally at the lower temperature Tc. Equations governing the heat transfer in the triangular wall and heat and nanofluid flow, based on the Darcy model, in the nanofluid-saturated porous medium together with the derived relation of the interface temperature are solved numerically using the over-successive relaxation finite-difference method. A temperature independent nanofluids properties model is adopted. Three nanoparticle types dispersed in one base fluid (water) are investigated. The investigated parameters are the nanoparticles volume fraction φ (0–0.2), Rayleigh number Ra (10–1000), solid wall to base-fluid saturated porous medium thermal conductivity ratio Kro (0.44, 1, 23.8), and the triangular wall thickness D (0.1–1). The results are presented in the conventional form; contours of streamlines and isotherms and the local and average Nusselt numbers. At a very low Rayleigh number Ra = 10, a significant enhancement in heat transfer within the porous cavity with φ is observed. Otherwise, the heat transfer may be enhanced or deteriorated with φ depending on the wall thickness D and the Rayleigh number Ra. At high Rayleigh numbers and low conductivity ratios, critical values of D, regardless of φ, are observed and accounted.

Non-Darcy mixed convection from a horizontal plate embedded in a nanofluid saturated porous media

The problem of steady mixed convection boundary-layer flow over an impermeable horizontal flat plate embedded in a porous medium saturated by a nanofluid is numerically studied. The model used for the nanofluid incorporates only the effect of the volume fraction parameter. The surface of the plate is maintained at a constant temperature and a constant nano-particle volume fraction. The resulting governing partial differential equations are transformed into a set of two ordinary (similar) equations, which are solved using the bvp4c function from Matlab. A comparison is made with the available results in the literature, and the present results are in very good agreement with the known results. A representative set of numerical results for the reduced heat transfer from the plate, dimensionless velocity and temperature profiles is graphically and tabularly presented. Also, the salient features of the results are analyzed and discussed.

Nonlinear Two-Dimensional Convection in a Nanofluid Saturated Porous Medium

In this article, we study the linear and nonlinear thermal instability in a horizontal porous medium saturated by a nanofluid. For this, the momentum equation with Brinkman model has been used. Also, it incorporates the effect of Brownian motion along with thermophoresis. The linear stability is based on normal mode technique, and for nonlinear analysis, the truncated Fourier series involving only two terms has been used. The expression of Rayleigh number for linear theory has been derived, and the effects of various parameters on Rayleigh number have been presented graphically. Weak nonlinear theory is used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is investigated and depicted graphically, by solving the finite amplitude equations using a numerical method.