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The proposed planer layer dynamo physical model has real-world applications, especially in the Earth’s liquid core. Thus, in this paper, an attempt is made to understand the finite amplitude convection when there exists a coupling between the Lorentz force and the Coriolis force. In particular, the effect of a horizontally applied magnetic field is studied on the Rayleigh–Bénard convection (RBC) that contains the electrically conducting fluid and rotates about its vertical axis. Free–free boundary conditions are assumed on the geometry. Attention is focused on the nonlinear convective flow behavior during the occurrence of cross rolls which are perpendicular to the applied magnetic field and parallel to the rotation axis. The visualization of cross rolls is achieved using the Fourier analysis of perturbations up to the O(ε8). The relationship of the Nusselt number (Nu) with respect to the Rayleigh number (R), the Ekman number (E), and the Elsasser number (Λ) is investigated. It is observed that E generates a strong damping effect on the flow velocity and on the heat transfer at high rotation rates. Using the heatline concept, it is observed that the temperature within the central regime is enhanced as the Λ increases. The results show that either E decreases or Λ increases, then the heat transfer rate increases.

Nonlinear free convection in an inclined rectangular porous cavity heated from below has been studied using a two-dimensional spectral decomposition. The code uses pseudo-arclength continuation to follow solution curves around fold bifurcations. The evolution with inclination of the pattern of convection is complicated and it relies strongly on both the Darcy–Rayleigh number and the aspect ratio of the cavity. When the inclination is large it is generally true that only one cell appears, and that it has a circulation that is consistent with the direction of the buoyancy forces along the heated and cooled boundaries. However, as the inclination decreases back towards the horizontal, this unicellular pattern evolves, sometimes initially via fold bifurcations, into patterns with different numbers of cells. Such evolutions always conserve the parity of the number of cells (such as one cell becoming three and then five, or two cells becoming four), but bifurcations also arise between patterns with different parities. These phenomena are illustrated using a suitable selection of solution curves that show the dependence of the Nusselt number on the inclination.

This paper presents computational procedures to formulate an algorithm based on the new iterative method (NIM) for the numerical solution of nonlinear convection-diffusion heat equation with constant coefficients. The newly formulated algorithm (NIA) was fully described the relationship between convection and diffusion constants. Three test cases (prototype) are consider to investigate the time distribution profiles in heat equation other study. The algorithm is easy and efficient to solve similar problems in physical sciences.

This paper studies the asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in ℝn. Firstly, the global existence and uniqueness of classical solutions for small initial data are established. Then, we obtain the Lp, 2 ⩽ p ⩽ +℞ decay rate of solutions. The approach is based on detailed analysis of the Green function of the linearized equation with the technique of long wave-short wave decomposition and the Fourier analysis.

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.

In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian radial basis function. According to the proposed scheme, there is no need to remove time-dependent variables during the whole solution process, which leads it to a really meshless method. The suggested meshless method is implemented to the challenging convection–diffusion problems in a direct way with ease. Numerical results show that the proposed meshless method is simple, accurate, stable, easy-to-program and efficient for both linear and nonlinear convection–diffusion equation with different values of Péclet number. To assess the accuracy absolute error, average absolute error and root-mean-square error are used.

A steady two-dimensional nonlinear convective flow of a viscous, incompressible, electrically conducting, and non-Newtonian Jeffrey fluid over an inclined stretching sheet with convective boundary conditions and entropy generation is studied under the influence of transverse magnetic field, electrical conductivity and thermal conductivity. The thermal conductivity and electrical conductivity are temperature dependent functions. The governing continuity, momentum and energy equations are transformed to ordinary differential equations (ODEs) using appropriate similarity variables. The resulting coupled ODEs and the corresponding boundary conditions, are solved numerically using Runge-Kutta fourth order method and shooting technique. The velocity, entropy generation rate, temperature and Bejan distributions are presented graphically and discussed. The numerical values of the skin-friction and Nusselt number are obtained and also discussed for various thermophysical parameters through a Table. Furthermore, a comparison with earlier work done with limiting case was carried out and found to be in excellent agreement.

This paper is concerned with the multidimensional stability of V-shaped traveling fronts for a reaction-diffusion equation with nonlinear convection term in $\mathbb{R}^n$ ($n\geq3$). We consider two cases for initial perturbations: one is that the initial perturbations decay at space infinity and another one is that the initial perturbations do not necessarily decay at space infinity. In the first case, we show that the V-shaped traveling fronts are asymptotically stable. In the second case, we first show that the V-shaped traveling fronts are also asymptotically stable under some further assumptions. At the same time, we also show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which means that the traveling fronts are not asymptotically stable under general bounded perturbations.

In this paper, we discuss the virtual element formulation for the nonlinear convection–diffusion–reaction equation. We consider the Streamline upwind Petrov–Galerkin stabilization to reduce the non...

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.

In this analysis, steady, laminar, and two-dimensional boundary layer flow of nonlinear convection micropolar nanofluid due to a rotating disk is considered. The mathematical formulation for the flow problem has been made. By means of appropriate similarity transformation and dimensionless variables, the governing nonlinear boundary value problems were reduced into coupled high-order nonlinear ordinary differential equations with numerically solved. The equations were calculated using method bvp4c from matlab software for various quantities of main parameters. The influences of different parameters on skin friction coefficients f″0 and G′0, wall duo stress coefficients H1′0, -H2′0, and -H3′0, the Nusselt number -θ′0, and Sherwood number Ω′0, as well as the velocities, temperature, and concentration are analysed and discussed through tables and plotted graphs. The findings indicate that an increase in the values of thermal and solutal nonlinear convection parameters allow to increase the value of velocities f′η and Gη near surface of the disk and reduce at far away from the disk as well as thermal and solutal Grashof numbers tolerate to increase in the value of radial velocity f′η near surface of the disk.

In this paper we have investigated the effect of throughflow on thermal convection in a viscoelastic fluid saturated porous media. The governing equations are modelled in the presence of throughflow. These equations are made dimensionless and the obtained nonlinear problem solved numerically. There are two types of throughflow effects on thermal instability inflow and outflow investigated by finite amplitude analysis. This finite amplitude equation is obtained using the complex Ginzburg-Landau amplitude equation (CGLE) for a weak nonlinear oscillatory convection. The heat transport analysis is given by complex Ginzburg-Landau amplitude equation (CGLE). The numerical results indicate that due to the non-uniform throughflow there is instability at the bottom plate and influence the heat transfer in the system. The vertical throughflow is having both stable and unstable modes depending on flow direction. The nature of viscoelastic fluid is having both effects either stabilize or destabilize. Further, it is found that the nonlinear throughflow effects have dual role on heat transport. The solutions of the present problem are obtained numerically by using Runge-Kutta fourth order method.

An implicit difference scheme with the truncation of order 2 − α ( 0 α 1 ) for time and order 2 for space is considered for the one-dimensional time-fractional Burgers equations. The L 1 -discretization formula of the fractional derivative in the Caputo sense is employed. The second-order spatial derivative is approximated by means of the three-point centered formula and the nonlinear convection term is discretized by the Galerkin method based on piecewise linear test functions. The stability and convergence in the L ∞ norm are proved by the energy method. Meanwhile, a novel iterative algorithm is proposed and implemented to solve the nonlinear systems. Numerical experiment shows that the results are consistent with our theoretical analysis, and the comparison between the proposed iterative algorithm and the existing methods shows the efficiency of our method.

Purpose The purpose of this paper is to study entropy generation in magneto-Jeffrey nanomaterial flow by impermeable moving boundary. Adopted nanomaterial model accounts Brownian and thermophoretic diffusions. Modeling is arranged for thermal radiation, nonlinear convection and viscous dissipation. In addition, the concept of Arrhenius activation energy associated with chemical reaction are introduced for description of mass transportation. Design/methodology/approach Homotopy algorithms are used to compute the system of ordinary differential equations. Findings The afore-stated analysis clearly notes that simultaneous aspects of activation energy and entropy generation are not yet investigated. Therefore, the intention here is to consider such effects to formulate and investigate the magneto-Jeffrey nanoliquid flow by impermeable moving surface. Originality/value As per the authors’ knowledge, no such work has yet been published in the literature.

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.

In this article, the polynomial based differential quadrature method is used to develop a numerical scheme for solving convection–diffusion–reaction model with a general reaction term. The ...

The studies conducted in the recent past reveals that the non-Newtonian are extensively applied in several engineering applications. The atypical Oldroyd-B fluid, a specific sub-category of non-Newtonian fluids, with fractional derivative constitutive equations, is very expedient to determine the approximation of many dilute polymer liquids. Since very few studies regarding the numerical solution of the aforesaid model are conducted, so the literature that can be referred to in this regard is scarce. The current article investigates the unsteady magneto-hydrodynamic flow of irregular Oldroyd-B fluid with a modified thermal flux restricted between two infinite parallel plates. Here, it is assumed that the thermal conductivity of the fluid is variable, and the impact of body forces like gravity is accordingly analyzed in terms of non-linear convection. The linear acceleration of the lower permeable plate in its plane prompts the flow. Further, we have investigated the heat transfer in the flow field through a modified fractional thermal gradient and internal heat source. The temperature gradient accelerates with time and exists among the flow boundaries. In order to determine the approximate solution unified with finite difference approximation for Caputo fractional time derivatives, we have utilized the standard Galerkin finite element method. Moreover, we have conducted a convergence analysis of the suggested numerical scheme and offered some valid error approximations. In the non-integer viscoelastic model, the local number and coefficient of skin friction are also deliberated. We have also performed some upright numerical simulations to highlight the ascendency of characteristic flow parameters of velocity and temperature fields in the proposed scheme. Here, we have analyzed that the resistive force increases by 40%, corresponding to an increment in α ranging from 0 to 0.4. Further, the heat transfer rate is diminish by 10.94% against an increase in variable thermal conductivity while it is enhanced by 37.78% corresponding to increased in Pr.

In this paper, we analyze the blow-up rates and uniqueness of entire large solutions to the equation $\Delta u=a(x)f(u)+ \mu b(x) |\nabla u|^{q}$ , $x\in \mathbb{R}^{N}$ ( $N\geq 3$ ), where $\mu > 0$ , $q > 0$ and $a, b\in \mathrm {C}^{\alpha }_{\mathrm{loc}}(\mathbb{R}^{N})$ ( $\alpha \in (0, 1)$ ). The weight a is nonnegative, b is able to change sign in $\mathbb{R}^{N}$ , and $f\in C^{1}[0, \infty )$ is positive and nondecreasing on $(0, \infty )$ and rapidly or regularly varying at infinity. Additionally, we investigate the uniqueness of entire large solutions.

In this paper, we consider the free boundary problem of a reaction diffusion equation with nonlinear convection term in one dimensional space. Our study contains three parts: in the first part we establish the existence and uniqueness of global solution, in the second part we obtain the spreading–vanishing dichotomy, and in third part, we obtain some estimations of the asymptotic speed of free boundaries when spreading happens.

In this article, a two-level meshless local Petrov Galerkin method (MLPG) is proposed to analyze nonlinear convection–diffusion equation based on the radial basis function (RBF) collocation method....

The simultaneous evaluation of heat/mass transference procures momentous significance in the polymer industry and engineering activities. Extensive utilization of such aspects includes propylene flares, heat exchangers, energy transfiguration in chilling towers, and amputation of post fortuitous heat in nuclear reactors. 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 for. Relevant transformations are exerted to achieve non-linear differential systems that are solved through the homotopy scheme. Influences of divers factors are exhibited via graphical benchmark.

An investigation is carried out to observe the impacts of non-linear convection and induced magnetic field in the flow of viscous fluid over a porous plate under the influence of chemical reaction and heat source/sink. The plate is subjected to a regular free stream velocity as well as a suction velocity. The subjected non-linear problem is non-dimensionalized and analytic solutions are presented via perturbation method. The graphs are plotted to analyze the effect of relevant parameters on velocity, induced magnetic field, heat and mass transfer fields as well as friction factor, current density, Nusselt and Sherwood numbers. It is established that nonlinear convection aspect is destructive for thermal field and its layer thickness. The magnetic field effect enhances the thermal field while it reduces the velocity field. Also, the nonlinear effect subsides heat transfer rate significantly.

In this article, we propose a meshless local Petrov Galerkin (MLPG) method based on least square radial basis function partition of unity method (LS-RBF-PUM), which is applied to the nonlinear conv...

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...

The inverse coefficient problem for the nonlinear convection-diffusion-reaction equation is considered. A velocity vector and a mass-transfer coefficient are considered as the unknown coefficients and are recovered with the help of the additional information about the boundary value problem’s solution. The inverse coefficient problem is reduced to a two-parameter problem of multiplicative control, the solvability of which is proved in a general form. For a cubic reaction coefficient the local stability estimates of the control problem’s solutions are obtained regarding to a rather small perturbation of either the cost functional or the specified functions of the boundary value problem.

This paper considers the problem of estimating the permeability in a nonlinear convection-diffusion equation. To overcome the large calculation burden of conventional methods, we apply an adaptive multigrid conjugate gradient method to solve this inverse problem. This new method combines the multigrid multiscale idea with the conjugate gradient method, and adopts the necessary condition that the optimum solution should be the fixed point of the multigrid inversion method. Some numerical results verify that the proposed method both dramatically reduces the required computations and improves the inversion quality.

This paper is concerned with the large time behavior of solutions to the initial value problem for the damped wave equations with nonlinear convection in one-dimensional whole space. In 2007, Ueda and Kawashima showed that the solution tends to a self similar solution of the Burgers equation. However, they did not mention that their decay estimate is optimal or not. Under this situation, the aim of this paper was to find out the sharp decay estimate by studying the second asymptotic profile of solutions. The explicit representation formula and the decay estimates of the solution for the linearized equation including the lower order term play crucial roles in our analysis.

Nonlinear thermal convection in heat and mass transfer mechanism of dissipating Jeffrey liquid is investigated. The impact of cross diffusion and convective conditions are also accounted. Before integrating pertinent partial differential equations; a set similarity variables are employed to reduce them into multidegree ordinary differential equations. The validation process comprised a comparison with existing data, reaching an excellent agreement. Later, the influence of distinct physical parameters on diverse flow characteristics are comprehensively discussed and analyzed. It is established that the nonlinear convection is favourable for the escalation of the thickness of momentum boundary layer. Further, the convective conditions are used as controlling constraints.

By using Karamata regular variation theory and upper and lower solution method, we investigate the existence and the global asymptotic behavior of large solutions to a class of semilinear elliptic equations with nonlinear convection terms. In our study, the weight and nonlinearity are controlled by some regularly varying functions or rapid functions, which is very different from the conditions of previous contexts. Our results largely extend the previous works, and prove that the nonlinear convection terms do not affect the global asymptotic behavior of classical solutions when the index of the convection terms change in a certain range.

The solvability of the boundary value and extremum problems for the convection–diffusion–reaction equation in which the reaction coefficient depends nonlinearly on the concentration of substances is proven. The role of the control in the extremum problem is played by the boundary function in the Dirichlet condition. For a particular reaction coefficient in the extremum problem, the optimality system and estimates of the local stability of its solution to small perturbations of the quality functional and one of specified functions is established.

We propose a weak Galerkin (WG) finite element method for solving one-dimensional nonlinear convection–diffusion problems. Based on a weak form, the semi-discrete WG finite element scheme is established and analyzed. We prove the stability of the semi-discrete solution and derive the optimal order error estimate in the discrete $$H^1$$ -norm and $$L^2$$ -norm, respectively. Numerical experiment is conducted to confirm the theoretical results.

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for a general nonlinear convection-diffusion equation (NCDE) and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the present DUGKS through some classic convection-diffusion equations, and we find that the numerical results are in good agreement with analytical solutions and that the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, the DUGKS can also adopt the nonuniform mesh. Besides, we perform some comparisons among the DUGKS, the finite-volume lattice Boltzmann model (FV-LBM), the single-relaxation-time lattice Boltzmann model (SLBM), and the multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the present DUGKS is more accurate than the FV-LBM, more stable than the SLBM, and almost has the same accuracy as the MRT-LBM. Moreover, the use of nonuniform mesh may make the DUGKS model more flexible.

We consider an identification problem for a stationary nonlinear convection–diffusion–reaction equation in which the reaction coefficient depends nonlinearly on the concentration of the substance. This problem is reduced to an inverse extremal problem by an optimization method. The solvability of the boundary value problem and the extremal problem is proved. In the case that the reaction coefficient is quadratic, when the equation acquires cubic nonlinearity, we deduce an optimality system. Analyzing it, we establish some estimates of the local stability of solutions to the extremal problem under small perturbations both of the quality functional and the given velocity vector which occurs multiplicatively in the convection–diffusion–reaction equation.

We discuss qualitative behavior of the solutions for the nonlinear parabolic equation which modeling nonlinear convection equation with absorption. This model represents the movement of growing population that is ruled by convection process. In this paper, we concentrate on proving the existence of traveling wave solutions for the nonlinear convection-reaction equations. In addition, we consider the model when the speed of advective wave may breakdown and the problem has a shock wave solution. The mathematical interesting of the waves comes from the behaviors of singular differential equation and discussing the stability of the solution.

In this paper, we obtain BV estimates and L 1 stability of solutions to a radiating gas model with nonlinear radiative inhomogeneity by using Lax-Friedrichs' scheme when a modified C-F-L (Courant-Friedrichs-Levy) condition is satisfied. Our result is a natural extension to that of the radiating gas model with linear radiative inhomogeneity so that it provides an understanding on the balance between nonlinear convection and nonlinear radiative inhomogeneity. The method for case of linear radiative inhomogeneity to obtain the key estimate on uniform bound does not work for the case of nonlinear radiative inhomogeneity. The difficulty is overcome by employing a simple but effective monotonic technic.