Double-diffusive Mixed Convection Flow Research Articles

Heat Generation/Absorption in MHD Double Diffusive Mixed Convection of Different Nanofluids in a Trapezoidal Enclosure

Numerical simulation of MHD double-diffusive mixed convection flow of different nanofluids in a trapezoidal enclosure is performed with an internal heat generation/absorption source inside the enclosure. The nondimensional momentum, heat and mass equations are solved numerically by using the finite difference method. The present study focused mainly on the increment of the rate of heat and mass transfer using internal heat generation or absorption sources inside a lid-driven trapezoidal cavity. Considering numerous governing parameters (Q = −5 to 5, Ha = 0 to 30, Ri = 0.01 to 100) the flow velosity, temperature and concentration profiles are calculated for various nanofluids. Graphs and numerical tables are utilized to examine how different physical entities affect the distribution of flow, temperature and concentration. It is noted that enhancing values of Ha reduces the mass and heat transfer rate. It is observed that heat generation/absorption significantly affect the heat transfer rate as internal heat generation source increases heat transmission rather than mass transfer. The involvement of heat generation/absorption source significantly affects the heat transfer rate. By considering Al2O3-water nanofluid, the solid volume percentage has an accelerating effect on the Nusselt and Sherwood numbers as compared to the other nanofluids in the study.

Entropy analysis for two-dimensional double-diffusive mixed convective flow of a Williamson nanofluid through a porous medium

The problem of double-diffusive convection is investigated by considering the MHD effect on non-Newtonian Williamson fluid flowing over a porous medium. The nature of fluid flow and the amount of heat and mass transfer are studied by the variation of MHD and porous parameters. The flow equations are coupled having more than one independent variable which can be transformed into a single independent variable by introducing similarity variables and solved numerically with the utilization of builtin MATLAB bvp4c package. The Brownian motion and thermophoresis effects on flow equations are studied graphically and the irreversibility of flow is considered. The presence of the Prandtl number in the momentum equation and its effect on physical parameters are taken into account. The variation of Williamson parameter on velocity, temperature, nanoparticle concentration, and concentration profiles are analyzed. The primary innovation of our research is shown in tables that contrast the acquired outcomes with the earlier conclusions found in the literature. The behavior of energy and concentration profiles are shown through graphs by differing numerical values of physical parameters.

Mixed convection instability in a viscosity stratified flow in a vertical channel

The present study examines the linear instability characteristics of double-diffusive mixed convective flow in a vertical channel with viscosity stratification. The viscosity of the fluid is modeled as an exponential function of temperature and concentration, with an activation energy parameter determining its sensitivity to temperature variation. Three scenarios are considered: buoyancy force due to thermal diffusion only, buoyancy force due to temperature and solute acting in the same direction, and buoyancy force due to temperature and solute acting in opposite directions. A generalized eigenvalue problem is derived and solved numerically for the linear stability analysis via the Chebyshev spectral collocation method. The results indicate that higher values of the activation energy parameter lead to an increased flow stability. Additionally, when both buoyant forces act in opposite directions, the Schmidt number has both stabilizing and destabilizing effects across the range of activation energy parameters, similar to the case of pure thermal diffusion. Furthermore, the solutal-buoyancy-opposed base flow is found to be the most stable, while the solutal-buoyancy-assisted base flow is the least stable. As expected, an increase in the Reynolds number is shown to decrease the critical Rayleigh number.

Double-diffusive stagnation point flow over a vertical surface with thermal radiation: Assisting and opposing flows.

In numerous industrial procedures, the main concern of design engineers is ensuring adequate heat and mass transfer, such as in the heating and cooling practices of solar water heaters, geothermal systems, extrusion of metal, insulation of buildings, electronics, turbines, aerodynamics, electronics, paper manufacturing, and glass fiber production. The unsteady double-diffusive mixed convection flow of boundary layer nanofluids above a vertical region near stagnation point flow is developed and examined here. The Brownian motion and thermophoresis effects are incorporated by using Buongiorno's model. In the thermal energy equations, diffusion of regular and cross types is also used. By the use of the local similarity method along with suitable similarity transformations, nonlinear unsteady partial differential equations are converted to nonlinear ordinary differential equations and are numerically solved by the Keller-Box method. The investigation expresses that these profiles of solute concentration and nanoparticle concentration, temperature, and velocity in their boundary layers, respectively, depending on several parameters. A graphic analysis of all these parameters' possessions on nature's boundary layers is depicted. The highest rate of heat transfer is obtained with negligible thermophoresis effect. Furthermore, it is perceived that an increase in Nc and Nt results in a reduction in the reduced Sherwood number of nanoparticles, whereas addition results in an increase in the Nb number. There is a reverse effect on the temperature field and layer thickness for heat generation. In the wake of the above-mentioned potential applications, the current study of fluid flow has been found to be very interesting and innovative in the analysis of the influence of Brownian motion and thermophoresis effects near stagnation point flow, which will further make revolutions in industrial fields. Moreover, Buongiorno's model predicts the characteristics of double-diffusive fluids in enhancing heat transfers. This investigation has been established as a result of the numerous industrial applications mentioned above.

Numerical Study of Non-Newtonian Fluid in a Cavity with Corrugated Bottom Wall Using Buongiorno’s Mathematical Model

A 2-dimensional computational analysis is carried out for a time dependent double diffusive mixed convection flow using non-Newtonian nanofluid. A square-shaped cavity with a corrugated bottom wall is taken with higher temperature and concentration on the top wall. The physical model under consideration is represented by a set of governing equations and solved using the Galerkin weighted residual method based on Finite Element Analysis. Solutions are done for 4 controlling parameters such as Richardson number (Ri = 0.1 - 15), Lewis number (Le = 0.5 - 3), and thermophoresis parameter (Nt = 0.2 - 0.9), and Brownian motion parameter (Nb = 0.2 - 1.0) at different values of τ. For the aforementioned parameters, heat and mass transfer rates, temperature distributions, velocity distributions, and mass distributions in terms of isotherm, streamlines, and iso-concentration are graphically presented. It has been observed that for higher values of Ri, both Nuav and Shav increased while Le decreased for higher values of Nt at any fixed time. It is worth noting that the considered parameter exhibits consistent behavior after a while. HIGHLIGHTS The numerical analysis of non-Newtonian nanofluid with a corrugated bottom wall and a sliding upward wall is performed using Buongiorno's mathematical model The effect of the Richardson number, Lewis number, Brownian motion, and thermophoresis parameters on different dimensionless time periods is addressed The heat and mass transfer rate is increased as the Richardson number, Lewis number, Brownian motion, and thermophoresis parameters increase in value GRAPHICAL ABSTRACT

Effects of Variable Fluid Properties on Double Diffusive Mixed Convection with Chemical Reaction Over an Accelerating Surface

In this study, we investigate the effect of variable fluid properties such as variable viscosity, porosity, permeability, thermal conductivity, and solutal diffusivity on double-diffusive mixed convective flow over an accelerating surface under the influence of a higher-order chemical reaction. The governing equations of the physical problem involve a coupled nonlinear partial differential equations and which are transformed into a coupled nonlinear ordinary differential equations using a suitable similarity transformation. Numerical computation using shooting technique is adopted to study the physical characteristics of velocity, temperature and concentration for various values of non-dimensional parameters like Prandtl number, Eckert number, buoyancy parameters, viscosity parameter, porous parameter, a ratio of thermal conductivities, a ratio of solutal diffusivities and chemical reaction parameter etc are involved in the problem. The computed numerical results are presented in the graphs to illustrate the details of the flow characteristics and their dependence on physical parameters. Our computed results are compared with earlier works of Seddeek in the absence of a magnetic field and found in good agreement.

Optimization of the effect of Prandtl number, inclination angle, magnetic field, and Richardson number on double-diffusive mixed convection flow in a rectangular domain

The effect of Prandtl number (Pr), inclination of the cavity (γ), magnetic field (Ha), and Richardson number (Ri) on double-diffusive mixed convection is numerically investigated. The study aims to understand and optimize all the selected parameters effect on heat and species transfer and fluid flow. The best combination of the selected parameter and their level for the optimum performance of the cavity is determined by the Taguchi method. The significance of the parameters considered is determined using the analysis of variance (ANOVA) method. The governing equations are solved using FVM based SIMPLE algorithm technique. Contour plots are used to present the numerical results. The combination of the factor levels for the optimum heat and mass transfer rate is found from the Taguchi analysis as Pr = 7.0, Ha = 0, γ = 60°, and Ri = 10. From the numerical analysis, the value of the average Nu and average Sh for the optimum combination is found as 27.35 and 34.79 respectively. From the ANOVA result, it is found that the Pr and γ have 47.74% and 25.49% contribution on average Nu and 47.41% and 25.59% contribution on average Sh respectively.

UNSTEADY MIXED CONVECTION OVER AN EXPONENTIALLY STRETCHING SURFACE: INFLUENCE OF DARCY-FORCHHEIMER POROUS MEDIUM AND CROSS DIFFUSION

This paper deals with the unsteady double-diffusive mixed convection flow over an exponentially permeable vertical stretching surface in the presence of Darcy-Forchheimer, Dufour, and Soret (cross diffusion) effects. The unsteadiness in the flow, temperature, and the species concentration fields are due to a time-dependent free stream velocity as well as an exponentially stretching surface velocity. The boundary layer equations are transformed into nondimensional form and solved numerically using an efficient, implicit finite difference scheme in combination with the quasilinearization technique for various governing physical parameters. Numerical computations are displayed graphically to illustrate the Soret, Dufour, and permeability effects on the velocity, temperature, and species concentration profiles. Numerical results for the skin friction coefficient, heat transfer, and mass transfer rates are also presented. The present results are compared with previously published work and are found to be in excellent agreement.

Effects of dissolved solute on unsteady double-diffusive mixed convective flow of a Buongiorno’s two-component nonhomogeneous nanofluid

PurposeThe purpose of this paper is to numerically study the unsteady double-diffusive mixed convective stagnation-point flow of a water-based nanofluid accompanied with one salt past a vertical flat plate. The effects of Brownian motion and thermophoresis parameters are also introduced through Buongiorno’s two-component nonhomogeneous equilibrium model in the governing equations.Design/methodology/approachIn the present explanation of double-diffusive mixed convective model, there are four boundary layers entitled: velocity, thermal, solutal concentration and nanoparticle concentration. The resulting basic equations are solved numerically via an efficient Runge–Kutta fourth-order method with shooting technique after the governing nonlinear partial differential equations are converted into a system of nonlinear ordinary differential equations by the use of similarity transformations.FindingsTo avail the physical insight of problem, the effects of the mixed convection parameter, unsteadiness parameter and salt/nanoparticle parameters on the boundary layers behavior are investigated. Moreover, four possible types of diffusion problems entitled: double-diffusive nanofluid (DDNF), double-diffusive regular fluid (DDRF), mono-diffusive nanofluid (MDNF) and mono-diffusive regular fluid (MDRF) are considered to analyze and compare them in concepts of heat and mass transfer.Originality/valueThe results demonstrate that, for a regular fluid, without nanoparticle and salt (MDRF), the dimensionless heat transfer rate is smaller than other diffusion cases. As we include nanoparticle and salt (DDNF), the rate of heat transfer increases due to an increase in thermal conductivity and rate of diffusion of salt. Moreover, it is observed that the highest heat transfer rate is obtained for the situation that the thermophoretic effect of nanoparticles is negligible. Besides, the heat transfer rate enhances with the increase in the regular double-diffusive buoyancy parameter of salt.

Double-diffusive mixed convection flow towards a convectively heated stretching sheet with non-linear thermal radiation

Double-diffusive mixed convection flow towards a convectively heated stretching sheet with non-linear thermal radiation

Double-diffusive mixed convection in a lid-driven cavity with non-uniform heating on sidewalls

The effect of sinusoidal heating on double-diffusive mixed convective flow with heat and mass transfer in a lid-driven square cavity is numerically investigated. The horizontal walls of the cavity are adiabatic and impermeable. Sinusoidal boundary temperatures and concentrations are imposed along the left and right sidewalls of the cavity. The governing unsteady equations for continuity, momentum, energy and species transfer are solved using the finite-volume method. The numerical solutions are computed for various parameters such as the Richardson number, amplitude ratio, buoyancy ratio and phase deviation. The obtained results are discussed in detail under different combinations of the pertinent parameters.

Double diffusive mixed convection flow from a vertical exponentially stretching surface in presence of the viscous dissipation

This paper is devoted to obtain non-similar solutions for the effect of viscous dissipation on the steady double diffusive mixed convection flow over a vertical exponentially permeable stretching surface. The non-linear partial differential equations governing the flow, thermal and species concentration fields are written in the non-dimensional form by using suitable group of transformations. The final non-dimensional set of coupled partial differential equations is solved using the implicit finite difference method in combination with the Newton’s linearization technique. The effects of various non-dimensional physical parameters on velocity, temperature and species concentration fields are discussed. The presence of the suction/injection at the surface expedites the mass transfer phenomena. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number and mass transfer rate in terms of Sherwood number shown graphically for various physical parameter involved in the problem. The present results are compared with previously published work, and these comparisons are found to be in excellent agreement.

Unsteady double diffusive mixed convection flow over a vertically stretching sheet in the presence of suction/injection

An unsteady double diffusive mixed convection boundary layer flow over a vertically stretching sheet in the presence of suction/injection is investigated in this paper. The governing partial differential equations are reduced by applying suitable transformations to a set of nonlinear ordinary differential equations, which is solved by the Keller box method. The influence of various flow parameters on the velocity, temperature, and species concentration profiles of the fluid is studied. The effect of some problem parameters on the skin friction coefficient in the presence of suction/injection is considered.

Unsteady Double Diffusive Mixed COnvection Flow over a Vertically Stretching Sheet in the Presence of Suction/Injection

Unsteady Double Diffusive Mixed COnvection Flow over a Vertically Stretching Sheet in the Presence of Suction/Injection

Hydromagnetic double-diffusive mixed convection in trapezoidal enclosure due to uniform and nonuniform heating at the bottom side: Effect of Lewis number

This paper presents unsteady numerical results of double diffusive mixed convection flow in a trapezoidal enclosure with the uniform magnetic field effect applied in negative horizontal direction. At the bottom wall, the uniform and non-uniform heat and mass are applied while the heat and mass absorbed uniformly at the top wall. Other side walls are impermeable and adiabatic. The top wall moves along x-axis direction with a constant velocity. The transport phenomenon of this problem can be expressed by the coupled governing equation derived from the conservation of mass and momentum along with the energy equation for temperature and concentration. The finite element method (FEM) based on Galerkin weighted residual technique is used to compute the numerical result from these governing equations. The numerical computation is carried out for Lewis number (Le=0.1–50) and Richardson’s number (Ri=0.1–100). Computed numerical results of mass, temperature and velocity distribution are expressed graphically as iso-concentration lines, isotherm lines and streamlines respectively. Average Sherwood and Nusselt number values are used to show the mass and heat transfer rate from the heated and concentrated surface of the enclosure. It is found from the analysis that mass transfer strongly depends on Lewis number. Heat and mass transfer for uniformly heated and concentrated bottom wall is larger than the non-uniformly heated and concentrated bottom wall. Finally, a correlation has been done for average Nusselt and Sherwood numbers for both of the cases.

Mixed convection flow over a slender cylinder due to the combined effects of thermal and mass diffusion

This paper deals with the similarity solution of double-diffusive mixed convection flow over a vertical slender cylinder due to the combined effects of thermal and mass diffusion. Local similarity method has been used to transform governing nonlinear partial differential equations into ordinary differential equations. With the help of a set of suitable similarity transformations, the nonlinear coupled partial differential equations governing select phenomena (such as flow, thermal and concentration field) have been reduced to a set of nonlinear coupled ordinary differential equations. Numerical solution of system of nonlinear ordinary differential equations are derived using an implicit finite difference scheme along with quasilinearisation technique. The significant observations of the study are as follows: 1) strong effect of buoyancy parameter λ on the flow and thermal field; 2) strong influence of Prandtl number (Pr) and Sherwood number (Sc) on heat transfer and mass transfer respectively.

Mixed convection flow over a slender cylinder due to the combined effects of thermal and mass diffusion

This paper deals with the similarity solution of double-diffusive mixed convection flow over a vertical slender cylinder due to the combined effects of thermal and mass diffusion. Local similarity method has been used to transform governing nonlinear partial differential equations into ordinary differential equations. With the help of a set of suitable similarity transformations, the nonlinear coupled partial differential equations governing select phenomena (such as flow, thermal and concentration field) have been reduced to a set of nonlinear coupled ordinary differential equations. Numerical solution of system of nonlinear ordinary differential equations are derived using an implicit finite difference scheme along with quasilinearisation technique. The significant observations of the study are as follows: 1) strong effect of buoyancy parameter λ on the flow and thermal field; 2) strong influence of Prandtl number (Pr) and Sherwood number (Sc) on heat transfer and mass transfer respectively.

The Numerical Simulation of Double-Diffusive Mixed Convection Flow in a Lid-Driven Porous Cavity with Magnetohydrodynamic Effect

In this paper, the numerical investigation of double-diffusive mixed convection with magnetohydrodynamic flow in an enclosed cavity is presented. The uniform temperature and concentration are imposed along the vertical walls and the horizontal walls which are considered as insulated. The flow behaviour is analysed for two different conditions. In first case, the top wall moves towards left at a constant velocity (U o), while the other walls remain stationary. In the second case, the top wall moves towards right with constant velocity (U o), while the other walls remain stationary. The convective flux in the transport equations is discretized using finite volume technique with third-order deferred quadratic upwind interpolation for convection kinematics scheme at the inner nodes and the second-order central difference scheme at the outer nodes. The pressure and velocity terms are coupled by SIMPLE algorithm. The present numerical simulation is compared with the reported literature and is found to be in good agreement. The Hartmann number (1 ≤ Ha ≤ 25), Lewis number (1 ≤ Le ≤ 50) and aspect ratio (1 ≤ A ≤ 2) are varied over a wide range to analyse the non-dimensional horizontal (U) and vertical velocities (V), stream line contours, temperature and concentration gradients. The present analysis is carried out at constant Buoyancy ratio (N = 1) and Prandtl (Pr = 0.7), Richardson (Ri = 1.0), Darcy (Da = 1.0) and Reynolds (Re = 100) numbers. The effect of Ha, Le and A on the average Nusselt (Nu) and Sherwood (Sh) numbers is also presented.

Double-Diffusive Mixed Convection in a Porous Open Cavity Filled with a Nanofluid Using Buongiorno’s Model

This work examines the steady double-diffusive mixed convection flow in a porous open cavity filled with a nanofluid using mathematical nanofluid model proposed by Buongiorno. The analysis uses a two-dimensional square cavity of size \(L\) with an inlet of size \(0.2\cdot L\) in the bottom part of the left vertical wall and an outlet of the same size in the upper part of the right vertical wall. The mathematical problem is represented by non-dimensional governing equations along with the corresponding boundary conditions, which are solved numerically using a second-order accurate finite difference method. The developed algorithm has been validated by direct comparisons with previously published papers, and the results have been found to be in good agreement. Particular efforts have been focused on the effects of the key parameters on the fluid flow, heat and mass transfer characteristics. In addition, numerical results for the average Nusselt and Sherwood numbers are presented in tabular forms for various parametric conditions and discussed.

Heat and Mass Transfer Due To Double Diffusive Mixed Convection in a Parallel Plate Reactor in Presence of Chemical Reaction and Heat Generation

The present paper aims to analyze numerically the heat and mass transfer for laminar double-diffusive mixed convection flow in a parallel plate reactor with heat generation and chemical reaction. The reactant fluid enters from the left inlet and exits from the right outlet. All solid walls of the reactor are assumed to be thermodynamically isolated. After entering the reactor, the fluid passes four heated cylinder. Two-dimensional continuity, momentum, energy and concentration equations govern the developed mathematical model. Galerkin finite element method with triangular grid discretization system is used to solve the governing non-dimensional equations. The aim of the investigation is to illustrate the effects of the energy expelled during the reaction, on velocity, the thermal field and concentration of the heat sensitive chemical. Numerical simulations are conducted for different combinations of chemical reaction parameter and heat generation parameter. Results are presented in terms of streamlines, temperature and concentration distributions. The results reveal that the heat and mass transfer rate strongly depend on the mentioned parameter.