Sima Samadpoor, Hadi Roohani Ghehsareh and Saeid Abbasbandy
The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions…
Abstract
Purpose
The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are investigated.
Design/methodology/approach
In this work, the governing partial differential equations are transformed to a nonlinear ordinary differential equation by using some proper similarity transformations. Then an efficient semi-analytical method, the Laplace Adomian decomposition method (LADM) is applied to obtain semi-analytical solutions of the similarity solutions in both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. To improve the accuracy and enlarges the convergence domain of the obtained results by the LADM, the study has combined it with Padé approximation.
Findings
Accuracy and efficiency of the presented method are illustrated and denoted through the tables and figures. Also the effects of the suction parameter λ and slip parameter K on the fluid velocity and on the tangential stress are investigated.
Originality/value
The similarity solutions of the governing partial differential equation are obtained analytically by using an efficient developed method, namely the Laplace Adomian decomposition-Padé method. The analytic solutions of nonlinear ordinary differential equation are constructed for both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface.
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S. Abbasbandy and H. Roohani Ghehsareh
In this paper, an analysis is performed to find the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet.
Abstract
Purpose
In this paper, an analysis is performed to find the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet.
Design/methodology/approach
The cases of two dimensional and axisymmetric shrinking have been discussed. When the sheet is shrinking in the x‐direction, the analytical solutions are obtained by the Hankel‐Padé method. Comparison to exact solutions reveals reliability and high accuracy of the procedure, even in the case of multiple solutions. The case of sheet shrinking in the y‐direction is also considered, with success.
Findings
When the sheet shrinks in the x‐direction, the analytical solutions are obtained by Hankel‐Padé method. Also, when the sheet shrinks in the y‐direction, the obtained results with Hankel‐Padé method are presented.
Practical implications
Comparison to exact solutions reveals reliability and high accuracy of the procedure and convincingly could be used to obtain multiple solutions for certain parameter domains of this case of the governing nonlinear problem.
Originality/value
The numerical solutions are given for both two‐dimensional and axisymmetric shrinking sheets by using Hankel‐Padé method. It is clear that the Hankel‐Padé method is, by far, more simple, straightforward and gives reasonable results for large Hartman numbers and suction parameters.
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Davood Rostamy and Kobra Karimi
The purpose of this paper is to introduce a novel approach based on the high-order matrix derivative of the Bernstein basis and collocation method and its employment to solve an…
Abstract
Purpose
The purpose of this paper is to introduce a novel approach based on the high-order matrix derivative of the Bernstein basis and collocation method and its employment to solve an interesting and ill-posed model in the heat conduction problems, homogeneous backward heat conduction problem (BHCP).
Design/methodology/approach
By using the properties of the Bernstein polynomials the problems are reduced to an ill-conditioned linear system of equations. To overcome the unstability of the standard methods for solving the system of equations an efficient technique based on the Tikhonov regularization technique with GCV function method is used for solving the ill-condition system.
Findings
The presented numerical results through table and figures demonstrate the validity and applicability and accuracy of the technique.
Originality/value
A novel method based on the high-order matrix derivative of the Bernstein basis and collocation method is developed and well-used to obtain the numerical solutions of an interesting and ill-posed model in heat conduction problems, homogeneous BHCP with high accuracy.
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Gladys Tharapatla, Glory Tharapatla and Jaladi Rajendra Kumar
This paper aims to explore the numerical simulation of MHD flow of Williamson hybrid nanofluid over a porous stretched sheet. Cattaneo–Christov thermal and specie fluxes were used…
Abstract
Purpose
This paper aims to explore the numerical simulation of MHD flow of Williamson hybrid nanofluid over a porous stretched sheet. Cattaneo–Christov thermal and specie fluxes were used in the model. Partial differential equations are exploit to model the underlying physics of the situation (PDEs).
Design/methodology/approach
Using an acceptable similarity functions, these equations were changed into total differential equations (ODEs). The spectral relaxation method (SRM) was used to solve the linked and nonlinear altered ODEs. The Gauss–Seidel procedure is used to figure out how to use Chebyshev pseudospectral techniques in SRM. This is an iterative process.
Findings
Increasing the heat relaxation flow increases temperature distributions; increasing the mass relaxation flux increases concentration distributions. A higher value of thermal radiation heat generation and Eckert number was noticed to improve temperature and velocity distributions. Due to the imposed electromagnetic force, a higher magnetic field is detected to cause an elevation in the velocity distribution. Also, a higher thermal radiation is observed to upsurge the velocity in company with temperature distributions.
Originality/value
This research benefits from biomedical engineering, biological sciences, astrophysics and geophysics. The rheological applications of Williamson fluid finds usefulness in biological sciences. The nanoparticles as considered in this study finds applications in the field of biomedical engineering. Also, the application of the imposed electromagnetic field and magnetic field strength is very useful in the area of astrophysics. A good agreement may be found in the literature on this study’s findings.