Optimal Homotopy Analysis Method Research Articles

Thermal Characteristics of 3D Nanofluid Flow over a Convectively Heated Riga Surface in a Darcy–Forchheimer Porous Material with Linear Thermal Radiation: An Optimal Analysis

This paper focuses primarily on the thermal analysis of the steady, three-dimensional flow of CMC (sodium carboxymethyl cellulose) base fluid with Cu nanoparticles through the implantation plate of Riga in a porous Darcy–Forchheimer material with internal heat generation (absorption) effects. Thermophysical feature of CMC is taken into account with Al2O3 nanoparticle in it. Also, thermal radiation and convective boundary constraint are considered into account. Adequate transformations of the issue controlling formulas produce a system of nonlinear ordinary differential equations. The optimal homotopy analysis method is used for calculating the parameters values impacts. The expressions of local Nusselt number and skin friction coefficient are studied and debated. The physical influences of all emerging parameters are debated on graphically forms. The findings suggest that with higher values of Hartmann number, the skin friction in y-direction decreases on the contrary in the case of x-direction, while the Hartmann number increases the rate of heat transportation. Besides, the addition values of thermal radiation and Biot number enhance the rate of heat transport. Comparisons have been made with published literature, and an excellent agreement is clear. This underlines the importance of the study in potential medical and industrial cooling applications.

Approximation solution of the squeezing flow by the modification of optimal homotopy asymptotic method

The approximate solution of the squeezing axisymmetric fluid flow between infinite plates is discussed in the present paper. An optimal homotopy analysis method with a modification function technique is proposed to solve a class of nonlocal boundary value problems, namely squeezing axisymmetric fluid flow equation. We first transform the nonlocal boundary value problems into an equivalent integral equation, and then the optimal homotopy analysis technique is utilized for an approximate solution. The numerical results confirm the reliability of the present method as it tackles such nonlocal problems without any limiting assumptions. The proposed method is tested upon squeezing axisymmetric fluid flow equation from the literature and the results are compared with the available approximate solutions including perturbation method (Ran et al. in Commun Nonlinear Sci Numer Simul, 2007. https://doi.org/10.1016/j.cnsns ), homotopy perturbation method (Ran et al. 2007), homotopy analysis method (Ran et al. 2007), and optimal homotopy asymptotic method (Idrees et al. in Math Comput Model 55:1324–1333, 2012). The convergence and error analysis of the proposed method is discussed. It can be said that squeezing the axisymmetric fluid flow equation exists in different dynamical behaviors. In addition, the physical behaviors of these new exact solutions are given with two and three-dimensional graphs.

Simulation and modeling of entropy optimized MHD flow of second grade fluid with dissipation effect

Here entropy optimized magnetohydrodynamic flow of second-grade fluid is addressed. The energy equation is developed through Joule heating and dissipation effects. Mass transportation along with an interface between two liquids due to surface tension gradient is called Gibbs–Marangoni effect (Marangoni effect). On the other hand, if there is thermal dependence case, then the phenomenon is called Bénard–Marangoni convection (thermo-capillary convection). Marangoni convection depends upon the difference of surface pressure computed by the gradient of temperature, magnetic effect, and concentration gradients. The basic concept of mass and heat transportation phenomenon in Marangoni boundary layer flow are comprehensively discussed. The physical feature of irreversibility exploration is developed with the help of thermodynamics second law. Here we discussed both first and second laws of thermodynamics. Nonlinear ODE's are obtained through adequate variables. Optimal homotopy analysis method (OHAM) is employed to construct the convergent solutions. Entropy optimization, temperature, Bejan number, concentration, and velocity variations for various secondary parameters are deliberated. Velocity enhances via the Marangoni ratio parameter. For larger Hartmann number the temperature and velocity have a reverse effect. The velocity field is amplifying against second grade fluid variable. A similar effect is noticed versus a larger fluid parameter and Eckert number. For a higher approximation of the Marangoni ratio variable, the concentration reduces. Larger fluid parameter rises the entropy generation rate.

Marangoni flow and mass transfer of power-law non-Newtonian fluids over a disk with suction and injection

We scrutinize the approximate analytical solutions by the optimal homotopy analysis method (OHAM) for the flow and mass transfer within the Marangoni boundary layer of power-law fluids over a disk with suction and injection in the present paper. Concentration distribution on the surface of a disk varies in a power-law form. The non-Newtonian fluid flow is due to the surface concentration gradient without considering gravity and buoyancy. According to the conservation of mass, momentum and concentration, the governing partial differential equations are established, and the appropriate generalized Kármán transformation is found to reduce them to the nonlinear ordinary differential equations. OHAM is used to access the approximate analytical solution. The influences of Marangoni the number, suction/injection parameters and power-law exponent on the flow and mass transfer are examined.

Featuring the radiative transmission of energy in viscoelastic nanofluid with swimming microorganisms

This article highlights the influence of thermal radiation, inclined magnetic field, and stratification on the third-grade nanofluid with swimming gyrotactic microorganisms. The fluid is flowing past a horizontal cylinder exposed to an inclined magnetic field. The boundary layer system of equations is reconstructed into ordinary differential equations using similarity transformations. The system of equations is resolved using the Optimal Homotopy Analysis Method (OHAM) and the results are visualized numerically and graphically. Physical properties have been taken into consideration and the repercussions of different parameters on these properties are analyzed through contour plots. The following upshots are prominent: (i) radiation augments diffusive energy to the system enhancing the temperature along with the heat transfer rates, (ii) the more inclined magnetic field causes more decrease in velocity (iii) the bioconvective aspect introduced due to the addition of microorganisms altered the transfer rates of microorganisms positively, and (iv) nanoparticles evidently brought down the concentration through Brownian motion effects and the overall influence of these particles hindered mass transport rates.

Unsteady MHD squeezing viscous Casson fluid flow in upright channel with cross-diffusion and thermal radiactive effects

The purpose of the present work is to analyse two-dimensional unsteady squeezing Casson fluid flow between porous channel along with cross-diffusion, viscous dissipation, radiation, and chemical reaction effects. To get the results of governing equations which are partial differential equations in nature, we have converted them into ordinary differential equations by utilizing suitable similarity transformation and then applied the optimal homotopy analysis method. The effects of various dimensionless parameters ascended in the velocity, temperature and concentration fields are discussed through graphs. Values of skin friction coefficient, Nusselt number, and Sherwood coefficients are derived and presented in tabular form. Results indicate that with enhancement in the values of the Casson parameter and magnetic parameter, the velocity decreases near the lower plate while it shows reverse behaviour near the upper one. The temperature of the fluid increases with an increase in both radiation parameter as well as with Eckert number while it decreases by augmenting values of the Casson parameter. Soret and Dufour number affect mass and heat transfer rate in reverse manner. Also, concentration decreases when chemical reaction parameter increases.

Entropy generation in MHD Casson fluid flow with variable heat conductance and thermal conductivity over non-linear bi-directional stretching surface

This consideration highlights the belongings of momentum, entropy generation, species and thermal dissemination on boundary layer flow (BLF) of Casson liquid over a linearly elongating surface considering radiation and Joule heating effects significant. Transportation of thermal and species are offered by using the temperature-dependent models of thermal conductivity and mass diffusion coefficient. Arising problem appear in the form of nonlinear partial differential equations (NPDEs) against the conservation laws of mass, momentum, thermal and species transportation. Appropriate renovation transfigures the demonstrated problem into ordinary differential equations. Numerical solutions of renovated boundary layer ordinary differential equations (ODEs) are attained by a proficient and reliable technique namely optimal homotopy analysis method (OHAM). A graphical and tabular interpretation is given for convergence of analytic solutions through error table and flow behavior of convoluted physical parameters on calculated solutions are presented and explicated in this examination. Reliability and effectiveness of the anticipated algorithm is established by comparing the results of present contemplation as a limiting case of available work, and it is found to be in excellent settlement. Decline in fluid velocity and enhancement in thermal and species transportation is recorded against the fluctuating values of Hartman number. Also reverse comportment of Prandtl number and radiation parameter is portrayed. Moreover, it is conveyed that supplementing values of the magnetic parameter condenses the fluid velocity and upsurges the thermal and concentration distributions. Negative impact of elevating Joule heating phenomenon is noted on the molecular stability of the system via Brinkman number left( {Br} right). Furthermore, the system’s stability at a molecular level is controlled by diminishing values of radiation left( R right), temperature difference left( { in_{1} } right), concentration difference left( { in_{2} } right), diffusion parameters left( { in_{3} } right) and Brinkman number left( {Br} right).

Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay

The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov regime switching. The optimal control problem is presented by making use of dynamic programming. In the case where the Markov chain has two states, the optimal homotopy analysis method (OHAM) is used to obtain an analytical approximation of the value function, which is compared to the finite difference approximation with successive updates of the nonlinear and coupling terms. As an example, the method is applied to controlled population growth with regime switching.

An iterative technique for solving a class of local and nonlocal elliptic boundary value problems

An optimal iterative method is proposed for a reliable solution of a class of Bratu-type, Troesch’s and nonlocal elliptic boundary value problems (BVPs). Due to the presence of parameter $$\delta $$ as well as strong nonlinearity, these problems pose difficulties in obtaining their solutions. With the help of Green’s function theory, we first transform the BVP into an equivalent integral equation, followed by applying the optimal homotopy analysis method to get the approximate solution of high accuracy level. Several examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The numerical results confirm the reliability of the present method as it tackles such nonlocal problems without any limiting assumptions. The convergence and error analysis of the proposed method is discussed.

Soret, Dufour, and activation energy effects on double diffusive convective couple stress micropolar nanofluid flow in a Hall MHD generator system

In this paper, the effect of activation energy, Soret, and Dufour on non-isothermal heat transfer via the non-linear wall of the steady convective flow of micropolar nanofluid magnetohydrodynamics is investigated. Variations in thermophoresis, Brownian motion, couple stress, and Hall current are also considered. Transformations are used to simplify and then solve the governing equations using the optimal homotopy analysis method and are numerically visualized for results. The behavior was examined and explained in all profile graphs. Tables are presented to illustrate the effect of dimensionless parameters on skin friction coefficients, Nusselt and Sherwood numbers. The concentration reduces via the chemical reaction rate, a temperature relative parameter, and increases with an increase in the activation energy and Soret number. It was found that the local skin-friction coefficient at the generator increases with an increase in the Hall current parameter, solutal Grashof number, and couple stress parameter on the x-axis, the local heat rate decreases through the Dufour number and Brownian motion parameter, and the mass transfer rate increases with an increase in the activation energy parameter and Schmitz and Reynolds numbers.

A Bessel collocation method for solving Bratu’s problem

In the present paper, we design a Bessel collocation method for solving one-dimensional nonlinear Bratu’s boundary value problem. Two numerical examples are provided to validate the efficiency and accuracy of the proposed method. Numerical results reveal that the present method yields very accurate approximation to the exact solution of Bratu’s problem. Moreover, the numerical results are compared with those obtained by two other existing methods, namely, optimal homotopy analysis method and the modified variational iteration method.

Effects of Variable Fluid Properties on Oblique Stagnation Point Flow of a Casson Nanofluid with Convective Boundary Conditions

Oblique stagnation point flow of a Casson nanofluid over a heated stretching surface is examined under the influence of variable fluid properties. The impact of variable fluid properties on the flow field is examined by taking a convective boundary condition into account. Momentum, energy and concentration equations are transformed into the non-linear ordinary differential system through suitable similarity transformations and are solved analytically via Optimal Homotopy Analysis Method (OHAM). Effect of pertinent parameters on dimensionless velocity, temperature and concentration are depicted graphically. Numerical values of skin friction, Nusselt number and Sherwood number have been calculated for various parameters. The results indicate that the axial velocity decreases with an increase in variable viscosity whereas the dual impact of variable viscosity is observed on transverse velocity.

Scrutiny of heat transfer and nanoparticle migration within a channel filled with nanofluid

AbstractIn this research article, we have examined the temperature and nanoparticle distribution within a channel filled with nanofluid. The flow is induced by walls of the channel stretching with a velocity proportional to the distance from origin. The analysis is carried out by assuming the presence of Navier's velocity slip. Buongiorno's modified nanofluid model that accounts the effects of nanoparticle migration due to thermophoresis and Brownian diffusion is used as model to analyze flow. We obtained similar solution of the problem numerically by the finite element method and validated it with the solution obtained by the optimal homotopy analysis method.

MHD Stagnation-Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Vertical Permeable Cylinder

The present literature analyzes the MHD stagnation-point flow of an incompressible fluidover an exponentially stretching/shrinking permeable cylinder in the presence of a transverse magnetic field, and suction/injection. The governing partial differential equations in cylindrical form aretransformed into coupled ordinary differential equations (ODEs) using suitable similarity transformations. These ODEs are solved using optimal homotopy analysis method (OHAM) via Mathematicasoftware BVPh 2.0 package. The effects of various governing parameters such as curvature parameter, magnetic parameter, wall transpiration parameter, velocity ratio parameter and Prandtl number onvelocity and temperature profiles have also been examined graphically.

IMPACT OF SUCTION/INJECTION AND HEAT TRANSFER ON UNSTEADY MHD FLOW OVER A STRETCHABLE ROTATING DISK

In this article, the unsteady magnetohydrodynamic two-dimensional boundary layer flow and heat transfer over a stretchable rotating disk with mass suction/injection is investigated. Temperature-dependent physical properties and convective boundary conditions are taken into account. The governing coupled nonlinear partial differential equations are transformed into a system of ordinary differential equations by adopting the well-known similarity transformations. Further, the solutions are obtained through the semi-analytical method called an Optimal Homotopy Analysis Method (OHAM). The obtained results are discussed graphically to predict the features of the involved key parameters which are monitoring the flow model. The skin friction coefficient and Nusselt number are also examined. The validation of the present work is verified with the earlier published results and is found to be in excellent agreement. It is noticed that an increase in the viscosity parameter leads to decay in momentum boundary layer thickness, and the inverse trend is observed in the case of the temperature profile.

On the Cattaneo–Christov Heat Flux Model and OHAM Analysis for Three Different Types of Nanofluids

In this article, the boundary layer flow of a viscous nanofluid induced by an exponentially stretching surface embedded in a permeable medium with the Cattaneo–Christov heat flux model (CCHFM) is scrutinized. We took three distinct kinds of nanoparticles, such as alumina (Al2O3), titania (TiO2) and copper (Cu) with pure water as the base fluid. The features of the heat transfer mechanism, as well as the influence of the relaxation parameter on the present viscous nanofluid flow are discussed here thoroughly. The thermal stratification is taken in this phenomenon. First of all, the problem is simplified mathematically by utilizing feasible similarity transformations and then solved analytically through the OHAM (optimal homotopy analysis method) to get accurate analytical solutions. The change in temperature distribution and axial velocity for the selected values of the specific parameters has been graphically portrayed in figures. An important fact is observed when the thermal relaxation parameter (TRP) is increased progressively. Graphically, it is found that an intensification in this parameter results in the exhaustion of the fluid temperature together with an enhancement in the heat transfer rate. A comparative discussion is also done over the Fourier’s law and Cattaneo–Christov model of heat.

Investigation of Jeffery-Hamel Flow for Nanofluid in the Presence of Magnetic Field by a New Approach in the Optimal Homotopy Analysis Method

In this article, numerical study of nanofluid flow between two inclined planes is carried out under the influence of magnetic field. Water-based nanofluid with nanoparticle of Copper (Cu) is taken into consideration for the present investigation. An efficient numerical method namely Optimal Homotopy Analysis Method (OHAM) is employed to get an approximate series solution for the related governing differential equation. A new approach is proposed to determine the convergence controller parameters used in OHAM. For the validation of the proposed technique, the convergence of the obtained results is shown for different values of involved parameters. Moreover, residual errors for the different number of terms in the obtained series solution are represented graphically. Obtained numerical results from the proposed method are incorporated with the previous results and they are found to be in very good agreement. Impacts of involved parameters like nanoparticle volume fraction, Hartmann number and Reynolds number on non-dimensional velocity are also discussed.

Inquiry of entropy generation in stratified Walters’ B nanofluid with swimming gyrotactic microorganisms

This article focuses on the study of Walters B nanofluid, under the impact of Joule heating, inclined magnetic field, viscous dissipation, swimming microorganisms, and stratification flowing past a horizontal cylindrical surface. The mathematical model is reduced to higher-order ordinary differential equations using Von Neumann similarity transformations. To obtain analytical solutions, the Optimal homotopy analysis method (OHAM) has been applied to the mathematical form. The analysis of skin friction, heat transfer rates and mass transfer rates of nanoparticles as well as swimming microorganisms is done using variation in different parameters and these results are portrayed using contour plots. Entropy is studied through dimensionless entropy generation parameter NG and Bejan number Be. The internal molecular stability is seen to reduce for temperature difference parameter Ω‾.

Impact of induced magnetic field on second-grade nanofluid flow past a convectively heated stretching sheet

Here, the main purpose of our current research work is to analyze the aspects of buoyancy force on viscoelastic (second grade fluid) magnetized nanofluid. Features of Brownian moment, viscous dissipation and thermophoretic aspects are introduced in the formulation of the problem. More specifically, the non-dimensionalization process is adopted to reduce governing system of equation (PDE) into self-similar form (ODE). Optimal homotopy analysis method (OHAM) is employed on ODE to analyze the behavior of the viscoelastic magnetized nanofluid. Moreover, comprehensive discussion related to arising physical parameters of viscoelastic liquids vs significant profiles is presented in this work. Quantities of physical interest such as Sherwood and Nusselt numbers are presented in tabular form. It has been observed that larger values of rise in the values of viscoelastic parameter (second grade fluid) results in an increment in temperature distribution.

Modified heat and mass transmission models in the magnetohydrodynamic flow of Sutterby nanofluid in stretching cylinder

This exploration addresses the boundary layer flow of Sutterby nanofluid by a stretched cylinder by incorporating the revised models for heat and mass transmissions by engaging Cattaneo–Christov theory. A mathematical model is developed under boundary layer analysis. The physical phenomenon is firstly derived in the form of partial differential equations by engaging the conservation laws. Modified Darcy’s law characterizes the porous medium. The nonlinear equations for the proposed model are analyzed optimally and dynamically. Nonlinear partial differential equations (PDEs) through conservation laws of mass, momentum, energy and concentration are established. Numerical solutions of the nonlinear systems are obtained by Optimal homotopy analysis method (OHAM). Stream plots are given for velocity solution. Graphs of velocity, temperature and concentration profiles are sketched and discussed with physical significances. It is reported that escalating values of the magnetic parameter boost the fluid temperature and concentration whereas the opposite impact on velocity is portrayed. Moreover, temperature and concentration fields decreases by growing the values of thermal and solutal relaxation parameters.