Combined Convection Flow Research Articles

Gyrotactic microorganisms bioconvection in combined convective magnetohydrodynamic Casson nanofluid flow over a vertically surfaced saturated porous media with variable viscosity

AbstractThe current article focuses on mass and thermal transfer analysis of a two‐dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature‐dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters.

MHD quadratic mixed convective Eyring-Powell nanofluid flow with multiple diffusions

In many industrial processes such as metal extrusion, paper manufacture, glass fibre production, metal and polymer extrusion, the process design engineers are concerned with efficient heat and mass transfer near the bounding surfaces of the fluid machineries. The applied magnetic field and nanoparticle additives in the fluid are often employed as control mechanisms for efficient heat and mass transport in the presence of multiple diffusive species. Further, the rheological behaviour of the industrial fluids is non-Newtonian behaviour. In this paper, the main objective is to investigate the magnetohydrodynamic triple diffusive quadratic combined convective Eyring-Powell nanoliquid flow over a moving vertical plate in the presence of diffusing liquid hydrogen and oxygen. The mathematical study of such flows is yet to be reported in the open literature. The present mathematical analysis reveals the fluid flow characteristics in terms of many physical parameters that could serve as process design parameters. The governing nonlinear coupled partial differential equations (NCPDEs) and boundary constraints that model the flow problem are converted into dimensionless equations by utilising non-similar transformations. The quasilinearization of the resulting dimensionless governing equations, followed by their implicit finite difference approximation, leads to a block tri-diagonal system, which is solved using Varga's algorithm. The numerical results for fluid velocity, temperature, species concentration, nanoparticle volume fraction distributions, and corresponding gradients correlate with the various physical parameters graphically. The computations have been performed for several values of physical parameters: quadratic mixed convective parameterγ(0≤γ≤1), thermophoresis parameterNt(0≤Nt≤1), Magnetic field parameter M(0≤M≤1), Eckert number Ec(−0.1≤Ec≤0.1), Lewis number Le(2≤Le≤10), Richardson number Ri(−1≤Ri≤10), Brownian diffusion parameterNb(0≤Nb≤1), Eyring-Powell fluid material parameters α*(0≤α*≤2) and β*(0≤β*≤2). The analysis of the numerical results has shown that the enhancing values of quadratic combine convection parameter enhance the magnitude of surface drag coefficient and heat transport rate. At the same time, it decreases for the Eyring-Powell fluid characteristics compared to that for a Newtonian liquid. Finally, the computed values of the heat transport coefficient in the present study are consistent with the previously published results in the literature.

Insight into the dynamics of micropolar fluid about a vertical cone when nonlinear thermal radiation is significant: The case of triple mixed convection

AbstractThis novel research investigates the nonlinear triple diffusive combined convective micropolar liquid flow past a vertical cone in the presence of nonlinear thermal radiation, cross‐diffusion, and a convective boundary condition. We aim to analyze this present problem using nonsimilar transformations. This report presents the significance of nonlinear mixed convection, energy flux due to the concentration gradient, and mass flux due to the temperature gradient and nonlinear thermal radiation in the dynamics of the fluid subject with micropolar fluid is presented. The differential equations defining the boundary‐layer parameters are then transformed into dimensionless view, taking into account the nonsimilar transformation. Furthermore, the method of quasilinearization and implicit finite difference approximation is used to work out the nondimensional governing equations for the solution. The velocity pattern diminishes, while dimensionless temperature and concentration distributions enhance with growing values of microrotation parameter. Furthermore, species concentrations of the fluid increase with increasing Soret effect values, while opposite results appear for mass transfer rates. Also, drag coefficient enhances for assisting buoyancy flow whilst diminishes for opposing buoyancy flow with increasing values of the microrotation parameter. The microrotation pattern reduces with growing values of the nonsimilarity characteristics. Furthermore, the Prandtl number is displayed on a comparison graph, and the results are very similar.

Numerical study on combined convection heat transfer flow problem in a porous corrugated enclosure

AbstractIn this study, we numerically analyzed the unsteady two‐dimensional combined convection flow problem in a porous‐corrugated enclosure whose upper wall is moving with uniform velocity associated with sinusoidal temperature distribution. The vertical sidewalls of the porous‐corrugated enclosure are kept at constant cold temperature while square‐shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending on the discrete isothermal heating. In this paper, we have used the vorticity‐stream‐function formulation of the Brinkmann‐extended Darcy model to numerically simulate the momentum transfer in a porous‐corrugated enclosure. A transformation‐free higher‐order compact (HOC) scheme is used to discretize the nonlinear coupled transport equations, and an advanced iterative solver, like the hybrid‐bi‐conjugate‐gradient stabilized technique, is used to solve the system of algebraic equations generated from the numerical discretization. The present higher‐order compact scheme is fourth‐order accurate in space coordinates and second‐order accurate in the time variable. The numerically simulated results are analyzed over a range of key parameters, like Darcy number , Reynolds Number , Prandtl number , and with fixed high Grashof number , to study the effects of these leading parameters on the characteristics of heat transfer, fluid flow and isothermal distributions in the porous‐corrugated enclosure. These numerically computed results are presented in the form of streamlines, isotherms, Nusselt number plots, and so forth. Our computed results show numerous flow features which have not been studied previously.

Convective nanofluid flow over a vertical cone with a rough surface

AbstractIn recent literature, the analysis of a combined convective flow over a cone has received a lot of attention. To explore the convection effects of flow over a cone in greater detail, in this investigation, we have considered a cone with a rough surface, which is entirely a new flow problem. Recent studies have shown the influence of roughness on fluid flow over several geometries, but flow over a rough conical surface has not been studied so far. In addition, we have analyzed the effects of nanoparticles, magnetohydrodynamic (MHD), and suction/blowing, which could have significant impacts on characteristics of fluid flow over the cone with a rough surface. Initially, the governing equations, which are partial differential equations with a high degree of nonlinearity, are nondimensionalized through Mangler's transformations. Later, linear equations are obtained via the method of quasilinearization, which is then solved numerically through finite difference approximations. The roughness of the cone's surface has notable effects on fluid flow, that too away from the origin. In fact, the roughness increases the friction at the cone's surface. Furthermore, the magnetic field applied at the wall increases the surface friction. Thus, the combination of roughness and MHD helps delay the boundary layer separation. On the other hand, the suction reduces the temperature of the fluid and increases the energy transport strength, while the thermophoresis parameter exhibits the contrary nature. Therefore, the combined consideration of these two could enhance energy transport strength in several industrial applications.

Dual Solutions in Mixed Convection Flow Along Non-Isothermal Inclined Cylinder Containing Gyrotactic Microorganism

The purpose of this research is to present dual solution for combined free and forced convection flow towards a non-isothermal permeable inclined cylinder containing gyrotactic microorganism. Though several researches were done on dual solutions for mixed convection and also along the vertical cylinder for the numerous engineering applications but very few works have done on dual solutions for mixed convection with gyrotactic microorganisms. Two steps are performed here to carry out numerical calculations. Firstly, the governing partial differential equations are simplified into set of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using bvp4c function from MATLAB. Dual solutions are observed for heat, mass and density of motile microorganism transfer rate and also for velocity, temperature, concentration, and microorganism profile beyond a critical point. The research is reached to excellent argument by comparison in few cases between the results obtained from MATLAB and Maple algorithm. The heat, mass and motile microorganism transfer rate decreases from free to mixed convection regime and then increases to forced convection regime with the influence of different flow control parameters. The results also indicate that dual solutions for different flow profiles exist only in free convection dominated regime.

A computational study of the triple-diffusive nonlinear convective nanoliquid flow over a wedge under convective boundary constraints

The present study is concerned with a triple-diffusive nonlinear (quadratic) combined convective nanoliquid flow at a wedge under the influence of convective boundary constraints and viscous dissipation. There would be many potential applications of this study of which a thermal system, geothermal power plants, aerodynamics, manufacturing of gate disk valves, nuclear power plants are just to name a few. In the wake of these potential applications, the study of fluid flow over the wedge has been found to be innovative and very interesting in the analysis of the influence of combined quadratic convection, viscous dissipation, diffusion of nanoparticles and hydrogen and oxygen in liquid state. A set of nonlinear coupled partial differential equations with boundary constraints constitute the modelled flow problem. Further, these equations are converted into non-dimensional form by employing the non-similar transformations. The equations thus obtained are then solved by utilizing the Quasilinearization technique and implicit finite difference approximation. The findings of the study reveals that the higher values Schmidt number reduce mass diffusivity of liquid oxygen as against liquid hydrogen. As a result, the fluid species' concentration profile varies inversely as increase corresponding surface gradient increases. Enhancing Biot number values enhances the magnitude of energy transfer rate.

Impact of moving walls on combined convection flow and thermal performance in a wavy chamber

The impact of wall movements in different directions on mixed convection flow and thermal performance in a wavy chamber is reported. The wavy wall of the chamber is heated non-uniformly, and the upper wall is kept at a constant cold temperature, while the vertical walls of the chamber are adiabatic. Four different cases, namely Case-1, Case-2, Case-3 and Case-4, are considered on the basis of multi-directional movements of the walls of the chamber. Mathematical model of the flow physics consists of the Navier–Stokes (N-S) equations in streamfunction ( $$\psi$$ ) —vorticity ( $$\zeta$$ ) formulation including the energy transport equations which are solved by higher-order compact (HOC) scheme on curvilinear grids Pandit SK, Chattopadhyay A.(Comput Math Appl 74(6):1414–34 2017) [45]. It is found that the fluid flow and thermal performance are both influenced by the direction of moving lids and the undulations of the wavy bottom surface of the chamber. Optimum thermal performance is noticed when the wavy bottom surface of the chamber is employed with one undulation at low Richardson number (Ri). Moreover, for $$Ri=0.01$$ , Case-2, in which the upper lid is moving in left direction and the left lid is moving in upward direction, gives better heat transfer rate with maximum value of average Nusselt number for one undulation. Furthermore, it is noticed that among all the cases, the cases (Case-2 and Case-4) in which upper lid is moving in left direction produce minimum entropy generation for every undulations of the wavy surface with each of the Ri values. So, on the basis of better heat transfer rate and the minimum entropy generation, Case-2 and Case-4 may be recommended as optimum configurations.

Impact of heat source on combined convection flow inside wavy-walled cavity filled with nanofluids via heatline concept

The appearance of a heat source at the bottom of a cavity against the cold part at the top wavy surface is examined in this work. The heat transportation, velocity of the fluid, and the temperature behaviour toward the mixed convection of nanofluids are obtained from the simulation of the Galerkin finite element technique and the Navier-Stokes equations. The other surfaces are considered adiabatic as well as both sides of the lid-driven cavity. It should be noted that the Grashof number, the volume fraction of alumina-nanoparticles, and the differentially-moving vertical walls are fixed at 105,0.02, the upward (right) and downward (left), respectively. To verify the computational code of derivation, the experimental and theoretical data from other researchers are compared. The results of the non-primitive variables, including the Richardson number, Reynolds number, number of undulations, dimensionless length, and the location of the heat source are compared. The numerical results indicate that larger values of the Richardson number and the Reynolds number enhance the rate of heat transfer. Not only two waves appear at the upper surface, but the heat source located at the centre with optimum height causes the entire cavity to have maximum heat transfer performance. The current problem is solved to benefit the installation of microelectronic cooling of a water-to-air heat exchanger or a pin-fin MHS heat transfer media.

Cross Diffusion and Internal Heat Generation Effects on Mixed Convection of Non-Newtonian Fluids Flow Adjacent to a Vertical VHF/VMF Wedge in Porous Media: the Entire Regime

The problem of cross diffusion (Soret/Dufour) and internal heat generation effects on combined convection flow of non-Newtonian fluids flow over the vertical wedge in a saturated porous medium with the entire regime is solved numerically. The internal heat generation is assumed to be an exponential decaying form. The power law model of Ostwald-de-Waele for non-Newtonian fluids is considered here. The entire regime of the combined convection is included, as the combined convection parameter varies from 0 (pure free convection) to 1 (pure forced convection). The transformed equations are obtained by using a suitable coordinate transformation and then Keller box method (KBM) is utilized to solve the non-similar equations for the variable heat flux and variable mass flux (VHF/VMF) conditions. Comparisons with the previously published article are performed and the good agreement is achieved. The main numerical results for the dimensionless temperature and concentration distributions, the local Nusselt and Sherwood numbers are obtained.

Numerical simulation on mixed magneto-convection in a tilted lid-driven box with sinusoidal heating

An unsteady combined convective flow and energy transfer in an inclined lid-driven square box with sinusoidal boundary temperatures at the vertical sidewalls in the presence of uniform magnetic field is numerically investigated. The horizontal sides of the box are thermally insulated. The governing equations are numerically solved by using finite difference method. The results are discussed for various groupings of the governing parameters, inclination angle, phase deviation, amplitude ratio, Richardson number and Hartmann number. The sinusoidal heating provides a higher energy transfer than a constant thermal distribution while the amplitude ratio can be raised to attain such heat distribution along any sidewall of the box.

Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ([Formula: see text] spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

The Investigation of a Fluid-Solid Interaction Mathematical Model under Combined Convective Jeffrey Flow and Radiation Effect Embedded Newtonian Heating as the Thermal Boundary Condition over a Vertical Stretching Sheet

The investigation on the interaction between solid and fluid under combined convective flow has been carried out mathematically. The Jeffrey fluid model is taken as the fluid phase and the model is being embedded with the dust particles (solid phase). This two-phase model is constructed by introducing the fluid-particles interaction forces in the momentum equations of the fluid and dust phases, respectively. The natural and forced convections together with the aligned magnetic field are considered on the fluid flow. Also, the Newtonian heating as thermal boundary condition is induced on the vertical stretching sheet. In order to reduce the complexity of the model, the governing equations are transformed from partial differential equation into ordinary differential equation via suitable similarity transformation. The solutions are obtained in terms of velocity and temperature profiles for the fluid and particles phases respectively whereby the Keller-box method is utilized to obtain the desired outcomes. The influences of several significant physical parameters are visualized graphically to clarify the flow and heat transfer characteristic for both phases. The investigation found that the fluid’s velocity is affected by the presence of the dust particles which led to decelerate the fluid transference. The present flow model is able to be compared with the single-phase fluid cases if the fluid-particle interaction parameter is ignored.

MHD combined convection flow of non-Newtonian liquid with viscous dissipation and thermophoretic effects

The present article is concerned with combined convection MHD flow of Oldroyd-B liquid past over a stretchable sheet. Mathematical formulation of the problem is designed with the existence of viscous dissipation, radiation, thermophoresis and chemical reaction. With the help of suitable similarity transformation governing PDE’s are modified into nonlinear ODE’s. Graphs are portrayed to mention the variance on the velocity, concentration and temperature distributions. Moreover, Mass and heat transfer rates are illustrated through graphically.

Thermosolutal combined convection in a lid-driven enclosure with time periodic heating and linearly salting

Thermosoutal combined convective flow with mass and energy transport in a lid-driven enclosure box with discrete time periodic heating and linearly varying mass transfer is numerically investigated. The segment of the left wall is heating periodically in time and the right wall is preserved at a lower temperature. The top and bottom walls are thermally insulated. Two different concentrations are imposed along the left and right walls. The mathematical systems are solved by finite volume method. The results are obtained for various values of factors, like, Richardson number, period and amplitude. It is observed that the oscillating frequency of averaged Nusselt number diminishes with raise in the period in the forced and free convection modes. The averaged Sherwood number rises as amplitude raise in the free convection mode. It is also attained that both averaged Sherwood and Nusselt numbers are diminished on raising the Richardson number.

Macrosegregation Formation in an Al\u2013Si Casting Sample with Cross-sectional Change During Directional Solidification

A unidirectional solidification experiment of hypoeutectic Al-7.0 wt% Si alloy against gravity direction in a cylindrical mold with cross-sectional change was made, and the macrosegregation in different parts of the as-solidified sample was investigated (Ghods et al. in J Cryst Growth 441:107–116, 2016; J Cryst Growth 449:134–147, 2016). The current study is to use a two-phase columnar solidification model to analyze the segregation mechanisms as used in this experiment. Following flow phenomena and their contributions to the formation of macrosegregation are simulated and compared: (1) solidification shrinkage-induced feeding flow; (2) thermo-solutal convection; and (3) combined thermo-solutal convection and shrinkage-induced feeding flow. The shrinkage-induced feeding flow leads to an inverse (positive) segregation in the bottom part, and a severe negative segregation in the part below cross-sectional change. Thermo-solutal buoyancy leads to a so-called steepling convection in the main part of the sample (away from the bottom and cross-sectional change), and this kind of flow leads to a positive macrosegregation near the sample surface. The calculations have successfully explained the experimental result of macrosegregation.

Effects of multiple slip on MHD combined convective flow of viscoelastic nanofluid over a stretchy sheet with heat absorption

We explore the impact of MHD combined convective flow of viscoelastic nanofluid over a stretchy sheet with heat absorption & multiple slip conditions. The similarity variables are employed to convert the PDE’s into dimensionless ODE’s and they are solved using homotopy analysis method (HAM). The impact of governing parameters on the velocity, temperature & nanoparticle concentration are analyzed with the help of tables and graphs.

Cross diffusion, radiation and chemical reaction effects on MHD combined convective flow towards a stagnation-point upon vertical plate with heat generation

The impacts of cross diffusion on stagnation point MHD combined convective flow approaching a plate which is upright in a porous surrounding subject to chemical reaction, heat generation and radiation is explored. Relations of similarity are employed for the conversion of flow relations as ordinary differential equations upon the application of relations of similarity, shooting method and Runge-Kutta algorithm are applied to find the solution. An analysis is made upon the graphical depictions on velocity of the liquid, its temperature and its concentration with respect to some physical entities and conclusions drawn. It is noticed that velocity shoots up across the boundary layer with a rise in heat generation, Dufour number and Biot number whereas it reduces for strong chemical reaction. For ascending values of Dufour number, chemical reaction parameter and Biot number, the temperature soars up and as a result, thickness of thermal boundary layer inflates.

Diffusion thermo effects on unsteady MHD free convection flow of a Kuvshinski fluid past a vertical porous plate in slip flow regime

The main purpose of this work is to investigate the diffusion-thermo effects on unsteady combined convection magneto-hydromagnetic boundary layer flow of viscous electrically conducting and chemically reacting fluid over a vertical permeable radiated plate embedded in a highly porous medium. The slip flow regime is applied at the porous interface a uniform magnetic field is applied normal to the fluid flow direction which absorbs the fluid with suction that varies with time. The dimensionless governing equations are solved analytically using two terms harmonic and non-harmonic functions. The expressions for the fields of velocity, temperature and concentration are obtained. For engineering interest we also calculated the physical quantities the skin friction coefficient, Nusselt and Sherwood number are derived. The effects of various physical parameters on the flow quantities are studied through graphs and tables. For the validity, we have checked our results with previously published work and found good agreement with already existing studies.

Hydro-magnetic mixed convection in a lid-driven cavity with partially thermally active walls

A numerical analysis has been made on mixed convection in a lid-driven square cavity when both vertical sidewalls are partially heated and cooled in the presence of uniform magnetic field. Three parallel locations and two dissimilar locations for heating and cooling on left and right sidewalls are considered. The top and bottom walls with the remaining locations free from heating and cooling on both vertical sidewalls are considered to be adiabatic. The governing equations are solved by the finite volume method. The resulting effects on combined convection flow and heat transfer for different heating and cooling locations are exhibited graphically for the variations of the Richardson and Hartmann numbers. The average heat transfer rate enhances in the similar locations than dissimilar locations