Precious Sibanda

University of KwaZulu-Natal, Pietermaritzburg Campus · School of Mathematics, Statistics and Computer Science

n this paper, we numerically solve the equations for hydromagnetic nanofluid flow past semi-infinite parallel plates where thermal radiation and a chemical reaction are assumed to be present and significant. The objective is to give insights on the important mechanisms that influence the flow of an electrically conducting nanofluid between parallel...

In most industrial processes it is of paramount importance to control the heat and mass transfer rates to ensure high-quality products. Several techniques including the use of nanofluids in place of ordinary fluids and in some cases motile microorganisms are some of the recent applications in this endeavour. In some recent studies of bioconvection...

The Cross viscosity model is a generalized non-Newtonian nanofluid model that has widespread engineering and industrial applications like in the synthesis of polymeric solutions, polymeric latex spheres, animal blood, biological fluids, and polyacrylamides. To analyze the micromotion of such nanofluids, a micropolar flow model is introduced. Entrop...

The heat and mass transport with Arrhenius activation energy has countless uses such as in nuclear reactors, the synthesis of chemical compounds, geothermal artificial lakes, and retrieval of thermal lubricants. The focus of this work is the analysis of Arrhenius activation energy and binary chemical reaction in a stagnation point Casson nanofluid...

This paper deals with a detailed investigation of the effects of various metal oxide nanoparticles on unsteady stagnation point flow of a hybrid base fluid impinging on a flat surface. The ‘single-phase’ nanofluid model, i.e., the Tiwari and Das model, is considered for the study. We consider water and ethylene glycol in 1:1 ratio as the base fluid...

A theoretical investigation of the influence of time-dependent rotational modulation on the stability, heat, and mass transfer in a Darcy porous medium with a couple stress fluid is presented. A perturbation technique dependent on the infinitesimal amplitude of the disturbance parameter is used to study the consolidated effects of modulating rotati...

The effect of sinusoidal (trigonometric cosine) and nonsinusoidal (square, sawtooth, and triangular) rotational modulations on triple‐diffusive convection in a Newtonian fluid is studied in this paper. The derived Ginzburg–Landau equation for the stationary mode of convection is used to quantify heat and mass transport. The enhancement of heat and...

The principal aim of this study is to explore the impact of relaxation-retardation viscous dissipation, nonlinear convection, variable chemical reaction, and nonlinear thermal radiation on the three-dimensional rotating flow of an Oldroyd-B nanofluid over an exponentially extended surface. The Buongiorno model that takes into account the Brownian m...

This study discusses the impact of the nonlinear relationship between nonlinear density‐temperature and density‐concentration on a nanofluid flow with Arrhenius activation energy and sinusoidal wall temperature variations. The highly nonlinear partial differential equations that model the nanofluid flow are solved using the bivariate spectral local...

This paper investigates entropy generation in a Casson nanofluid flow past an electromagnetic stretching Riga plate. Entropy generation is a measure of irreversibility factors in thermodynamic processes. It is a common feature in heat transfer studies, and as such, the study includes the effect of viscous dissipation. We solve the model equations u...

We introduce a model that precisely accounts the flow of fluid of Casson nanofluid over a stretched surface with activation energy and analyze entropy generation. The model is an attempt to investigate heat transfer and entropy generation in the laminar boundary layer near a stagnation point. The modified Arrhenius function for activation energy is...

Several studies have been carried out on the squeezing flow of mono‐nanofluids. However, this study investigates numerical and machine learning analyses of entropy generated in an unsteady squeezing flow of a copper–aluminum oxide/water hybrid nanofluid. Numerical analysis and the flow model simulation are done using the hybridization of Chebyshev...

In this work, we introduce and apply the overlapping multi-domain bivariate spectral relaxation method (OMD-BSRM) to scrutinize the unsteady MHD flow of a couple stress fluid over an oscillatory stretching surface with thermophoresis, electric field and Soret effects. The uniform magnetic field and an electric field are considered perpendicular to...

The problem of the numerical analysis of natural convection from a spinning cone with variable wall temperature, viscous dissipation and pressure work effect is studied. The numerical method used is based on the spectral analysis. The method used to solve the system of partial differential equations is the multi-domain bivariate spectral quasi-line...

This communication reports on an innovative study of two-dimensional couple stress fluid 3 with effect of viscosity and conductivity. We proposed a new model based on temperature dependent variable thermal conductivity on kinetic theory. Our model assumes that thermal conductivity is a decreasing function of temperature rather than an increasing fu...

The current study investigates the intrinsic irreversibility phenomenon of a mixed convection and electrically conducting couple stress Casson fluid motion over a thermally stretching sheet. We have considered the combined effect of applied magnetic field, Brownian motion, thermal radiation, permeability, Casson parameter, and the stretching parame...

We investigate the micropolar nanofluid model equations of MHD fluid in attendance of entropy generation on boundary layer over stretching surface and a chemical reaction to be significant. The heat and mass transfer are observed due to solutal and thermal stratification with thermal ration and viscous dissipation. The novel bivariate spectral quas...

An efficient overlapping multi-domain spectral method is presented and used in the analysis of a two-dimensional steady laminar MHD mixed convection flow, heat and mass transfer over a vertical flat plate embedded in a porous medium. The effect of chemical reaction, thermal radiation, heat source/sink and other parameters influencing the flow has b...

The study is concerned with entropy minimization on three-dimensional magnetohydrodynamic Oldroyd-B fluid flow with relaxation–retardation viscous dissipation and a mixed chemical reaction. A numerical solution of the nonlinear transport equations is obtained using an overlapping grid spectral collocation numerical scheme. We investigate strategies...

An efficient overlapping multi-domain bivariate spectral quasilinearization method (OMD-BSQLM) is introduced for non-similar boundary layer equations arising in fluid mechanics. Previously, the multi-domain approach has been applied to either space or time interval but not both. The new method applies the multi-domain technique in both space and ti...

The bivariate spectral quasilinearization method (BSQLM) on overlapping grids is presented and applied in the analysis of unsteady magnetohydrodynamic mixed convection flow of Eyring‐Powell fluid over an oscillatory stretching sheet embedded in a non‐Darcy porous medium with nonlinear radiative heat flux and variable thermophysical properties. The...

This article presents an analytical investigation of the effect of Hall current, magnetic field, and chemical reaction on an unsteady MHD transient free convection heat and mass transfer flow of viscous incompressible, electrically conducting Casson fluid past an infinite vertical cylinder subject to heat source and sink. Closed-form solutions are...

Purpose This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow...

In this study, we analyze the flow and heat transfer in a two-phase non-homogeneous Buongiorno fluid model over a thin needle immersed in a porous medium filled with an Al2O3-water nanofluid. The model takes into account particle Brownian movement and thermophoresis that significantly influence the thermal conductivity and other properties of the n...

In this study, we investigate entropy generation in a Casson nanofluid flow over a moving wedge. The system is subjected to radiation‐conduction interaction while the fluid transport properties are variable. In some earlier studies, fluid transport properties like viscosity and thermal conductivity, if not constant, depended on the fluid temperatur...

This study reports on combined thermal radiation, chemical reaction, and magnetic field effects on entropy generation in an unsteady nanofluid flow past an inclined cylinder using the Buongiorno model. We consider the impact of viscous dissipation, velocity slip conditions, thermal slip conditions, and the Brownian motion. The transport equations g...

In this work, three pseudospectral methods, namely bivariate spectral relaxation method, spectral local linearization, and bivariate spectral quasilinearization method are analyzed for steady nonlinear nonsimilar boundary layer partial differential equations. Their accuracy and general performance are discussed. A system of three nonlinear coupled...

Overlapping multi-domain bivariate spectral quasilinearization method is applied on magnetohydrodynamic mixed convection slip flow over an exponentially decreasing mainstream with convective boundary conditions and nonuniform heat source/sink effects. The method is employed in solving the transformed flow equations. The convergence properties and a...

In this paper, we analyze magnetohydrodynamic bioconvective flow of Casson nanofluid comprising gyrotactic microorganisms from a vertical surface with variable thermo-physical features, nonlinear radiation, chemical reaction, Hall and ion-slip currents. The Casson fluid model incorporates zero nanoparticle mass flux at the boundary along with aspec...

In thermal processes, the choice of the thermofluid plays an essential role in minimizing entropy generation and thereby improving thermal efficiency. In this study, entropy generation in a viscous hybrid nanofluid described by the Eyring‐Powell model is investigated. The model accounts for the effect of the nanoparticle volume fraction and viscous...

Objective In this paper, we present a rheological analysis of suspended single-walled Carbon nanotubes in a Walters' B fluid. Methods We assume that the viscosity varies exponentially as a function of the temperature use the Reynolds model of viscosity for the study. A variable thermal conductivity is also assumed along with buoyancy, magnetic fie...

In this work, we present a new modification to the bivariate spectral collocation method in solving Emden-Fowler equations. The novelty of the modified approach is the use of overlapping grids when applying the Chebyshev spectral collocation method. In the case of nonlinear partial differential equations, the quasilinearisation method is used to li...

Theoretically, micropolar fluids are used in the biomedical investigations. This study analyzes the flow, heat and mass transfer in a magneto-micropolar reactive fluid over a nonlinear stretching sheet in a saturated non-Darcy porous medium. The impact of velocity, thermal and concentration slips with prescribed surface temperature and concentratio...

In this article, a novel approach for solving systems of nonlinear partial differential equations over a large time domain is presented. The method is termed a multidomain bivariate spectral quasilinearization method (MD‐BSQLM). This method makes use of the Legendre‐Gauss‐Lobatto grid points, a linearization technique, and the spectral collocation...

In this article, we use the Buongiorno model to study the three‐dimensional tangent hyperbolic nanofluid flow over a stretched sheet. The study investigates the impact of velocity slip on the flow and heat transfer features in a tangent hyperbolic nanofluid. For a better fit with experimental observations. We assume that the nanoparticle mass flux...

In this study, we investigate the steady, two‐dimensional, incompressible viscous boundary layer flow of an electrically conducting Casson fluid over a horizontal circular cylinder. The cylinder is impermeable and the flow is assumed to be subject to homogeneous–heterogeneous reactions. The homogeneous–heterogeneous reactions are also assumed to ha...

In this study, we considered the three-dimensional flow of a rotating viscous, incompressible electrically conducting nanofluid with oxytactic microorganisms and an insulated plate floating in the fluid. Three scenarios were considered in this study. The first case is when the fluid drags the plate, the second is when the plate drags the fluid and...

We present an analysis of the significance of exponentially varying viscosity and thermal conductivity in the magnetohydrodynamic flow of a tangent hyperbolic fluid. The study assumes the combined impact of viscous dissipation, chemical reaction and variable transport properties on the flow. The model equations are reduced to a system of parabolic...

This paper investigates the magnetohydrodynamic flow, heat and mass transfer characteristics in a silver water nanofluid about a vertical slender cylinder by considering diffusion-thermal, thermo-diffusion, chemical reaction and Hall effects. The nonlinear partial differential equations modelling the flow problem are non-dimensionalized and the ove...

The present article gives an analysis of the impact of Darcy–Forchheimer flow and partial slip along with heat transfer in single-wall carbon nanotube/multi-wall carbon nanotube (SWCNT/MWCNT)-water nanofluid flow over a stretching/shrinking rotating disk. The study considers the heat transfer in nanofluids, using both static and dynamic models, nam...

In this paper, we present a numerical study of three-dimensional tangent hyperbolic Casson-nanofluid flow past a horizontally stretched surface with a magnetic field and double-diffusion convection. Double-diffusion convection in three-dimensional tangent hyperbolic Casson nanofluid flow together with slip coefficients, to the authors’ observation,...

In this paper, we investigate the boundary layer flow of a steady viscous nanofluid with activation energy and a high order chemical reaction. The flow equations are solved to a high degree of accuracy using the spectral quasi-linearization method with residual errors less than 10−08. The changes in the local skin friction coefficient, local Nussel...

Purpose This paper aims to investigate entropy generation in an incompressible magneto-micropolar nanofluid flow over a nonlinear stretching sheet. The flow is subjected to thermal radiation and viscous dissipation. The energy equation is extended by considering the impact of the Joule heating term because of an imposed magnetic field. Design/meth...

New applications of nanofluids that have enhanced thermo-physical properties have spurred new studies into the flow and heat transfer in nanofluids in the last decade. Most reported studies have considered the case where the fluid viscosity and thermal conductivity depend only on the size of nanoparticles. However, experimental data show that these...

An efficient overlapping multi-domain spectral method is presented and used in the analysis of a two-dimensional steady laminar MHD mixed convection flow, heat and mass transfer over a vertical flat plate embedded in a porous medium. The effect of chemical reaction, thermal radiation, heat source/sink and other parameters influencing the flow has b...

In this study, we present a geometrically convergent numerical method for solving multi–dimensional two–sided space–time fractional differential equations. The approach represents the solutions of the differential equations in terms of the shifted Chebyshev polynomials. The expansions are evaluated at the shifted Chebyshev–Gauss–Lobatto nodes. We p...

Many pseudospectral schemes have been developed for time fractional partial differential equations, most of which use the spectral tau method. In this study, we develop an accurate numerical scheme using a combination of Lagrange and Chebyshev polynomials of the first kind for the multi-dimensional fractional Rayleigh problem integrated using the G...

In some recent studies, it has been suggested that non–Newtonian fluid flow can be modeled by a spatially non–local velocity, whose dynamics are described by a fractional derivative. In this study, we use the space fractional constitutive relation to model heat and mass transfer in a nanofluid. We present a numerically accurate algorithm for approx...

This paper presents a formulation for simulating magnetohydrodynamic three-dimensional convective flow and heat transfer in a nanofluid by incorporating the complete viscous dissipation function in the energy equation. A novel feature of this investigation of entropy generation and dual solutions is the use of the spectral quasilinearization method...

Purpose The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in...

We investigate flow in a square cavity filled with a porous medium saturated with a nanofluid and subjected to an applied magnetic field. The cavity walls, except the top, are at rest. The vertical walls of the cavity are adiabatic and bottom wall is kept at a fixed temperature. Flow is generated by the motion of the top wall. The entropy generated...

We investigate the impact of nonlinear thermal radiation and variable transport properties on the two-dimensional flow of an electrically conducting Casson nanofluid containing gyrotactic microorganisms along a moving wedge. In some previous studies, it has been assumed that the fluid viscosity and thermal conductivity are temperature dependent. Ho...

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generati...

Purpose The purpose of this paper is to investigate the dynamical behavior of heat and mass transfer of non-Newtonian nanofluid flow through parallel horizontal sheet with heat-dependent thermal conductivity and magnetic field. The effects of thermophoresis and Brownian motion on the Eyring‒Powell nanofluid heat and concentration are also considere...

In this paper we present a new innovative technique for solving nonlinear systems of partial differential equations with quadratic convergence rate. We demonstrate the use of the method by solving a system of nonlinear differential equations of non-similar boundary layer equations. The model equations describe the problem of magnetohydrodynamic for...

This study deals with the transfer of mass and heat of nanofluid flow over three different geometries of the non‐Darcy permeable vertical cone/wedge/vertical plate. Influence of the Brownian motion and thermophoresis takes place due to the nanofluid. Boundary condition on the temperature is introduced at the surface where the thermal conductivity o...

The continuous generation of entropy leads to exergy destruction which reduces the performance of a physical system. Hence, entropy minimization becomes necessary. New applications of nanofluids due to their enhanced thermo-physical properties has spurred new studies into the heat transfer and entropy generation rate in nanofluids in the last decad...

The optimal design of heating and cooling systems must take into account heat radiation which is a non-linear process. In this study, the mixed convection in a radiative magnetohydrodynamic Eyring-Powell copper-water nanofluid over a stretching cylinder was investigated. The energy balance is modeled, taking into account the non-linear thermal radi...

The purpose of this paper is to consider a two dimensional free convective flow of a nanofluid due to the combined effects of thermal and mass diffusion in the presence of a chemical reaction of first order. The objective of the present investigation is to analyze the free convective flow in the presence of prescribed wall heat flux and mass flux c...

We develop a delay ordinary differential equation model that captures the effects of prophylactic vaccination, reactive vaccination, prophylactic treatment and reactive culling on the spread of foot and mouth disease (FMD) with time delays. Simulation results from the study suggest that increasing time delay while increasing the control strategies...

This paper presents a two-dimensional unsteady laminar boundary layer mixed convection flow heat and mass transfer along a vertical plate filled with Casson nanofluid located in a porous quiescent medium that contains both nanoparticles and gyrotactic microorganisms. This permeable vertical plate is assumed to be moving in the same direction as the...

This study presents the boundary layer flow of a second grade fluid in a rotating reference frame. The model equations are solved numerically using the bivariate spectral quasi-linearization method to obtain the fluid properties. We investigate the effects of measurable quantities such as the rate of rotation, thermal diffusivity, energy dissipatio...

In this paper, we have studied the effects of thermal radiation parameters on an incompressible boundary layer liquid metal (e.g., Mercury) flow over a flat plate in the presence of magnetic field. The governing nonlinear partial differential equations have been transformed using Görtler transformation on coupled non-similar ordinary differential e...

A mathematical model of MHD micropolar-nanofluid flow deformed by a stretchable surface is presented with a homogeneous–heterogeneous reactions given by isothermal cubic autocatalator kinetics and first order kinetics. We assumed the existence of an induced magnetic field. The basic microrotation flow and heat mass transfer nonlinear equations are...

The present study explores the effects of thermal radiation, chemical reaction, viscous dissipation, Soret and Dufour on Marangoni convection over a steady and laminar boundary layer flow. A nanofluid, consisting of copper, silver, and alumina metallic nanoparticles suspended in water, is considered. Similarity transformations are used to solve the...

We study the thermoconvective instability in a rotating ferromagnetic fluid confined between two parallel infinite plates with temperature modulation at the boundaries. We use weakly nonlinear stability theory to analyze the stationary convection in terms of critical Rayleigh numbers. The influence of parameters such as the Taylor number, the ratio...

We present a study of heat and mass transfer for a couple stress nanofluid flow in a magneto-porous medium with thermal radiation and heat generation. The flow is generated by a stretching surface and the temperature and concentration distributions are studied subject to nanoparticle Brownian motion and thermophoresis effects. The nonlinear model e...

In this paper, we studying the entropy generation in Sakiadis nanofluid flowing along a moving plate subject to magnetic field and a Cattaneo-Christov heat flux model that may predict the effects of thermal relaxation time on the boundary layer flow. The nonlinear transport equations are solved using a spectral quasi-linearization method. An analys...