Soret and Dufour effects on convective instabilities in binary nanofluids for absorption application

Thermodiffusion (Soret effect) and diffusionthermo (Dufour effect) effects on convective instabilities in nanofluids have been theoretically investigated. Thermodiffusion implies that mass diffusion is induced by thermal gradient, which is so-called the Soret effect. Diffusionthermo implies that heat transfer is induced by concentration gradient, which is so-called the Dufour effect. By using the linear stability theory under one-fluid model, a characteristic dimensionless parameter was newly obtained. From the instability analysis with given conditions, it is found that the convective motion in nanofluids sets in easily as the Soret and Dufour effects and the initial concentration of nanoparticles increase.     

Unsteady forced and free convection flow with mass‐transfer and chemical reaction past an infinite vertical porous plate with oscillating plate temperature

Abstract

An approximate analysis of a two‐dimensional unsteady flow of chemically reacting gases is presented under the following conditions: (1) Constant suction at the plate, (2) the plate temperature is oscillating about a non‐zero constant mean, (3) the uniform free‐stream velocity, (4) presence of foreign mass with negligible Soret‐Dufour effects, (5) first‐order chemical reaction, and (6) small amplitude. Solutions to the mean velocity, the mean temperature, the transient velocity, the transient temperature, the amplitude and phase of the skin‐friction and the rate of heat transfer are derived. It is observed that due to the presence of a chemical reaction, the mean skin‐friction decreases but the mean rate of heat transfer increases.     

Numerical study of Soret and Dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with variable heat fluxes embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. The buoyancy induced boundary layer adjacent to a vertical surface is analyzed using a non-Darcy flow model. The parameters for inertia, buoyancy ratio, exponent of heat flux, position and diffusion have been examined. The governing differential equations of continuity, momentum, energy and concentration are transformed into a set of coupled equations and solved using similarity analysis with numerical technique. Results show the velocity, temperature and concentration profiles related to local Nusselt and Sherwood numbers at different magnitude of Soret and Dufour numbers.     

Effects of mass transfer and heat sources on the flow past an accelerated infinite vertical plate

An exact solution of the flow of an incompressible viscous fluid past an accelerated vertical infinite plate is carried out on taking into account the presence of foreign mass and temperature dependent heat source. Solutions are derived for the velocity profile, skin-friction. It is observed that the skin-friction increases with an increase in the Schmidt number Sc, heat source parameter S, but decreases with increasing the Grashof number G and the buoyancy force parameter N. The velocity profiles become of oscillatory nature when the heat source parameter S increases.     

Finite element analysis of combined heat and mass transfer in hydromagnetic micropolar flow along a stretching sheet

This paper presents a finite element solution of the problem of heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching sheet. The transformed equations for the flow regime are solved numerically by using finite element method. The effect of important parameters namely magnetic field parameter, material parameter, Eckert number and Schmidt number over velocity, microrotation, temperature and concentration functions has been studied. It has been observed that the magnetic field parameter has the effect of reducing the velocity and increasing the microrotation, temperature and concentration while the micropolar parameter has the opposite effect on these functions except temperature function. Temperature increases with the increase in Eckert number and concentration decreases with the increase in Schmidt number.     

Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective flow and mass transfer over an accelerating surface with a heat source in the presence of suction and blowing in the case of variable viscosity

Summary. An analysis has been carried out to obtain the thermal-diffusion and the diffusion-thermo effects on the mixed free-forced convective and mass transfer steady laminar boundary-layer flow over an accelerating surface with a heat source in the presence of suction and blowing. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which is solved numerically by applying the shooting method. The results for an impermeable accelerating surface are discussed. The effects of the variable viscosity parameter _r, the thermal diffusion parameter Sr, the diffusion-thermo parameter Df, suction or blowing parameter m, heat flux parameter s and Schmidt number Sc have been examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The effects of varying these parameters are studied in the case of a surface with prescribed wall temperature and a surface with prescribed wall heat flux.     

Mixed convection of micropolar fluids along a vertical wavy surface

Summary This paper presents numerical results for the steady-state mixed convection in micropolar fluids along a vertical wavy surface. The problem has been formulated by a simple trnasposition theorem, and the spline alternating-direction implicit method has been applied to solve the governing momentum, angular momentum and energy equations. The influence of the micropolar parameters (R and ), the amplitude-wave length ratio and the Gr/Re² number on the skin-friction coefficient and Nusselt number have been studied. Results demonstrate that the skin friction coefficient and local Nusselt number consist of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases but the skin friction increases. In addition, when the spin gradient viscosity parameter () increases, the heat transfer rate and the skin friction decreases. However, the heat transfer rate of a micropolar fluid is smaller than a Newtonian fluid, but the skin friction of a micropolar fluid is larger than a Newtonian fluid under all circumstances.     

Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate

Summary The forced convective heat and mass transfer along a semi-infinite vertical flat plate is investigated for non–Newtonian power law fluids in the presence of a strong nonuniform magnetic field, and the Hall currents are taken into account. The similarity solutions are obtained using transformations group theory. These are the only symmetry transformations admitted by the field equations. The application of one-parameter groups reduces the number of independent variables by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. Furthermore the similarity equations are solved numerically by using a fourth-order Runge-Kutta scheme with the shooting method. Numerical results for the velocity profiles, the temperature profiles and the concentration profiles are presented graphically for various values of the power-law viscosity index n, generalized Schmidt number Sc, generalized Prandtl number Pr, the magnetic parameter M and the Hall parameter m.     

Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption

The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model. The formulation of the flow model is based on basic universal equations of conservation of momentum, energy and mass. The prescribed flow model is converted to non-dimensional form by using suitable scaling. The obtained transformed equations are solved numerically by using finite difference scheme. For the analysis of above said behavior the computed numerical data for fluid velocity, temperature profile, and mass concentration for several constraints that is mixed convection parameter λ_t, modified mixed convection parameter λ_c, Prandtl number Pr, heat generation/absorption parameter δ, Schmidt number Sc, thermophoresis parameter N_t, and thermophoretic coefficient k are sketched in graphical form. Numerical results for skin friction, heat transfer rate and the mass transfer rate are tabulated for various emerging physical parameters. It is reported that in enhancement in heat, generation boosts up the fluid temperature at some positions of the surface of the sphere. As heat absorption parameter is decreased temperature field increases at position X = π/4 on the other hand, no alteration at other considered circumferential positions is noticed.     

Effects of suction on heat and mass transfer along a moving vertical surface in the presence of chemical reaction

Heat and mass transfer effects on a continuously moving vertical surface with chemical reaction of first order is considered. The velocity and concentration profiles are studied for different parameters like Schmidt number, Prandtl number and Chemical reaction parameter. It is observed that the velocity and concentration increases during generative reaction and decreases in destructive reaction.     

Meshless local Petrov-Galerkin analysis of free convection of nanofluid in a cavity with wavy side walls

The problem of laminar natural convection of Al₂O₃-water nanofluid in a cavity with wavy side walls has been investigated using the meshless local Petrov-Galerkin method. The considered cavity is a square enclosure having left and right wavy side walls. The left and right vertical wavy walls of the enclosure are maintained at constant temperatures T_h and T_c, respectively, with T_h>T_c. The horizontal top and bottom walls of the cavity are kept insulated. To carry out the numerical simulations, the developed governing equations are determined in terms of the stream function-vorticity formulation. The weighting function in the weak formulation of the governing equations is taken as unity, and the field variables are approximated using the MLS interpolation. Capability and adaptability of the proposed meshless technique is verified by comparisons of the obtained results through the present meshless method with those existing in the literature. Two different models proposed in the literature are considered for the effective dynamic viscosity of the nanofluid. Using the developed code, a parametric study is performed incorporating the two viscosity formulas, and the effects of the Rayleigh number and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the wavy enclosure are investigated in each case. The results show that significant differences exist between the rates of heat transfer in the cavity for the two viscosity models employed. At Ra=10³ the average Nusselt number of the hot wall increases with increase in the volume fraction of the nanoparticles for both considered viscosity models. At other Rayleigh numbers (Ra=10⁴, 10⁵, and 10⁶) the average Nusselt number estimated for Brinkman formula increases with increase in volume fraction of the nanoparticles while it decreases for Maiga's correlation.     

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.     

Entropy generation due to natural convection of a nanofluid in a partially open triangular cavity

A numerical analysis of laminar natural convection with entropy generation in a partially heated open triangular cavity filled with a Cu-water nanofluid has been carried out. Mathematical model including partial differential equations and boundary conditions has been solved by using finite difference method. Particular efforts have been focused on the effects of Rayleigh number, nanoparticles volume fraction and position of the local heater on streamlines, isotherms, local entropy generation as well as local and average Nusselt number, average Bejan number, average entropy generation and fluid flow rate. Obtained results have demonstrated that the heat transfer enhancement and fluid flow attenuation with nanoparticles volume fraction, mainly for high values of Rayleigh number.     

Effects of radiation on flow past an impulsively started infinite vertical plate with mass transfer

The effect of radiation on the flow past an impulsively started vertical plate in the presence of mass transfer is analyzed. The fluid is a gray, absorbing-emitting, and nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. A rise of the velocity due to the presence of a foreign mass is observed. An increase in the Schmidt number (Sc < 1) and in the radiation parameter N leads to a decrease in the velocity. The skin friction increases due to the presence of a foreign mass when Sc < 1 and decreases at Sc = 1. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 1, pp. 64–71, January–February, 2006.     

Effect of cross diffusion on double diffusive convection in the presence of horizontal gradients

The effect of cross diffusion namely Soret coefficient and Dufour coefficient on the double diffusive convection in an unbounded vertically stratified two component system with compensating horizontal thermal and solute gradients is investigated in this paper. The conditions for the onset of stationary instability and oscillatory instability are established by the use of normal mode analysis. The effect of various physical parameters on the stability of the system is shown graphically. It is shown that the maximum growth rate of instability, the slope of the wave front and the wave number depend on both Soret and Dufour parameters. We also found the flux ratio corresponding to the maximum growth rate. Some of the known results of the former problems are deduced as special cases.     

Numerical simulation of free convection of MHD non-Newtonian nanofluid within a square wavy enclosure using Meshfree method

Abstract

In this article, flow and heat transfer of nanofluids inside a wavy square enclosure filled with non-Newtonian (shear thinning) nanofluid under magnetic field has been simulated numerically. Single-phase model is used. The governing equations have been solved numerically using element free Galerkin method. The results are obtained for isotherms, streamlines, and average Nusselt number for various values of Hartmann number, Rayleigh number, nanoparticles volume fraction, and power-law index. Here, the main objective is to explore the effect of power-law index, Rayleigh number, Hartmann number, and volume fraction on average Nusselt number. It is found that in the absence of magnetic field, Nusselt number drops on increasing the value of power-law index whereas in the presence of magnetic field, heat transfer rate increases with increase in power-law index. With the increase in Rayleigh number and volume fraction of nanoparticles, the heat transfer rate increase in all cases. This type of problem has a direct application in the coolant systems, solar collector where the structure used is wavy in order to increase the rate of heat flow. Here, EFGM is efficiently applied for simulation due to irregular domain, which creates a novelty in the work.     

Numerical study of an unsteady free convective magnetohydrodynamic flow of a dissipative fluid along a vertical plate subject to a constant heat flux

A new method is presented to solve the transient free convection MHD flow of a dissipative fluid along a semi-infinite vertical plate with mass transfer, the surface of which is exposed to a constant heat flux. The non-linear system of partial differential equations is numerically solved by means of the network simulation method, based on the thermo–electric analogy. This method permits the direct visualisation and evolution of the local and/or integrated transport variables (temperatures, velocities, concentrations and fluxes) at any point or section of the medium. At the same time, the solution for both transient and steady-state problems is obtained, the only requirement being finite-difference schemes for the spatial variable, while its programming does not involve manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The technique is always stable and convergent. Velocity, temperature and concentration profiles, local skin-friction, local Nusselt and local Sherwood numbers are plotted for air. The influence of the viscous dissipation, buoyancy ratio parameter, Schmidt number and magnetic parameter on heat and mass transfer and on the time needed to reach the steady-state are discussed.     

Numerical investigation on the effect of four constant temperature pipes on natural cooling of electronic heat sink by nanofluids: A multifunctional optimization

In the present study, natural-convective heat transfer along with the effects of radiation of aluminum/water nano-fluid between two blades of a heat sink, which is under the impact of a uniform magnetic-field, is studied numerically. The space between two blades of the heat sink is considered as a two-dimensional square enclosure. In the square cavity, there are four pipes with constant temperature T_h with a circular cross section. The RSM method is used to optimize the geometric parameters of the pipes. The results show that the heat transfer rate from the pipes and the irreversibility generation augment and the Bejan number reduces by augmenting the Rayleigh number. The heat transfer intensified 7% and 16% by doubling of the aspect ratio of the pipes at the Rayleigh number of 10³ and 10⁶, respectively. As the distance between constant-temperature pipes intensified, Nusselt number augments. As the horizontal enclosure rotates 90°, i.e., it becomes a vertical enclosure, the heat transfer decreases by 22% and total irreversibility decreases by 21%. The optimum physical conditions of the pipes are is in the diameter of 0.15 and 0.25 of distance from each other to have maximum heat transfer and the minimum irreversibility generation.     

Heat or mass transfer from an open cavity

Summary This paper presents a mathematical model for heat or mass transfer from an open cavity. It is assumed that the Péclet number, based on conditions at the cavity, and the Prandtl number are both large. The model assumes heat- or mass-transfer boundary layers at the rim of the cavity vortex flow. Heat or mass exchange with the surrounding fluid occurs in a free boundary layer which spans the mouth of the cavity. It is shown that the solution depends upon a single parameter only. This parameter is determined by the flow field. For small and large values of matched asymptotic expansions are presented. The model is illustrated for a few simple flows in closed cavities. Etching, clot formation in flowing blood, lubrication and cooling of rough surfaces are mentioned as possible fields of application.     

Unsteady attachment line flow on a flat plate with attached cylinder

The unsteady laminar incompressible boundary-layer attachment-line flow on a flat plate with attached cylinder with heat and mass transfer has been studied when the free stream velocity, mass transfer and surface wall temperature vary arbitrarily with time. The governing partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme. The heat transfer was found to be strongly dependent on the Prandtl number, variation of wall temperature with time and dissipation parameter (for large times). However, the free stream velocity distribution and mass transfer affect both the heat transfer and skin friction.