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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]

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]

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]

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]

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]

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]

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]

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]

Here, the nonlinear convective transport of non-Newtonian fluids embedded with dust particles over a stretched surface is investigated. The silent features of non-Newtonian fluid are considered by Casson and Carreau fluid models. The heat transfer mechanism involves the influences of a magnetic dipole, nonlinear radiative heat and non-uniform heat source/sink. The convective condition is also retained at the boundary. The non-linear partial differential equations that model the transport phenomenon was transformed, non-dimensionalized and parameterized. The subsequent boundary value problems were computed numerically for distinct pertinent parameters using Runge–Kutta based shooting techniques. The present results are validated with the existing literature by direct comparison. The heat transfer rate in Casson/Carreau fluid phase is significantly higher than that of dust phase. • Casson parameter β has opposite effects on velocity and temperature profiles. • The nonlinear convection parameter increases the momentum boundary layer thickness. • The dimensionless temperature increases with rise in thermal radiation. • The skin friction coefficient and the local Nusselt number increases by increasing values of λ. [ABSTRACT FROM AUTHOR]