In this article, the velocity profile of squeezing flow of an incompressible viscous fluid in a p... more In this article, the velocity profile of squeezing flow of an incompressible viscous fluid in a porous medium under the influence of uniform transverse magnetic field is argued. Both the continuity and momentum equations, with the help of vorticity and stream functions, are simultaneously transformed to an ordinary differential equation. Boundary conditions are also transformed with the help of transformation ψ(r, z) = rT (z). Homotopy Perturbation Method (HPM) is used to solve the boundary value problem obtained. Efficiency of the proposed scheme is examined with the help of residual. Effect of different parameters on the velocity profile is discussed through graphs. It is observed that both imposed magnetic field and electro conductivity are directly proportional to the velocity of fluid.
Advances in Materials Science and Engineering, 2017
This article presents a scheme for the analysis of an unsteady axisymmetric flow of incompressibl... more This article presents a scheme for the analysis of an unsteady axisymmetric flow of incompressible Newtonian material in the form of liquid squeezed between two circular plates. The scheme combines traditional perturbation technique with homotopy using an adaptation of the Laplace Transform. The proposed method is tested against other schemes such as the Regular Perturbation Method (RPM), Homotopy Perturbation Method (HPM), Optimal Homotopy Asymptotic Method (OHAM), and the fourth-order Explicit Runge-Kutta Method (ERK4). Comparison of the solutions along with absolute residual errors confirms that the proposed scheme surpasses HPM, OHAM, RPM, and ERK4 in terms of accuracy. The article also investigates the effect of Reynolds number on the velocity profile and pressure variation graphically.
An unsteady squeezing flow of Casson fluid having magnetohydrodynamic (MHD) effect and passing th... more An unsteady squeezing flow of Casson fluid having magnetohydrodynamic (MHD) effect and passing through porous medium channel is modeled and investigated. Similarity transformations are used to convert the partial differential equations (PDEs) of non-Newtonian fluid to a highly nonlinear fourth-order ordinary differential equation (ODE). The obtained boundary value problem is solved analytically by Homotopy Perturbation Method (HPM) and numerically by explicit Runge-Kutta method of order 4. For validity purpose, we compare the analytical and numerical results which show excellent agreement. Furthermore, comprehensive graphical analysis has been made to investigate the effects of various fluid parameters on the velocity profile. Analysis shows that positive and negative squeeze numberSqhave opposite effect on the velocity profile. It is also observed that Casson parameterβshows opposite effect on the velocity profile in case of positive and negative squeeze numberSq. MHD parameterMgan...
We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHA... more We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM). The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM), variational iteration (VIM), homotopy perturbation (HPM), and variational iteration decomposition method (VIDM). The results show that the proposed method is more effective and reliable.
We investigate squeezing flow between two large parallel plates by transforming the basic governi... more We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functionsur(r,z,t)=(1/r)(∂ψ/∂z)anduz(r,z,t)=−(1/r)(∂ψ/∂r)and a transformationψ(r,z)=r2F(z). The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.
International Journal of Technology Diffusion, 2010
This work presents an improvement on the simple algorithms of matrix inversion (Farooq & Hamid, 2... more This work presents an improvement on the simple algorithms of matrix inversion (Farooq & Hamid, 2010). This generalized algorithm supports selection of pivot randomly in the matrix thus supporting partial and full pivoting. The freedom in pivot selection can be used in minimizing the numerical error and prioritizing the variable to find the solution first. The algorithm is more suitable for finding inverse and determinant of dense matrices. The algorithm requires a mechanism for selection of pivot (e.g., selection of absolute maximum value) in the available sub-matrix and the mechanism to get the inverse from the final resultant matrix by rearranging the rows and columns. A method for assigning the sign of the determinant is also given. The algorithm is explained through solved examples. The number of arithmetic calculations performed by the algorithm is of O () however. The efficiency and simplicity of coding remains the same as of the original algorithm.
In this manuscript, An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed betw... more In this manuscript, An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates is studied with slip and no-slip boundaries. Using similarity transformation, the system of nonlinear partial differential equations is reduced to a single fourth order ordinary differential equation. The resulting boundary value problems are solved by optimal homotopy asymptotic method (OHAM) and fourth order explicit Runge-Kutta method (RK4). It is observed that the results obtained from OHAM are in good agreement with numerical results by means of residuals. Furthermore, the effects of various dimensionless parameters on the velocity profiles are investigated graphically.
A general investigation has been made and analytic solutions are provided corresponding to the fl... more A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper.
In the present work, in the presence of magnetic field and with slip boundary condition, squeezin... more In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.
International Journal of Technology Diffusion, 2010
In this paper, a new algorithm is proposed for finding inverse and determinant of a given matrix ... more In this paper, a new algorithm is proposed for finding inverse and determinant of a given matrix in one instance. The algorithm is straightforward in understanding and manual calculations. Computer implementation of the algorithm is extremely simple and is quite efficient in time and memory utilization. The algorithm is supported by an example. The number of multiplication/division performed by the algorithm is exactly; however, its efficiency lies in the simplicity of coding and minimal utilization of memory. Simple applicability and reduced execution time of the method is validated form the numerical experiments performed on test problems. The algorithm is applicable in the cases of pseudo inverses for non-square matrices and solution of system of linear equations with minor modification.
In this article, the velocity profile of squeezing flow of an incompressible viscous fluid in a p... more In this article, the velocity profile of squeezing flow of an incompressible viscous fluid in a porous medium under the influence of uniform transverse magnetic field is argued. Both the continuity and momentum equations, with the help of vorticity and stream functions, are simultaneously transformed to an ordinary differential equation. Boundary conditions are also transformed with the help of transformation ψ(r, z) = rT (z). Homotopy Perturbation Method (HPM) is used to solve the boundary value problem obtained. Efficiency of the proposed scheme is examined with the help of residual. Effect of different parameters on the velocity profile is discussed through graphs. It is observed that both imposed magnetic field and electro conductivity are directly proportional to the velocity of fluid.
Advances in Materials Science and Engineering, 2017
This article presents a scheme for the analysis of an unsteady axisymmetric flow of incompressibl... more This article presents a scheme for the analysis of an unsteady axisymmetric flow of incompressible Newtonian material in the form of liquid squeezed between two circular plates. The scheme combines traditional perturbation technique with homotopy using an adaptation of the Laplace Transform. The proposed method is tested against other schemes such as the Regular Perturbation Method (RPM), Homotopy Perturbation Method (HPM), Optimal Homotopy Asymptotic Method (OHAM), and the fourth-order Explicit Runge-Kutta Method (ERK4). Comparison of the solutions along with absolute residual errors confirms that the proposed scheme surpasses HPM, OHAM, RPM, and ERK4 in terms of accuracy. The article also investigates the effect of Reynolds number on the velocity profile and pressure variation graphically.
An unsteady squeezing flow of Casson fluid having magnetohydrodynamic (MHD) effect and passing th... more An unsteady squeezing flow of Casson fluid having magnetohydrodynamic (MHD) effect and passing through porous medium channel is modeled and investigated. Similarity transformations are used to convert the partial differential equations (PDEs) of non-Newtonian fluid to a highly nonlinear fourth-order ordinary differential equation (ODE). The obtained boundary value problem is solved analytically by Homotopy Perturbation Method (HPM) and numerically by explicit Runge-Kutta method of order 4. For validity purpose, we compare the analytical and numerical results which show excellent agreement. Furthermore, comprehensive graphical analysis has been made to investigate the effects of various fluid parameters on the velocity profile. Analysis shows that positive and negative squeeze numberSqhave opposite effect on the velocity profile. It is also observed that Casson parameterβshows opposite effect on the velocity profile in case of positive and negative squeeze numberSq. MHD parameterMgan...
We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHA... more We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM). The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM), variational iteration (VIM), homotopy perturbation (HPM), and variational iteration decomposition method (VIDM). The results show that the proposed method is more effective and reliable.
We investigate squeezing flow between two large parallel plates by transforming the basic governi... more We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functionsur(r,z,t)=(1/r)(∂ψ/∂z)anduz(r,z,t)=−(1/r)(∂ψ/∂r)and a transformationψ(r,z)=r2F(z). The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.
International Journal of Technology Diffusion, 2010
This work presents an improvement on the simple algorithms of matrix inversion (Farooq & Hamid, 2... more This work presents an improvement on the simple algorithms of matrix inversion (Farooq & Hamid, 2010). This generalized algorithm supports selection of pivot randomly in the matrix thus supporting partial and full pivoting. The freedom in pivot selection can be used in minimizing the numerical error and prioritizing the variable to find the solution first. The algorithm is more suitable for finding inverse and determinant of dense matrices. The algorithm requires a mechanism for selection of pivot (e.g., selection of absolute maximum value) in the available sub-matrix and the mechanism to get the inverse from the final resultant matrix by rearranging the rows and columns. A method for assigning the sign of the determinant is also given. The algorithm is explained through solved examples. The number of arithmetic calculations performed by the algorithm is of O () however. The efficiency and simplicity of coding remains the same as of the original algorithm.
In this manuscript, An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed betw... more In this manuscript, An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates is studied with slip and no-slip boundaries. Using similarity transformation, the system of nonlinear partial differential equations is reduced to a single fourth order ordinary differential equation. The resulting boundary value problems are solved by optimal homotopy asymptotic method (OHAM) and fourth order explicit Runge-Kutta method (RK4). It is observed that the results obtained from OHAM are in good agreement with numerical results by means of residuals. Furthermore, the effects of various dimensionless parameters on the velocity profiles are investigated graphically.
A general investigation has been made and analytic solutions are provided corresponding to the fl... more A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper.
In the present work, in the presence of magnetic field and with slip boundary condition, squeezin... more In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.
International Journal of Technology Diffusion, 2010
In this paper, a new algorithm is proposed for finding inverse and determinant of a given matrix ... more In this paper, a new algorithm is proposed for finding inverse and determinant of a given matrix in one instance. The algorithm is straightforward in understanding and manual calculations. Computer implementation of the algorithm is extremely simple and is quite efficient in time and memory utilization. The algorithm is supported by an example. The number of multiplication/division performed by the algorithm is exactly; however, its efficiency lies in the simplicity of coding and minimal utilization of memory. Simple applicability and reduced execution time of the method is validated form the numerical experiments performed on test problems. The algorithm is applicable in the cases of pseudo inverses for non-square matrices and solution of system of linear equations with minor modification.
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