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Present analysis deals with the impact of nonlinear convection on MHD non-Newtonian fluid flow considering exponentially stretched sheet through porous media. Additionally, the effects of radiation, Joule heating and energy dissipation have been taken into account. The considered flow situation of nonlinear PDEs is transmuted to nonlinear ODEs using similarity analysis. The numerical computations are derived using a fourth-order Runge–Kutta scheme with a shooting technique. Meaningful observations are discussed for velocity and energy profiles. Further, the impact of pertinent parameters considering pseudoplastic fluids (n = 0. 6) and dilatant fluids (n = 1. 3) is briefed through graphs. It is noted that the escalation in the values of the power-law index declines the velocity and energy profile. Higher values of the nonlinear parameter decline the energy profile. [ABSTRACT FROM AUTHOR]

This article investigates the nonlinear convection transport of heat transfer in a nanoparticle laden two-layer flow in a vertical channel under the additional effects of magneto hydrodynamic (MHD) and radiation. Water and compressed air are chosen as the fluids in two-layer flow. This type of flow is commonly seen in the transportation of oil and gas in pipelines, therefore, correct understanding of flow dynamics including convective transport phenomenon, layers interaction, and graphical interpretation of flow variables is important for better designing of equipments. Titanium dioxide (Ti O 2 ) nanoparticles are added into the air to magnify the transport mechanism. The mathematical model incorporating buoyancy, nonlinear convection, MHD, viscous dissipation, and radiation effects is presented in the form of nonlinear Ordinary Differential Equation (ODE's). Then utilizing homotopy analysis method, these interconnected differential equations are resolved. A visual illustration shows how different physical factors affect fluid rate and temperature. Tabulated values of Nusselt number at both walls are presented to discuss the numerical data of convection and found that it decreases toward the left boundary but rises toward the right wall by increasing Eckert number and Prandtl number. The results of this two-layer flow will help in understanding this complex flow which has practical applications in various engineering processes and further enhance the scientific knowledge related to multilayer problems. [ABSTRACT FROM AUTHOR]

Entropy generation analysis combined with hybrid nanofluid flow principles contribute to the development of more efficient drug delivery systems for cancer treatment. By using nanofluids, it is possible to improve the transport and targeted release of therapeutic agents to specific sites in the body, allowing for better control and efficiency in treating cancerous cells. Keeping these important applications in view, in the current analysis, the production of irreversibility and stagnant point hybrid nanofluid flow has been considered on a Riga plate. The impacts of nonlinear convection and solar radiations have also been used in this study. Glycol (C3H8O2) is taken as base fluid, while nanoparticles of copper (Cu) and aluminum oxide (Al2O3) have been mixed in it to obtain a hybrid nanofluid. The leading equations for the study have converted to dimensionless form by employing a set of suitable variables and then have been solved by using an artificial neural network (ANN). In order to evaluate the effectiveness of the least mean square neural network algorithm (LMS-NNA), statistical neural network techniques are employed, encompassing error analysis and curve-fitting graphs. It has been revealed in this work that an upsurge in EMHD Riga plate factor and the Grashof number escalates the velocity distribution for both nanoparticles as well as hybrid nanoparticles and is opposed by augmentation in width factor for electrode/magnet. The increase in the nanoparticle volume fraction from 0.01 to 0.05 escalates the heat transfer rate up to 7.6% in the case of nanofluid with Cu-nanoparticles while this increase is 9.3% using hybrid nanofluid Cu + Al2O3. These results show that HNF are more efficient in improving the HT rate. [ABSTRACT FROM AUTHOR]

The motivation for this comparative examination is to verify and account for the appropriate source of heat energy needed in production industries, and to expunge the contradictions between Fourier's law and the theory of relativity. In heat management such as in engineering systems, the required heat for effective melting, production rate, etc. dictates the appropriate heat generation/injection module to be deployed. However, the material medium of heat transmission can be a hindering factor for a successful convection process, to this, an investigation of the instantaneous heat propagation paradox is required. An assumption of induced flow due to stretching characteristics is made, and an appropriate similarity transformation is deployed for the governing systems. By means of the Galerkin-weighted residual method, numerical solutions to the system of equations are approximated and validated. In a limited case, the solution compares favourably with existing literature, while the novel comparative investigation predicts the dominance of the Temperature-Dependent Heat Source (TDHS) capable of weakening the fluid cohesive force and upsurging the energy rate in short time in contrast to the Space-Dependent Heat Source (SDHS) module. The material relaxation phenomenon indicated that more time will be needed for prosperous/equal heat energy transfer. Further heat transfer enhancement is called for higher discharge of radiation and boosting of thermal conductivity, while TDHS module is strongly recommended in highly required heat systems. [ABSTRACT FROM AUTHOR]

AbstractDue to practical applications, we are motivated in the present study to analyze the effects of nonlinear natural convection in a nanofluid flow past a vertical plate in the presence of a first-order chemical reaction and thermophoresis (the normal flux of the nanoparticles is zero at the boundary). The two-phase model for the nanofluid is also considered. The governing partial differential equations (PDEs) are transformed to ordinary differential equations (ODEs) using similarity transformations. Numerical solutions for the transformed equations are attained by using a Runge-Kutta method with a shooting technique. The effects of the relevant physical parameters on the velocity, the temperature, and the nanoparticle volume fraction are analyzed. Also, the consequences of the parameters on the flow, heat, and mass transport phenomena are observed and analyzed explicitly. The results of this study are interesting and motivating for further investigations on the problem for different situations and with different geometries. [ABSTRACT FROM AUTHOR]

The focus of the study in this article is the bioconvection in a nonlinear mixed convective flow of an Eyring–Powell nanoliquid over a vertical slender cylinder with entropy generation. The two-phase Buongiorno’s model is used to investigate the Brownian motion and thermophoresis mechanisms of nanoparticles. The Boussinesq approximation for the body force term in the equations, which govern the convection flow leads to nonlinear coupled partial differential equations (PDEs). Nonsimilar transformations are considered to handle the equations in the non-dimensional form. Further, the technique of Quasilinearization and the implicit finite difference method are utilized for numerical simulation of the mathematical solution of the problem. The heat transfer rate diminishes by about 75% when the Eckert number rises from −0.5 to 0.5. The microorganism density number is enhanced by about 19% as the bioconvection Lewis number increases from 1 to 2. The skin friction coefficient is higher for the Newtonian fluid as compared to the non-Newtonian Eyring–Powell fluid and it is decreased about 8% when fluid parameter varies from 0 to 0.1. The entropy generation intensifies for higher nanoparticles diffusion and microorganism’s density parameters. An excellent agreement is noticed when the current solutions are compared with the outcomes reported in the existing results. [ABSTRACT FROM AUTHOR]

In the era of nanotechnology and advanced manufacturing, many industrial applications involve the flow control over the rotating disk. Rotating machineries, computer storage devices, dynamic filtration processes, gas turbine engines, bio inspired electro-catalysis processes are a few of them. Considering the wide applications of flow over rotating permeable disks, this paper presents the investigation of flow, temperature and pressure characteristics of water-based titanium oxide nanofluid with temperature dependent properties. The quadratic Boussinesq approximation is considered to incorporate the density variations due to temperature change. The numerical computation is carried out using metaheuristic based hybrid shooting technique. Temperature dependent dynamic viscosity and thermal conductivity models for nanofluid are considered and the numerical results for velocity components, pressure and temperature distributions are investigated. The investigation unveiled reduction in skin friction and heat transfer rate with increasing value of quadratic convection parameter. The suction parameter is found to be very significant in terms of increasing heat transfer rates. An 80% increase in local Nusselt number is observed for a small change in suction parameter from −1 to −1.5. [ABSTRACT FROM AUTHOR]

The thermodynamics modeling of a Reiner–Philippoff‐type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear‐thinning, Newtonian, or shear‐thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature‐ and concentration‐induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral‐based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature‐dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer. [ABSTRACT FROM AUTHOR]

In this study, a Keller box calculation of magnetic nanopolymer coating flow over a circular cylinder in the presence of nonlinear convection is performed. A two-phase nanofluid model (Buongiorno model) is used to model the equations for nanofluid flow and heat and mass transfer. The problem at hand is first formulated in the dimensional form of nonlinear partial differential equations (PDEs) and then transformed into the dimensionless PDEs form by manipulating non-similar variables. The Keller box approach (implicit finite differences) is used for the calculations of the transformed PDEs. The characteristics of critical thermophysical physical parameters on the flow field, viz thermal convection, Brownian motion, Weissenberg number, thermophoresis, magnetic field, heat source/sink, Biot number, buoyancy ration parameter, Eckert number, and mixed convection, are graphically manifested. In addition, the flow control parameters estimate the sheath friction, heat transfer rate, and mass transfer rate in the flow coordinate. A significant increase in the velocity of the Williamson nanofluid is accompanied by an increase in the Biot number, magnetic field, and mixed convection. The isotherms show a higher fluid temperature near the wall in the absence of convection. The Weissenberg number, Biot number, and thermophoresis significantly increase the temperature of the Williamson nanofluid. The density of the streamlines is lowered with a larger buoyancy ratio parameter. The total entropy generation of the Williamson nanofluid is improved by increasing the Brinkman number and the Weissenberg number. [ABSTRACT FROM AUTHOR]

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers. [ABSTRACT FROM AUTHOR]

This 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. [ABSTRACT FROM AUTHOR]

The present study addresses the heat transfer efficiency and entropy production of electrically conducting kerosene-based liquid led by the combined impact of electroosmosis and peristalsis mechanisms. Effects of nonlinear mixed convection heat transfer, temperature-dependent viscosity, radiative heat flux, electric and magnetic fields, porous medium, heat sink/source, viscous dissipation, and Joule heating are presented. The Debye–Huckel linearization approximation is employed in the electrohydrodynamic problem. Mathematical modeling is conducted within the limitations of δ << 1 and Re → 0. Coupled differential equations after implementing a lubrication approach are numerically solved. The essential characteristics of the production of entropy, the factors influencing it, and the characteristics of heat and fluid in relation to various physical parameters are graphically evaluated by assigning them a growing list of numeric values. This analysis reveals that heat transfer enhances by enhancing nonlinear convection and Joule heating parameters. The irreversibility analysis ensures that the minimization of entropy generation is observed when the parameters of viscosity and radiation are held under control. Fluid velocity can be regulated by adjusting the Helmholtz–Smoluchowski velocity and magnetic field strength. [ABSTRACT FROM AUTHOR]

The present work explores the analysis of magnetohydrodynamics nonlinear mixed conv ective nanofluid flow over a vertical slender cylinder in the presence of surface roughness. The application of the present study can be found in the process of coating wires. In fact, during such a process, thin wires in the slender cylinder need to be cooled, and also heat and mass transfer rates need to be controlled through nanofluid and liquid hydrogen to yield better results. By employing nonsimilar transformations, the partial differential equations governing the flow problem are reduced to dimensionless equations. Furthermore, the Quasilinearization technique and implicit finite difference scheme are used to solve the dimensionless governing equations. The novelty of the analysis is the impacts of surface roughness, diffusion of liquid hydrogen, and the presence of nonlinear mixed convective flow over a slender cylinder. The numerical results reveal that the energy transport strength and surface drag coefficient enhance with the roughness parameter values. The nanoparticle volume fraction profile reduces, while nanoparticle Sherwood number enhances with increasing values of velocity ratio parameter. The presence of nanoparticles in the conventional fluid diminishes the energy transfer value significantly for both smooth and rough surfaces. The velocity of the fluid enhances with increasing values of the mixed convection parameter. Due to surface roughness (α ≠ 0), sinusoidal variations of the drag are observed along the length of the cylinder in comparison to smooth surface case (α = 0). The friction between the fluid and the wall rises for a rough surface because pockets of fluid are formed in the cavities due to surface asperities. [ABSTRACT FROM AUTHOR]

The current article investigates the effects of nonlinear mixed convection flow in an upright channel with asymmetric or symmetric heating and cooling conditions, considering the influence of temperature-dependent thermal conductivity. The momentum equation is approximated using the nonlinear Boussinesq approximation in the buoyancy force term. Computational solutions for the dimensionless partial differential equations are obtained through the use of an unconditionally stable and convergent implicit finite difference technique. A regular perturbation series approach is employed to ascertain steady-state solutions, facilitating the assessment of the correctness of the numerical approach. During the numerical computing process, it is observed that the nonlinearity in density variation with temperature, along with the mixed convection parameter and the symmetric or asymmetric heating and cooling of the plates, significantly influences flow generation. It is also noted that in the scenario of asymmetric heating, fluid motion is stronger at the bottom plate, whereas in the case of symmetric heating/cooling settings, the highest velocity is observed in the center of the channel. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem for semi-linear wave equations with structural damping term ν (− Δ) 2 u t , where ν > 0 is a constant. As is now well known, the linear principal part brings both the diffusion phenomenon and the regularity loss of solutions. This implies that, for the nonlinear problems, the choice of solution spaces plays an important role to obtain the global solutions with the sharp decay properties in time. Our main purpose in this paper is to prove the global (in time) existence of solutions for the small data and their decay properties for the supercritical nonlinearities. [ABSTRACT FROM AUTHOR]

The nonlinear convection study on the flow of a dissipative Casson nanofluid through a porous medium of an inclined micro-annular channel is presented. The cylindrical surfaces were conditioned to temperature increase and velocity slip effects. A uniform magnetic field strength was applied perpendicular to the cylinder surface. The heat source and Darcy number influence are explored in the examination of the blood rheological model (Casson) through the annular cylinder. Appropriate dimensionless variables are imposed on the dimensional equations encompassing Casson nanofluid rheology through an annular microchannel. The resulting systems of equations were solved and computed numerically via Chebyshev-based collocation approach. Thus, the solutions of flow distributions, volumetric flow rate, and other flow characteristics were obtained. The result shows that both nonlinear convection parameters decrease the nanoparticle volume fraction, whereas they increase the energy and momentum distributions. Moreover, the volumetric flow rate is upsurged significantly by a wider porous medium, annular gap, a higher Casson parameter, and nonlinear convection influence. [ABSTRACT FROM AUTHOR]

The present problem shares out the influences of convective heating and thermal dispersion on thermally stable stratified power-law fluid flow over the vertical frustum of a cone situated in a non-Darcy porous medium. For the first time, it is considered in both aiding and opposing flow cases as it is readily applicable in realistic, practical situations. The local nonsimilarity approach, along with the spectral local linearization method, is used to analyze the fluid behavior and heat transfer within the boundary layer region. In addition, error analysis and comparison with the existing results are also included to validate the obtained results wherever feasible. It is significant to perceive the existence of flow separation in this study as more gain of the velocity of a power-law fluid is seen for aiding flow case in comparison with the opposing flow case. Also, it is evident from these results that the separation of flow is less in the presence of thermal stratification, but it is more in the absence of thermal stratification. Finally, thermal stratification significantly affects the heat transfer rate of power-law fluids besides delaying the boundary layer separation. [ABSTRACT FROM AUTHOR]

In the existence of an aligned magnetic field over the inclined shrinking/stretching stratified sheet in a non-Darcy porous medium, the two-dimensional boundary layer flow of an upper-convected Maxwell fluid is analyzed. The heat transfer effects are acknowledged by using the nonlinear convection. The system of partial differential equations, which administrates the distinctive properties of flow and heat transfer, is depleted into ordinary differential equations with the use of similarity variables. The governing equations are determined numerically by utilizing the shooting technique. The response of varied implicated parameters on velocity, skin friction, and temperature accounts is inspected graphically and displayed in the table. It is noted that local inertia coefficient is accountable for the reduction in the velocity profile and the aligned magnetic field has the opposite relation for the shrinking and stretching sheet. [ABSTRACT FROM AUTHOR]

This paper investigates the Sakiadis flow of a Al2O3-H2O nanoliquid with consistently scattered dust particles over a vertical plate. To account for the effect of the Brownian movement, the Koo-Kleinstreuer-Li model is considered. In some thermal systems such as reactor safety areas, and solar collectors, combustion works from moderate to high temperature, making the relationship between the temperature and density nonlinear. To consider this temperature-dependent density, the nonlinear Boussinesq estimation is utilized. The present physical structure, which includes energy and momentum equations, is converted into a system of ordinary, coupled, and nonlinear differential conditions through the help of similarity transformations. By using the finite difference code, the subsequent equations have been numerically solved. The impact on the velocity and the thermal profiles of the non-dimensional parameters is visualized through graphs. Both the Nusselt number and friction factor strengthen with a higher nonlinear thermal parameter in the case of nonlinear Boussinesq approximation compared to the linear Boussinesq case. Growing estimations of nonlinear thermal parameter deteriorate the thermal profile but it boosts the velocity profile of both liquid and dust phases. [ABSTRACT FROM AUTHOR]

The study deals with nonlinear convection in a three-layered porous-air-porous enclosure with zero temperature difference at the external impermeable thermally conductive boundaries. The upper and lower porous matrices are internally heated with a uniform energy source. To describe redistribution of heat energy between the top and bottom surfaces of the enclosure, we introduce a relative heat transfer coefficient q r that has the conduction and convection parts. The former part tends to unity in the fully filled porous domain. The symmetry of heat transfer from the inner area towards the outer surfaces breaks down if one adds an intermediate air layer with low thermal conductivity. Two sandwiched systems which have equal depth ratio d but distinct air layer location are considered. In system 1, the air layer is located in the upper unstably stratified half of the enclosure. In system 2, this layer is in the lower stably stratified half. The total value of q r always increases due to penetrative convection. At d = 0.1, local convection in system 1 is easily initiated in contrast to the hard-to-generate large-scale convection in system 2 due to a strong destabilization. The latter most effectively enhances heat transport though the top surface with increasing the supercriticality. • Nonlinear convection in a porous-air-porous enclosure, induced by energy source. • Air layer effect on redistribution of heat energy between top and bottom surfaces. • Comparing a relative heat transfer rate at different air layer locations and depths. • Local convection is easily initiated due to strong destabilization by depth ratio. • Hard-to-generate large-scale convection is more effective in heat transferring. [ABSTRACT FROM AUTHOR]

Flows configured by moving surface holds considerable importance in fluid mechanics. The moving surface finds widespread usages in distinct real-world scenarios, for illustration rubber sheets, hot rolling, plastic drawing, paper manufacturing, glass blowing and wire fabrication. The rate of stretching/cooling during these processes play a vital role in ensuring the production of high-excellence end-products. This attempt features entropy optimized slip flow featuring rate type (Jeffrey) liquid subjected to Cattaneo–Christov (CC) dual diffusion and nonlinear convection aspects. Variable fluid aspects (i.e., thermal conductivity and mass diffusivity) along with thermal source and first order chemical reaction are scrutinized. The problem is formulated by employing fundamental laws of fluid dynamics. The non-linear partial differential equations are transformed into the ordinary ones using suitable transformations. Subsequently, optimal homotopic methodology (OHAM) is employed to achieve computational results. Developed nonlinear problems are determined for velocity, temperature and concentration fields. Bejan number, skin friction and the graphs of entropy generation parameters have been plotted and argued. To validate the problem, the comparison for different parameters has been addressed through Shooting and OHAM techniques. Total residual error is calculated. Main outcomes are presented in conclusions. [ABSTRACT FROM AUTHOR]

The forthright intention of the present investigation is to analyze the up-to-date progress in Jeffrey nanofluid flow past an electromagnetic sheet by utilizing the properties of nonlinear convection, radiation, convective boundary condition, zero mass flux condition and Arrhenius activation energy. The flow equations are transformed by applying appropriate transformations into a pair of self-similarity equations. Further similarity equivalences are numerically solved through Runge–Kutta-based shooting method. Graphs and tables are structured to analyze the behavior of sundry influential variables. The results acquired showed good agreement with the previous notable works. Through this study we observed that improvement in Lorentz force in the positive x-direction strengthens the momentum, which intensifies the transfer of heat energy from the boundary, resulting in reduced fluid temperature. [ABSTRACT FROM AUTHOR]

This investigation focuses on the influence of thermal radiation on the magnetohydrodynamic flow of a Williamson nanofluid over a stretching sheet with chemical reaction. The phenomena at the stretching wall assume convective heat and mass exchange. The novelty of the present study is the thermodynamic analysis in the nonlinear convective flow of a Williamson nanofluid. The resulting set of the differential equations are solved by the homotopy analysis method. We explored the impacts of the emerging parameters on flow, heat, and mass characteristics, including the rate of entropy generation and the Bejan number through graphs, and extensive discussions are provided. The expressions for skin friction, Nusselt and the Sherwood numbers are also analyzed and explored through tables. It is concluded that the rate of mass transfer may be maximized with the variation of the Williamson and chemical reaction parameters. Moreover, the entropy generation rate and the Bejan number are augmented via increasing the Williamson parameter. [ABSTRACT FROM AUTHOR]

By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy‐Oldroyd‐B model, and the fluid and solid phase temperatures are represented using a two‐field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimension‐two points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the effects of nonlinear convection on boundary layer flow of micropolar fluid over an exponentially stretching sheet in presence of exponentially moving free stream. Radiative heat transfer has also been considered. Using similarity transformations the governing partial differential equations are reduced to ordinary differential equations and the nonlinear equations are then solved numerically with the help of shooting technique and Runge-Kutta method. The influences of the various interesting parameters on flow and heat transfer are analyzed and discussed in detail through the tables and plotted graphs. It is found that fluid velocity increases but angular velocity and temperature decrease with an increase in the mixed convection parameter. [ABSTRACT FROM AUTHOR]

Purpose: The nonlinear density thermal/solutal fluctuations in the buoyancy force term cannot be ignored when the temperature/concentration difference between the surface and fluid is large. The purpose of this paper is to investigate the nonlinear density fluctuations across a flowing fluid with heat mass transfer effects on a non-axial rotating plate. Therefore, the impact of nonlinear convection in the flow of Casson fluid over an oscillating plate has been analytically investigated. Design/methodology/approach: The governing equations are modeled with the help of conservation equations of velocity, energy and concentration under the transient-state situation. The dimensional governing equations are non-dimensionalized by utilizing non-dimensional variables. Later, the subsequent non-dimensional problem has been solved analytically using Laplace transform method. Findings: The effects of thermal Grashof number, solute Grashof number, nonlinear convection parameters, Casson fluid parameter, unsteady parameter, Prandtl number as well as Schmidt number on hydrodynamic, thermal and solute characteristics have been quantified. The numeric data for skin friction coefficient, Nusselt number and Sherwood number are presented. It is established the nonlinear convection aspect has a significant influence on heat and mass transport characteristics. Originality/value: The effect of nonlinear convection in the dynamics of Casson fluid past an oscillating plate which is rotating non-axially is investigated for the first time. [ABSTRACT FROM AUTHOR]

The present research focuses on three-dimensional nonlinear convective flow of viscoelastic nanofluid. Here, the flow is generated due to stretching of a impermeable surface. The phenomenon of heat transport is analyzed by considering thermal radiation and prescribed heat flux condition. Nanofluid model comprises of Brownian motion and thermophoresis. An electrically conducting fluid is accounted due to consideration of an applied magnetic field. The dimensionless variables are introduced for the conversion of partial differential equations into sets of ordinary differential systems. The transformed expressions are explored through homotopic algorithm. Behavior of different dimensionless parameters on the non-dimensional velocities, temperature and concentration are scrutinized graphically. The values of skin friction coefficients, Nusselt and Sherwood numbers are also calculated and elaborated. It is visualized that the heat transfer rate increases with Prandtl number and radiation parameter is higher. [ABSTRACT FROM AUTHOR]

An analysis is introduced to investigate the salient features of nonlinear convective flow of thixotropic fluid in the version of Cattaneo-Christov heat flux theory. The stagnation point flow is present. The flow phenomenon is by an impermeable stretching sheet. The energy expression is modeled through the theory of Cattaneo-Christov heat flux. Characteristics of heat transfer phenomenon are described within the frame of variable thermal conductivity. Suitable variables reduced to the nonlinear partial differential expressions to the ordinary differential expressions. Series solutions of resulting systems are acquired within the frame of homotopy theory. Convergence analysis is achieved and suitable values are determined by capturing the so-called ℏ−curves. Graphical results for velocity and temperature are displayed and argued for sundry physical variables. Expression of skin friction coefficient is calculated through numerical values. Higher values of mixed convection parameter, Prandtl number, and thermal relaxation time lead to decay the temperature and layer thickness. [ABSTRACT FROM AUTHOR]

A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic (MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg (RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number. [ABSTRACT FROM AUTHOR]

Main objective of present analysis is to study the magnetohydrodynamic (MHD) nonlinear convective flow of thixotropic nanofluid. Flow is due to nonlinear stretching surface with variable thickness. Nonlinear thermal radiation and heat generation/absorption are utilized in the energy expression. Convective conditions and zero mass flux at sheet are considered. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Appropriate transformations are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been scrutinized through homotopic algorithm. Behavior of various sundry variables on velocity, temperature, nanoparticle concentration, skin friction coefficient and local Nusselt number are displayed through graphs. It is concluded that qualitative behaviors of temperature and thermal layer thickness are similar for radiation and temperature ratio variables. Moreover an enhancement in heat generation/absorption show rise to thermal field. [ABSTRACT FROM AUTHOR]

The present study aims to investigate the thermal radiation heat transfer effect on unsteady magnetohydrodynamic flow of micropolar fluid over a uniformly heated vertical hollow cylinder using Bejan's heat function concept. The normalized conservation equations emerge as a system of time-dependent non-linear coupled partial differential equations. Under appropriate wall and free stream conditions these equations are solved with an efficient unconditionally stable implicit scheme of Crank-Nicolson type. Important thermo-physical parameters featured include the magnetic body force parameter ( M ), Grashof (free convection) parameter ( Gr ), Eringen micropolar material parameter ( K ), Prandtl number ( Pr ), conjugate heat transfer parameter ( P ) and radiative-conductive Rosseland parameter ( N ), are analyzed on the flow-field with ranges 0–3, 10 5 –10 6 , 0–1.2, 0.7–7.0, 0–0.5 and 0–15, respectively. The time-histories of average values of momentum and heat transport coefficients, as well as the steady-state flow variables are presented for selected values of these non-dimensional parameters. With elevation in magnetic parameter or radiation parameter, the time taken for the flow-field variables to attain the time-independent state increases. The dimensionless thermal radiative heat function values are closely correlated with the overall rate of heat transfer on the outer hot cylindrical wall. Bejan's heat flow visualization implies that the thermal radiative heat function contours are compact in the neighbourhood of leading edge of the boundary layer on the outer hot cylindrical wall. Increasing radiation or magnetic parameter values result in an increase in the deviation of heat lines from the hot wall. Also, the heat lines are observed to depart slightly away from the hot wall with greater values of vortex viscosity. Furthermore, the deviations of flow variables from the hot wall for a micropolar fluid are significant compared to the Newtonian fluid (vanishing micropolar vortex viscosity). [ABSTRACT FROM AUTHOR]

In this paper we study the following Cauchy problem: u t = u x x + ( u n ) x , ( x , t ) ∈ R × ( 0 , ∞ ) , u ( x , 0 ) = 0 , x ≠ 0 , where parameter n ≥ 0 . Its nonnegative solution is called singular solution when u ( x , t ) satisfies the equation in the sense of distribution, initial conditions in the classical sense and also u ( x , t ) exhibits a singularity at the origin ( 0 , 0 ) . As we know, the singular solution is called source-type solution if the initial is M δ ( x ) , where δ ( x ) is Dirac measure and constant M > 0 . The solution is called very singular solution if it possesses more singularity than that of source-type solution at the origin. Here we focus on what happens in the interactive effect between the diffusion and convection in a whole physical process. We find critical values n 2 < n 1 < n 0 such that there exists unique source-type solution in the exponent range of 0 < n < n 0 , while there exists no nonnegative singular solution if n ≥ n 0 . Only in the case of n 2 < n < n 1 there exists a very singular solution, but in the case of n ≥ n 1 or n ≤ n 2 there is no solution that exhibits more singular than source-type solution at the origin. Furthermore we describe the short time asymptotic behavior of the singular solutions when such Cauchy problem is solvability for source-type solution or very singular solution. [ABSTRACT FROM AUTHOR]

Main purpose here is to analysis magnetohydrodynamic (MHD) nonlinear convective flow of Jeffrey nanofluid by a nonlinear convectively heated stretching sheet of variable thickness. Nonlinear thermal radiation, heat generation/absorption and chemical reaction are considered. Brownian motion and thermophoresis have been utilized in energy and concentration expressions. Recently suggested condition employing volume fraction of nanoparticle at the surface to be controlled passively rather than actively is utilized. Appropriate variables lead to development of nonlinear ordinary differential systems. Effect of various pertinent variables for velocity, temperature and nanoparticle concentration have been displayed and explored. Skin friction coefficient and local Nusselt number are calculated and addressed. It is revealed that larger values of relaxation and retardation times ratio diminish velocity distribution. Moreover impact of heat generation/absorption on the temperature and heat transfer rate are quite reverse. [ABSTRACT FROM AUTHOR]

Mathematical analysis for magnetohydrodynamic (MHD) nonlinear convective flow of Walter-B nanofluid over a nonlinear stretching sheet with variable thickness is introduced. Heat transfer phenomenon is based through involvement of nonlinear thermal radiation and heat generation/absorption. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Boundary layer approximation is applied to partial differential equations. Governing equations are then converted into ordinary differential equations by invoking appropriate variables. The transformed expressions are explored through homotopic algorithm. Plots for velocity, temperature and concentration fields are presented and their behavior is deliberated for several sets of values of governing variables. Skin friction coefficient and local Nusselt number are inspected through numerical values. It is concluded that viscoelasticity reduces the velocity field while reverse situation is observed due to wall thickness parameter. Thermal field and heat transfer rate are enhanced for temperature ratio parameter. Moreover effect of Brownian motion and thermophoresis parameter are quite reverse for the concentration field. [ABSTRACT FROM AUTHOR]

The present article investigates the magnetohydrodynamic (MHD) three-dimensional nonlinear convective flow of an Oldroyd-B nanofluid over a stretching sheet. Heat transfer analysis is reported in the presence of nonlinear thermal radiation and heat generation/absorption. The effects of Brownian motion and thermophoresis are considered in energy and concentration expressions. Meaningful solutions are established for the velocity, temperature and concentration. It is observed that both components of velocity show opposite behavior for mixed convection parameter, ratio of concentration to thermal buoyancy forces and ratio parameter. Local Nusselt and Sherwood numbers are analyzed for the pertinent parameters. Temperature and heat transfer rate are enhanced for thermal radiation and temperature ratio parameters. It is observed that the impact of Brownian motion on the temperature and nanoparticle concentration is quite reverse. [ABSTRACT FROM AUTHOR]

We investigate the effects of momentum, thermal, and solute slip boundary conditions on nanofluid boundary layer flow along a permeable surface. The conventional no-slip boundary conditions at the surface are replaced by slip boundary conditions. At moderate to high temperatures, the temperature-concentration dependence relation is nonlinear and the Soret effect is significant. The governing partial differential equations are solved numerically. The influence of significant parameters on the fluid properties as well as on the skin friction, local Nusselt number, local Sherwood number, and the local nanoparticle Sherwood number are determined. We show, among other results, that the existence and uniqueness of the solutions depends on the slip parameters, and that the region of existence of the dual solution increases with the slip parameters. [ABSTRACT FROM AUTHOR]

The time-dependent enhanced heat transport and nonlinear thermal buoyancy-driven flow of the MWCNT-MgO/EG hybrid nanofluid at the stagnation-point of the rotating sphere subjected to the thermal jump boundary condition are studied theoretically. The quadratic density-temperature variation is also examined together with the quadratic Rosseland thermal radiation. For realistic modelling, experimental data of MWCNT-MgO/EG viscosity and thermal conductivity are used. The monophasic model and the concept of the boundary layer are used to derive the governing partial differential equations, and then they are handled for self-similar solutions using the Finite Element Method (FEM). The effects of driving parameters are examined using 3D contour and surface plots. The further goal of the study is to optimize the heat transport and shear stress of the flow system by applying the central composite-response surface method (RSM) based on the desirability approach. The hybrid nanoparticles volume fraction (NVF) improves friction factors and heat transport. Thermal buoyancy and Coriolis forces condense the thickness of the thermal layer. Heat transport is greater for quadratic thermal convection/radiation than for linear thermal radiation/convection. By RSM, the maximum heat transport (19.0894), the minimum friction factor in the x-direction (2.2564), and the minimum friction factor in the z direction (0.7333) are simultaneously conquered at the low level of NVF, and mixed convection factor and at a high level of QTR factor. [ABSTRACT FROM AUTHOR]

In this paper, we study the effects of nonlinear convection and thermophoresis in steady boundary layer flow over a vertical impermeable wall in a non-Darcy porous medium. Both the fluid temperature and the solute concentration are assumed to be nonlinear while at the wall, both the temperature and concentration are maintained at a constant value. A similarity transformation was used to obtain a system of nonlinear ordinary dif-ferential equations, which were then solved numerically using the Matlab bvp4c solver. A comparison of the numerical results with previously published results for special cases shows a good agreement. The effects of the nonlinear temperature and concentration pa-rameters on the velocity and heat and mass transfer are shown graphically. A representa-tive sample of the results is presented showing the effects of thermophoresis on the fluid velocity and heat and mass transfer rates. It is found among other results, that the con-centration profiles decreased with increasing values of the thermophoretic parameter. [ABSTRACT FROM AUTHOR]

This paper seeks to analyze the core effects of entropy generation on the peristaltic flow of an incompressible fluid with nonlinear convective heat transfer. The analysis is carried out inside an asymmetric channel with flow subjected to the second order velocity slip conditions. The flow is firstly modeled by the system of partial differential equations (PDEs) and then is simplified using the assumptions of long wavelength and low Reynolds number, in wave frame of reference. Entropy production, its contributing factors and performance of heat and fluid against various parameters is described, discussed, and displayed graphically by assigning an increasing list of numerical values to them. Trapping of the fluid is also portrayed by streamline graphs. Entropy generation is witnessed to be minimized when first order velocity slip and thermal slip parameters are held in check account. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Nagumo equation with nonlinear degenerate diffusion and convection which arises in several problems of population dynamics, chemical reactions and others. A sharp front-type solution with a minimum speed to this model equation is analysed using different methods. One of the methods is to solve the travelling wave equations and compute an exact solution which describes the sharp travelling wavefront. The second method is to solve numerically an initial-moving boundary-value problem for the partial differential equation and obtain an approximation for this sharp front-type solution. [ABSTRACT FROM AUTHOR]

In this paper we consider the extended Fisher/KPP equation with density-dependent diffusion and nonlinear convection. We analyze the traveling wave problem and explicitly find a finite traveling wave solution for this extended equation. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of nonlinear compositional convection in horizontal mushy layers during the solidification of binary alloys. Under a near-eutectic approximation and the limit of large far-field temperature, we determine a number of weakly nonlinear oscillatory solutions, and the stability of these solutions with respect to arbitrary disturbances is then investigated. The present investigation is an extension of the problem of the oscillatory modes of convection, which was investigated by [D.N. Riahi, On nonlinear convection in mushy layers. Part 1. Oscillatory modes of convection, J. Fluid Mech. 467 (2002) 331–359] in the absence of the main permeability parameter and very recently by [P. Guba, M.G. Worster, Nonlinear oscillatory convection in mushy layers, J. Fluid Mech. 553 (2006) 419–443] for two-dimensional cases in the presence of , to include the effects of , over a range of values of the other parameters, and for both two- and three-dimensional motion. It was found, in particular, that the results reported in [D.N. Riahi, On nonlinear convection in mushy layers. Part 1. Oscillatory modes of convection, J. Fluid Mech. 467 (2002) 331–359; P. Guba, M.G. Worster, Nonlinear oscillatory convection in mushy layers, J. Fluid Mech. 553 (2006) 419–443] are recovered if is zero or sufficiently small. In such cases two-dimensional solutions in the form of simple-travelling rolls are mostly the only stable and preferred solutions. However, as in the more realistic cases, if is not sufficiently small, then such solutions are replaced by preferred and stable three-dimensional solutions, which are mostly simple-travelling waves in the form of rectangles, squares or hexagons. [Copyright &y& Elsevier]

Abstract: A numerical study is described of a quasi-geostrophic model for thermal convection in rapidly rotating planetary systems where the effect of Coriolis forces is dynamically predominant. In the quasi-geostrophic convection model, a spherical shell is divided into the three domains: a spherical annulus outside the tangent cylinder touching the equator of the inner sphere, the southern and northern polar regions inside the tangent cylinder. Convection in the rotating spherical annulus is investigated using a quasi-two-dimensional geostrophic approximation. Both linear stability analysis and fully nonlinear simulations are carried out. A new domain decomposition method suitable for massively parallel computers is employed in numerical simulations. It is found that, while the structure of mildly nonlinear flows at , where R denotes the Rayleigh number and is its critical value at the onset of convection, is spatially complicated and irregular, the structure of strongly nonlinear flows at is dominated by an axisymmetric zonal flow that is largely laminar, stable and nearly time-independent, similar to that on giant planets Jupiter and Saturn. We also model the atmospheric circulation of a 51 Pegasus b-type extrasolar planet which is synchronized with its parent star and receives an intensive radiation on its dayside. [Copyright &y& Elsevier]

We report the results of fully three-dimensional numerical simulations of nonlinear convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral no-slip or stress-free sidewalls, stress-free top and bottom, uniformly heated from below, a problem first studied by Davies-Jones and Gilman (1971) and Gilman (1973). A substantial range of the Rayleigh number R ( R c ≤R≤O(100 R c ) ), where R c denotes the critical value at the onset of convection) is considered. It is found that the wall-localized convection mode, unaffected by the velocity boundary condition imposed on the sidewalls, is nonlinearly robust. Both directions of travelling waves, one propagating against the sense of rotation near the outer sidewall and the other propagating in the same sense as the rotation in the vicinity of the inner sidewall, are always present in the nonlinear solutions. In contrast to nonlinear convection in a rotating Bénard layer, neither convection rolls nor the Küpper–Lortz instability can exist in a rotating annular channel because of the effect of the sidewalls. It is the nonlinear interaction between the wall-localized modes and the internal mode that plays an essential role in determining the nonlinear properties of convection in a rotating annular channel. Our studies reveal systematically the various nonlinear phenomena, from steady travelling waves trapped in the vicinities of the sidewalls to convective turbulence exhibiting columnar structure. [ABSTRACT FROM AUTHOR]

The nonlinear stability of the motionless state of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme, for stress-free and rigid-rigid boundary conditions and Schmidt numbers PC greater than Prandtl numbers PT , is studied in the region around the bifurcation point &scriptC;02 = &scriptR;B2 (PT +1)/[PT (p-1)] of linear instability.An improvement of the results in Mulone [11] is found for small values of p = PC/PT and PT. For p suf.ciently large the critical nonlinear Rayleigh number is very close to the linear one (with relative difference less than 1% in the sea water case) [ABSTRACT FROM AUTHOR]

The fluid flow over a yawed cylinder is useful in understanding practical significance for undersea applications, for example, managing transference and/or separation of the boundary layer above submerged blocks and in suppressing recirculating bubbles. The present analysis examines nonlinear mixed convection flow past a moving yawed cylinder with diffusion of liquid hydrogen. The coupled nonlinear control relations and the border restrictions pertinent to the present flow problem are nondimensionalized by using nonsimilar reduction. Further, implicit finite difference schemes and Quasilinearization methods are employed to solve the nondimensional governing equations. Impact of several nondimensional parameters of the analysis on the dimensionless velocity, temperature and species concentration patterns and also on Nusselt number, Sherwood number and friction parameter defined at the cylinder shell is analyzed through numerical results presented in various graphs. Velocity profiles can be enhanced, and the coefficients of friction at the surface can be reduced, for increasing values of velocity ratio parameters along chordwise as well as spanwise directions. Species concentration profile is reduced, while the Sherwood number is enhanced, for growth of the Schmidt number and yaw angles. Furthermore, for an increasing value of yaw angle, skin-friction coefficient in chordwise direction diminishes in opposing buoyancy flow case, whereas the results exhibit the opposite trend in assisting buoyancy flow case. Moreover, very importantly, for increasing magnitude of nonlinear convection characteristic, the liquid velocity and surface friction enhance in spanwise direction. Further, for increasing magnitude of combined convection characteristics, velocity profiles and coefficient of friction at the surface enhance in both spanwise and chordwise directions. Moreover, we have observed that there is no deviation for zero yaw angle in Nusselt number and Sherwood number. [ABSTRACT FROM AUTHOR]

This paper is concerned with traveling curved fronts of bistable reaction–diffusion equations with nonlinear convection in a two-dimensional space. By constructing super- and subsolutions, we establish the existence of traveling curved fronts. Furthermore, we show that the traveling curved front is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

Stretching flows subject to heat/mass transference have implication in contemporary research era and industry because of their diverse demands in chemical systems and engineering. Such demands encompass filaments, paper fabrication, glass fiber and polymer sheets. Owing to such prospective demands, we interpreted the Jeffrey liquid reactive flow under non-linear convection. We scrutinized the transference of heat/mass under generalized Fourier-Fick relations. Thermal conductivity depends on temperature while mass diffusivity is dependent on concentration. Besides, heat source along with first-order chemical reaction aspects are accounted. Relevant transformations are exerted to achieve non-linear differential systems which are solved through homotopy scheme. Influences of significant factors are exhibited via graphical benchmark. [ABSTRACT FROM AUTHOR]