We investigate the steady two‐dimensional flow of a viscous incompressible fluid in rectangular domain that is bounded by two permeable surfaces. The governing fourth‐order nonlinear differential equation solved applying spectral‐homotopy analysis method and novel successive linearisation method. Semianalytical results are obtained convergence rate solution series was compared with numerical approximations earlier where homotopy perturbation methods were used. show both computationally...

Abstract In this study we use the spectral relaxation method (SRM) for solution of steady von Kármán flow a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The is new Chebyshev collocation based iteration that developed from Gauss-Seidel idea decoupling systems equations. work, investigate applicability in solving strongly nonlinear boundary value problems type. SRM results are validated against previous present literature those obtained using bvp4c, MATLAB inbuilt routine...

Magnetohydrodynamic (MHD) stagnation point flow and heat transfer problem from a stretching sheet in the presence of source/sink suction/injection porous media is studied this paper. The governing partial differential equations are solved using Chebyshev spectral method based perturbation approach. method, namely (SPM), series expansion technique which extends use standard approach by coupling it with pseudo-spectral method. Series solutions for small velocity ratio asymptotic large...

Purpose The purpose of this paper is to study the steady laminar flow a pressure driven third‐grade fluid with heat transfer in horizontal channel. serves two purposes: correct inaccurate results presented Siddiqui et al., where homotopy perturbation method was used, and demonstrate computational efficiency accuracy spectral‐homotopy analysis methods (SHAM MSHAM) solving problems that arise mechanics. Design/methodology/approach Exact approximate analytical series solutions non‐linear...

Purpose – The purpose of this paper is to study heat and mass transfer in copper-water silver-water nanofluid flow over stretching sheet placed saturated porous medium with internal generation or absorption. authors further introduce a new algorithm for solving problems fluid mechanics. model used the incorporates nanoparticle volume fraction parameter consideration chemical reaction effects among other features. Design/methodology/approach partial differential equations were transformed...

The present work introduces a spectral local linearisation method (SLLM) to solve natural convection boundary layer flow problem with domain transformation. It is customary find solutions of semi-infinite interval problems by first truncating the and subsequently applying suitable numerical method. However, this gives rise increased error terms in solution. Carrying out transformation into singular posed on finite can avoid truncation enables efficient application collocation methods. SLLM...

The spectral homotopy analysis method is extended to solutions of systems nonlinear partial differential equations. SHAM has previously been successfully used find ordinary We solve the system equations that model unsteady convective flow caused by an impulsively stretching sheet. numerical results generated using were compared with those found quasilinearisation (SQLM) and two in good agreement.

We use recent innovative solution techniques to investigate the problem of MHD viscous flow due a shrinking sheet with chemical reaction. A comparison is made convergence rates, ease use, and expensiveness (the number iterations required give convergent results) three seminumerical in solving systems nonlinear boundary value problems. The results were validated using multistep, multimethod approach comprising shooting method, Matlab bvp4c numerical routine, literature.

A spectral relaxation method used with bivariate Lagrange interpolation is to find numerical solutions for the unsteady three-dimensional flow problem of an Oldroyd-B fluid variable thermal conductivity and heat generation. The governed by a set three highly coupled nonlinear partial differential equations. method, originally systems ordinary equations extended modified approach involves seeking that are expressed as interpolating polynomials applying pseudo-spectral collocation in both...

The present study investigates entropy generation on a magnetohydrodynamic flow and heat transfer of Maxwell fluid using spectral relaxation method.The method is based simple iteration schemes formed by reduction the order momentum equation followed rearrangement resulting governing nonlinear systems which are then solved methods.The velocity temperature profiles obtained numerically used to generate number.Entropy increased with Reynolds number, magnetic parameter dimensionless group while...

A steady two-dimensional laminar boundary layer flow of an incompressible viscous fluid over a semi-infinite surface is considered to investigate the accuracy homotopy analysis method. The governing coupled nonlinear system differential equations solved by means HAM approach. Explicit analytical series solutions are obtained and compared with numerical solutions. Good agreement observed between results

In this paper, we introduce a modified inertial subgradient extragradient algorithm in 2-uniformly convex and uniformly smooth real Banach space prove strong convergence theorem for approximating common solution of fixed point equation with demigeneralized mapping variational inequality problem monotone Lipschitz mapping. We present an example to validate our new findings. This work substantially improves generalizes some well-known results the literature.

The steady flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipationis studied. We present novel technique for accelerating the convergence spectral-homotopy analysis method. Solutions nonlinear momentum energy equations are obtained using improved spectral homotopy were also generated method benchmarked against results in literature. Mathematical subject classification: Primary: 76A05, 76N05; Secondary: 76M25.

Biodiesel is an alternative diesel fuel chemically defined as the mono-alkyl esters of long chain fatty acids derived from vegetable oils or animal fat. It becoming more attractive due to depleting fossil resources. A mathematical model for synthesis biodiesel and fats presented in this study. Numerical solutions are found using a spectral relaxation method. The method, originally developed boundary value problems, iterative scheme based on Chebyshev collocation method by decoupling systems...

A spectral homotopy analysis method (SHAM) is used to find numerical solutions for the unsteady viscous flow problem due an infinite rotating disk.The governed by a set of two fully coupled nonlinear partial differential equations.The was originally introduced ordinary equations.In this study, its application extended system equations (PDEs) that model von Kàrmàn swirling flow.Numerical values pertinent properties were generated and validated against results obtained using Keller-box...

A bivariate spectral homotopy analysis method (BSHAM) is extended to solutions of systems nonlinear coupled partial differential equations (PDEs). The has been used successfully solve a PDE and now tested with systems. based on new idea finding that obey rule solution expression defined in terms the Lagrange interpolation polynomials. BSHAM system modeling unsteady mixed convection boundary layer flow, heat, mass transfer due stretching surface rotating fluid, taking into consideration...