Homotopy Perturbation Method and the Stagnation Point Flow

The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution

Optimal Homotopy Asymptotic Solution for Thermal Radiation and Chemical Reaction Effects on Electrical MHD Jeffrey Fluid Flow Over a Stretching Sheet through Porous Media with Heat Source

In this paper, the problem of thermal radiation and chemical reaction effects on electrical MHD Jeffrey fluid flow over a stretching surface through a porous medium with the heat source is presented. We obtained the approximate analytical solution of the nonlinear differential equations governing the problem using the Optimal Homotopy Asymptotic Method (OHAM). Comparison of results has been made with the numerical solutions from the literature, and a very good agreement has been observed. Subsequently, effects of governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed

Analysis of Various Complex Flows of Micropolar Fluids in the Slip Flow Regime

Four mathematical models have been developed to study the slip flow of micropolar fluids over a stretching/shrinking sheet under the influence of slip and the Newtonian heating conditions at the boundary. The optimal homotopy analysis method is applied for the solutions of these models. The results obtained from this study are useful in liquid crystals, polymeric suspensions, polishing artificial heart valves and internal cavities

Mixed convective flow of a Casson fluid over a vertical stretching sheet

A coupled nonlinear boundary value problem arising from a mixed convective flow of a non-Newtonian fluid at a vertical stretching sheet with variable thermal conductivity is investigated in this paper. Casson fluid model is used to describe the non-Newtonian fluid behavior. Using a similarity transformation, the governing equations are transformed into a system of coupled, nonlinear ordinary differential equations and the analytical solutions for the velocity and temperature fields are obtained via a semi-analytical algorithm based on the optimal homotopy analysis method. To validate the method, comparisons are made with the available results in the literature for some special cases and the results are found to be in excellent agreement. The characteristics of the velocity and the temperature fields in the boundary layer have been analyzed for several sets of values of the Casson parameter, the Prandtl number, the temperature dependent thermal conductivity parameter, the velocity exponent parameter and the mixed convection parameter. The presented results through graphs and tables reveal substantial effects of the pertinent parameters on the flow and heat transfer characteristics. Furthermore, an error analysis is offered using an exact residual error and average residual error methods.postprin

Lie group analysis of nanofluid slip flow with Stefan Blowing effect via modified Buongiorno’s Model : entropy generation analysis

This article presents a detailed theoretical and computational analysis of alumina and titania-water nanofluid flow from a horizontal stretching sheet. At the boundary of the sheet (wall), velocity slip, thermal slip and Stefan blowing effects are considered. The Pak-Cho viscosity and thermal conductivity model is employed together with the non-homogeneous Buongiorno nanofluid model. The equations for mass, momentum, energy and nanoparticle species conservation are transformed via Lie-group transformations into a dimensionless system. The partial differential boundary value problem is therefore rendered into nonlinear ordinary differential form. With appropriate boundary conditions, the emerging normalized equations are solved with the semi-numerical homotopy analysis method (HAM). To consider entropy generation affects a second law thermodynamic analysis is also carried out. The impact of some physical parameters on the skin friction, Nusselt number, velocity, temperature and entropy generation number (EGM) are represented graphically. This analysis shows that diffusion parameter is a key factor to retards the friction and rate of heat transfer at the surface. Further, temperature of fluid decreases for the higher value of thermal slip parameter. In addition, entropy generation number enhances with nanoparticles ambient concentration and Reynolds number. A numerical validation of HAM results is also included. The computations are relevant to thermodynamic optimization of nano-material processing operations

Recent Trends in Coatings and Thin Film–Modeling and Application

Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value

Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non-Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non-Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The non-dimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter, unsteadiness parameter, Prandtl number (Pr), buoyancy parameter. The semi-analytical Differential Transform Method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built in solver ‘bvp4c’ to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid) whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach

Analytical analysis of the magnetic field, heat generation and absorption, viscous dissipation on couple stress casson hybrid nano fluid over a nonlinear stretching surface

The aim of this research paper is to study two-dimension flow of Casson hybrid nanofluid along with magnetic field, heat generation and absorption, and viscous dissipation on a nonlinear extending surface. The primary goal of this study is to improve the heat transfer relationship, which is in high demand in the manufacturing and engineering industries. The outputs of this study will be used to reduce the energy consumption in industry and other engineering fields,for example, the achievement of energy is not enough, but also to adjust the con-sumptions of energy and this is possible only to approve the development heat transmission liquids to mechanism the expenditures of energy and to improvement. The described similarity transformation is used to convert the non-dimensionless form of the nonlinear partial differential equation to the dimensionless form of the nonlinear ordinary differential equation. An approximate analytical method is used to solve the derived dimensionless form of nonlinear ordinary differential equations, one for velocity and the other for temperature. Graphs are used to highlight the most relevant results acquired from velocity and temperature. Tables are used to describe the skin friction coefficient and the Nusselt number.The work of U·F.G. was supported by the government of the Basque Country for the ELKARTEK21/10KK-2021/00014 and ELKARTEK22/85 research programs, respectively

Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). It is clear that by the use of second auxiliary parameter, the straight line region in ℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a) prescribed surface temperature (PST) and (b) prescribed heat flux (PHF). The effect of involved parameters on velocity and temperature is investigated