Quasilinearization Method Research Articles

Influence of Slip Parameter, Viscous Dissipation and Joule Heating Effect on Boundary Layer Flow and Heat Transfer Over a Power-Law Stretching Wedge-Shaped Surface with the Correlation Coefficient and Multiple Regressions

The influence of slip parameter, viscous dissipation, and Joule heating parameter on MHD boundary layer nanofluid flow over a permeable wedge-shaped surface was analysed. The PDEs and the associated boundary conditions were transformed to a set of non-similar ODEs and the obtained system of equations was solved numerically with the help of the spectral quasi-linearization method (SQLM) by applying suitable software. This method helps to identify the accuracy and convergence of the present problem. The current numerical results were compared with previously published work and are found to be similar. The fluid velocity, fluid temperature, and nanoparticle concentration within the boundary layer region for various values of the parameters such as the slip effect, magnetic strength, Prandtl number, Lewis number, stretching ratio, viscous dissipation, suction, Brownian motion, Joule heating, heat generation, and thermophoresis are studied. It is observed that the Brownian motion, Joule heating, viscous dissipation, and thermophoresis lead to decreases in the heat and mass transfer rate. The skin friction coefficient enhances with slip, magnetic, permeability, and suction parameters, but reduces with the Brownian motion, wedge angle, and stretching ratio parameters whereas there is no effect of mixed convection, thermophoresis, heat generation parameters, the Prandtl and Eckert number.

Mixed convection flow over a vertical cone saturated porous medium with double dispersion effect

The objective of this study is to examine the influence of double dispersion on mixed convection flow over a vertical cone of an incompressible viscous fluid saturated porous medium. The mathematical model of the problem is designed in forms of governing equations and the non-dimensionalization is performed via appropriate transformations, to employ the numerical technique; the obtained non-similarity equations are solved numerically by the bivariate Chebyshev spectral collocation quasi-linearization method. The outcomes are reflected graphically and numerically for variation of the governing parameters Prandtl number, Schmidt number, buoyancy parameter, thermal and Solutal dispersion parameters on the velocity, temperature, and concentration profiles at the various stream-wise locations, respectively. Further, skin friction, heat, and mass transfer coefficients are also reflected. To authenticate the accuracy of the present computations, we have enclosed a comparison with a prior published results and it found in great consent. The residual analysis study is also pictured in the results and discussion section, which reflects the convergence and stability of the present computations.

Equivalent linear roll damping of a FPSO coupled with liquid sloshing in a pair of two-row tanks

The increased risk of reduced transverse stability by free surfaces in cargo tanks in floating vessels such as Floating Production Storage and Offloading (FPSO) units, is well known. Roll decay testing remains the most common method for determining roll damping characteristics. Few works evaluating roll characteristics coupled with the effect of liquid motion exist. In this paper, a series of roll decay tests are carried out for a FPSO model with a pair of two-row prismatic tanks. The four compartment tanks are filled to different levels, and the equivalent linear damping is obtained using the Quasilinear (Logarithmic Decrement) method and the Froude Energy method. The effect of draft change for each loading condition is analyzed based on the average equivalent linear damping coefficient and the effect of the liquid cargo sloshing is also discussed. The results show that an increase in liquid cargo, the location of cargo load, and the geometry of the cargo tank affect the damping of the vessel.

A numerical iterative method for solving two-point BVPs in infinite-horizon nonzero-sum differential games: Economic applications

In this work, the Nash equilibrium solution of nonlinear infinite-horizon nonzero-sum differential games with open-loop information is investigated numerically. For this class of games, some difficulties are involved in finding an open-loop Nash equilibrium. For instance, we must solve a nonlinear differential equations system with split boundary conditions, namely the two-point boundary value problem (TPBVP), in which some of the boundary conditions are specified at the initial time and some at the infinite final time. In the current study, we provide a combined numerical algorithm based on a new set of basis functions on the half-line, called the exponential Chelyshkov functions (ECFs), and quasilinearization (QL) method to solve TPBVPs. In the first step, we reduce the nonlinear TPBVP to a sequence of linear differential equations by using the QL method. Although we have now a linearized system, another difficulty is finding the approximate solution of this linear system such that the transversality conditions at the infinite final time are satisfied. So, in the second step, we apply a collocation method based on the ECFs to solve the obtained linear system in the semi-infinite domain. The convergence of the proposed method is discussed in detail. To confirm the validity and efficiency of the proposed scheme, we compute the approximate solution of TPBVP as well as the open-loop Nash equilibrium for four applications of differential games in economics and management science.

Study of MHD Mixed Convention Flow and Heat Transfer Through Porous Media

In this present paper, the effects of chemical reaction on two-dimensional mixed convection flow and heat transfer of an electrically conducting micropolar fluid in a porous medium between two parallel plates with Soret and Dufour have been considered. The reduced flow field equations are solved using the quasilinearization method. The effects of various parameters such as Hartmann number, inverse Darcy's parameter, Schmidt number, Prandtl number, chemical reaction rate, Soret and Dufour numbers on the velocity components, microrotation, temperature distribution, and concentration are studied in detail and presented in the form of graphs. The flow through porous boundaries has many applications in science and technology such as water waves over a shallow beach, mechanics of the cochlea in the human ear, aerodynamic heating, flow of blood in the arteries, and petroleum industry. Several authors have studied theoretically the laminar flow in porous channels. Berman [1] considered the viscous fluid and analyzed the flow characteristics when it passed through the porous walls. Later the same problem for different permeability was studied by Terril and Shrestha [2]. The theory of micropolar fluids was introduced by Eringen [3] which are considered as an extension of generalized viscous fluids with microstructure. Examples for micropolar fluids include lubricants, colloidal suspensions, porous rocks, aerogels, polymer blends, and microemulsions. The same Berman problem with micropolar fluid was discussed by Sastry and Rama Mohan Rao [4]. The flow and heat transfer of micropolar fluid between two porous parallel plates was analyzed by Ojjela and Naresh Kumar [5]. Srinivasacharya et al. [6] obtained an analytical solution for the unsteady Stokes flow of micropolar fluid between two parallel plates. The effect of buoyancy parameter on flow and heat transfer of micropolar fluid between two vertical parallel plates was investigated by Maiti [7].

Quasi-linearization analysis for heat and mass transfer of magnetically driven 3rd-grade (Cu-TiO2/engine oil) nanofluid via a convectively heated surface

The features of heat transferral capability between metallic (Cu) and non-metallic (TiO2) nanoparticles suspended in the engine-oil (EO) third-grade base-liquid has been analysed under the influence of strong magnetic field. The numerical investigation of system of coupled differential equations for third-grade nanofluid flow model is accomplished via Quasi-linearization method (QLM). The stretching horizontal sheet is heated through convective heat process assuming the special effects of thermal radiation, joule heating, heat generation and viscous dissipation in the energy equation. The mass suction and slip velocity at the boundary of the sheet has been taken into account to enhance fluidity of the engine-oil nanofluid. The prominent non-dimensional parameters controlling the flow and heat transfer characteristics of Cu-TiO2/ Engine-Oil nanofluid are estimated through graphical and tabular data. A novel graphical analysis for entropy generation versus magnetic retardation is projected for various parameters. Entropy generation is reduced by the velocity slip parameter but it is increased by the Reynolds number and Brinkman number. The enhanced lubricating properties of engine oil with mixing of TiO2-nanoparticles might be a useful industrial lubricant for magnetic refrigeration applications.

A Novel Learning Approach for Different Profile Shapes of Convecting–Radiating Fins Based on Shifted Gegenbauer LSSVM

The purpose of this paper is to introduce a novel learning approach to solve the heat transfer problem from convecting-radiating fin model. This model is a nonlinear differential equation in which different boundary conditions cause different profile shapes including rectangular, triangular, trapezoidal and concave parabolic. We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. Our method is based on using the quasilinearization method to linearize the nonlinear models and applying shifted Gegenbauer polynomials as new kernel in least squares support vector machines method. The results of fin efficiency and heat transfer rate of the problems which compared with available previous results indicate better efficiency and accuracy of the proposed approach.

Magneto-hydrodynamics effects over a three-dimensional nanofluid flow through a stretching surface in a porous medium

This paper examines the approximate solution of the three-dimensional nanofluid flow. The viscous dissipation and non-uniform heat source are accounted for in the energy equation over the stretching sheet. The numerical solutions of the governing partial differential equation are solved using spectral quasi-linearization method (SQLM). The nonlinear differential equations are obtained from the ordinary differential equations using suitable similarity transformation. A comparison between the obtained results with solutions obtained early in the literature and the numerical solution has been made to test the validity, accuracy, and convergence of the SQLM. Physical parameters on the velocity, temperature, and concentration are determined and discussed. The thermophoresis parameter greatly influenced concentration level with nanofluid flow across the stretching surface with a high Schmidt number.

An Unsteady Nanofluid Flow Past Parallel Porous Plates: A Numerical Study

Background: This study investigates an unsteady, two-dimensional, incompressible viscous boundary layer flow of an electrically conducting nanofluid past parallel plates. The plates are permeable to allow both suction and injection to take place. It is assumed that viscosity, thermal conductivity and mass diffusivity of the nanofluid vary with temperature. The novelty of this study is in consideration of the combined effects of chemical reaction, permeability, externally applied magnetic field, and momentum diffusivity on the flow varibles. The magnetic field force is significant because it provides information regarding the boundary layer characteristics. Methods: The highly nonlinear partial differential equations are solved numerically using the newly developed bivariate spectral quasilinearization method (BSQLM) along with varying thermal and concentration boundary conditions. The BSQLM method is an innovative technique that is more reliable and robust as it demands fewer grid points and has a global approach to solving PDEs. Results: An analysis and comparison of results with existing literature are reported. Excellent agreement has been found between our results and those previously published. Among the findings, we show, inter alia, a significant increase in the profiles for fluid velocity, temperature and concentration with an increase in the chemical reaction, applied magnetic field, and thermal radiation. The BSQLM converges fast and is computationally efficient when applied to boundary layer problems that are defined on a large computational domain. Conclusions: A numerical study on nanofluid flow between parallel porous plates has been carried out, and here are the key findings: 1. Heat flux is directly related to thermal radiation, the applied magnetic field, permeability, and the chemical reaction involved. 2. Mass flux increases with increased chemical reaction, permeability, and the magnetic parameters. 3. The nanofluid concentration is directly related to the Prandtl and magnetic numbers and inversely related to the Reynolds number and chemical reaction. 4. The skin-friction coefficient reduces with higher values of magnetic field and permeability parameters and increases with an increment in thermal radiation and chemical reaction. 5. The BSQLM has a high convergence rate with high accuracy.

On the mathematical model of Eyring–Powell nanofluid flow with non-linear radiation, variable thermal conductivity and viscosity

It is well known that the significance of dynamic viscosity and thermal conductivity cannot be overemphasized in the movement of any fluid. In the present investigation, the impact of variable viscosity, variable thermal conductivity, Brownian motion, thermophoresis, heat and chemical reaction effects on an unsteady Eyring–Powell nanofluid flow in a stretching sheet is extensively discussed. The governing non-linear coupled partial differential equations describing the problem were derived. Similarity variables were used to transform the governing partial differential equations into ordinary differential equations. After which the Spectral quasi-linearization method (SQLM) was employed to numerically handle the emerging governing differential equations after validating the convergence of the method with existing results in literature. The novel flow features which include fluid velocity, skin friction, heat transfer coefficient and rate of mass transfer were discussed therein as a function of sundry parameters entering flow formation. Findings reveal that the Brownian motion and thermophoresis parameters increase the temperature profile. Also, fluid concentration was found to be a decreasing and increasing function of Brownian motion parameter and thermophoresis parameter respectively. For accuracy check, tabular representations are carried out with published work in the literature; excellent agreement were found.

Entropy generation analysis of radiative heat transfer in Williamson fluid flowing in a microchannel with nonlinear mixed convection and Joule heating

In this article, the spectral quasi-linearization (SQLM) method is implemented to solve the complicated differential equations governing the nonlinear mixed convective heat transfer of a Williamson fluid through a vertical microchannel. Unlike the conventional Boussinesq approximation, the quadratic Boussinesq approximation is taken into account in the formulation. The effects of Rosseland thermal radiation, Joule heating, and viscous dissipation are described in the thermal analysis subjected to the boundary conditions of convective thermal heating. The analysis of entropy production is also performed. The importance of various parameters governing velocity, Bejan number, temperature, and entropy generation was explored using graphic illustrations. It was found that the nonlinear density change with a temperature significantly affects the heat transport in the microchannel and thus increases the magnitude of the Bejan number and the production of entropy. Entropy production occurs maximum due to the boundary conditions of convection heating at the walls of the microchannel. Furthermore, due to a stronger viscous heating mechanism, the magnitude of the Bejan number is reduced, while the production of entropy increases significantly. As a limiting case of the problem, a comparison was made with results previously published in the literature and excellent agreement was established. The calculations provide a solid reference point for future CFD models and are relevant to the dynamics of polymers in microfluidic devices and the polymer industries.

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

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

Entropy generation optimisation for unsteady stagnation Casson nanofluid flow over a stretching sheet with binary chemical reaction and Arrhenius activation energy using the bivariate spectral quasi-linearisation method

The heat and mass transport with Arrhenius activation energy has countless uses such as in nuclear reactors, the synthesis of chemical compounds, geothermal artificial lakes, and retrieval of thermal lubricants. The focus of this work is the analysis of Arrhenius activation energy and binary chemical reaction in a stagnation point Casson nanofluid flow over a stretching sheet. The system is subjected to a nonlinear radiation and a magnetic field. The transport equations are simplified using the Williams and Rhyne non-similar transformation. The solution to the transformed coupled system of nonlinear partial differential equations is obtained using the bivariate spectral quasi-linearisation method. Entropy generation that measures the degenerate useful energy and deprivation of the performance of engineering systems is analysed. Numerical results describing changes in the fluid velocity, temperature, concentration, entropy generation and Bejan number are presented and discussed for different fluid parameters. Activation energy parameter boosts up the solute concentration at the surface while an opposite is observed far away from the surface. The entropy generation decreases with an increase in the unsteady parameter and Casson number, while the opposite response was observed for a higher Reynolds number. Brinkman number gears up the entropy generation while it shows an opposite phenomenon for Bejan number.

An effective scheme for solving a class of nonlinear boundary value problems of stress concentration through quasilinearisation approach

The approximate analytical solution to the problem for an infinite plate with the central circular hole subjected to uniaxial tension under creep regime is obtained by the quasilinearisation method. Three approximations of the solution for the nonlinear creep problem are found. It is shown that with increasing the number of approximations the solution converges to the limit numerical solution. Using SUMULIA Abaqus soft-package several numerical solutions for various creep exponent values are obtained It is worth to note that the tangential stress reaches its maximum value not at the circular hole but at the internal point of the plate. It is shown that quasilinearisation method is the effective method for nonlinear problems.

Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems

In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling the subgame perfect equilibrium solutions to time-inconsistent dynamic choice problems, which are motivated by the study of behavioral economics. Different types of nonlocal parabolic systems were studied but left behind the fully-nonlinear case and the connections among them. This paper shows the equivalence in solvability between nonlocal fully-nonlinear and the associated quasilinear systems, given their solutions are regular enough. Moreover, we establish the well-posedness results for the nonlocal quasilinear parabolic systems, so do that for the nonlocal fully-nonlinear parabolic systems. The quasilinear case alone is interesting in its own right from mathematical and modelling perspectives.

Calculation of depressurization coordinate in underground and offshore gas pipelines

The paper introduces a method for calculating the depressurization coordinate of an extended ultra-high pressure gas pipeline from the data measurements of pressure and flow rate at the outlet. The method is based on a mathematical model of a non-isothermal steady single-phase gas mixture flow through a pipeline of constant section on the quasi-linearization method. It allows to calculate the depressurization coordinate for extended underground and offshore ultra-high pressure gas pipelines with high accuracy, while considering varying leakage size and location. Examples of solving problems of practical interest are given. The influence of the flow rate and pressure settings error on the coordinate of depressurization calculating error has been demonstrated.

Convective nanofluid flow over a vertical cone with a rough surface

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

Casson fluid flow with heat and mass transfer in a channel using the differential transform method

In the present investigation, we consider the heat and mass transfer characteristics of steady, incompressible and electrically conducting Casson fluid flow in a channel. The effect of chemical reactions have also been considered. The differential transform method (DTM) is applied to a system of non-linear ODEs, and the results are obtained in the form of DTM series. The principal gain of this approach is that it applies to the non-linear ODEs without requiring any discretization, linearization or perturbation. The velocity, mass and heat transfer profiles thus obtained are in good agreement with those provided by the quasi-linearization method (QLM). Graphical results for velocity, concentration and temperature fields are presented for a certain range of values of the governing parameters.

Effects of Ion-Slip and Hall Currents on Magnetohydrodynamic Nanofluid Flow with Thermal Diffusion Using Spectral Quasi-Linearization Method

We scrutinize and numerically investigate the behavior of magnetic nanofluid flow in stagnation region in the presence of ion-slip and Hall currents. Employing similarity technique, the governing equations modeling the boundary layer flow are switched into highly nonlinear ODEs. The resultant equations are then solved numerically by the method of spectral quasi-linearization. The effect of varying various pertinent parameters within the fluid flow are taken into account and the results are analyzed graphically. It may be noted that the velocity increases in the x- as well as z-directions with an increment in the Hall parameter. The concentration indicates a decreasing trend with increasing values of the Eckert number. The computed results also show that the volume fraction effects diminishes as the Schmidt number increases.

A comparative study of three dimensional flow of Casson–Williamson nanofluids past a riga plate: Spectral quasi-linearization approach

In the present investigation, the impact of variable transport properties on the magnetized three dimensional motion of Casson–Williamson nanofluids with nonlinear radiation influence past a Riga plate is discussed. For proper utilization of nanoliquids, a good account of distinct fluid transport variables in any flow geometry is essential. The governing flow equations of a stretching Riga plate of variable viscosity, mass diffusivity and thermal conductivity are obtained after imposing an appropriate similarity variables. The spectral quasi-linearization method (SQLM) was employed to get good account of all pertinent flow parameters. Apart from excellent agreement with earlier known work in literature, the method performance (numerical estimation tools) are discussed via CPU time, errors (L∞ and L1), and comparison with Galerkin weighted residual method. Also engineering dimensionless parameters were presented for the present problem. The results therein established that flow resistivity of Williamson fluid is higher when compared to the Casson fluid. In addition, Casson fluid diffuses and conduct lesser in respect to Williamson fluid. With opposing characterization of viscosity parameter, variable thermal conductivity and mass diffusivity enhances the species and thermal boundary layer, while the viscosity property appreciated the momentum(s) profiles. This study is found applicable while forecasting the right fluid rheology to use, proffer solution to noise/turbulence effect, to safeguard boundary layer isolation, and establishing a force parallel to the surface for both industrial, engineering and biomedical use.