Mohammad Mehdi Rashidi - Academia.edu (original) (raw)

Papers by Mohammad Mehdi Rashidi

In this paper, performance analysis one of the EG methods i.e. 2-Point Explicit Group Successive ... more In this paper, performance analysis one of the EG methods i.e. 2-Point Explicit Group Successive Over-Relaxation (2-EGSOR) will be investigated. The 2-EGSOR method will be applied sequentially in solving first order composite closed Newton-Cotes (1-CCNC) algebraic equations associated with the numerical solutions of the linear Fredholm integral equations of the second kind. Numerical results are included in order to verify the performance of the method compared with the 2-Point Explicit Group Gauss-Seidel (2-EGGS) method. Based on the numerical results obtained, the results show that 2-EGSOR method is better than 2-EGGS method in terms of number of iterations and CPU time.

Advanced Powder Technology, 2015

The nano-fluids in view of the fabulous thermal conductivity enhancement have been recognized use... more The nano-fluids in view of the fabulous thermal conductivity enhancement have been recognized useful in several industrial and engineering applications. Present study provides an analytical investigation of the fluid flow, heat and mass transfer and entropy generation for the steady laminar non-Newtonian nano-fluid flow induced by a stretching sheet in the presence of velocity slip and convective surface boundary conditions using Optimal Homotopy Analysis Method (OHAM). In contrast to the conventional no-slip condition at the surface, Navier's slip condition is applied. The governing partial differential equations (PDEs) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) consist of the momentum, energy and concentration equations via appropriate similarity transformations. Entropy generation equations, for the first time in this problem, are derived as a function of velocity, temperature and concentration gradients. The current OHAM solution demonstrates very good correlation with those of the previously published studies in the especial cases. The influences of different flow physical parameters on fluid velocity component, temperature distribution and concentration profile as well as the entropy generation number are discussed in details. Increasing the Brownian motion parameter and thermophoresis parameter, Biot number, Reynolds number, and Brinkman number or decreasing the Casson parameter and velocity slip parameter cause an increase in the entropy generation number. (M.H. Abolbashari). Advanced Powder Technology xxx (2015) xxx-xxx Contents lists available at ScienceDirect Advanced Powder Technology j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p t Please cite this article in press as: M.H. Abolbashari et al., Analytical modeling of entropy generation for Casson nano-fluid flow induced by a stretching surface, Advanced Powder Technology (2015), http://dx.

In this paper, a novel analytical method (DTM-Padé) is proposed for solving nonlinear differentia... more In this paper, a novel analytical method (DTM-Padé) is proposed for solving nonlinear differential equations, especially for boundary-layer and natural convection problems. This method is based on combination of the differential transform method and the Padé approximant that we use for solve the thermal boundary-layer over a flat plate with a convective surface boundary condition. This technique is extended to give solutions for nonlinear differential equations whit boundary conditions at the infinity. In order to show the effectiveness of the DTM-Padé, the results obtained from the DTM-Padé is compared with available solutions obtained using Runge-Kutta-Fehlberg fourth-fifth order (RFK45) method to generate the numerical solution. Numerical comparisons between the DTM-Padé and the RFK45 reveal that the new technique introduced here is a promising tool for solving nonlinear differential equations whit infinity boundary conditions.

I. INTRODUCTION Magnetohydrodynamics (MHD) is the study of the interaction of conducting fluids w... more I. INTRODUCTION Magnetohydrodynamics (MHD) is the study of the interaction of conducting fluids with electromagnetic phenomena. The flow of an electrically conducting fluid in the presence of a magnetic field is of importance in various areas of technology and engineering such ...

Purpose -The purpose of this paper is to investigate the nano boundary-layer flows over stretchin... more Purpose -The purpose of this paper is to investigate the nano boundary-layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary differential equation by presented similarity transformation. The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method. The authors consider two types of flows: viscous flows over a two-dimensional stretching surface; and viscous flows over an axisymmetric stretching surface. Design/methodology/approach -The governing equation is solved analytically by applying a newly developed method, namely the differential transform method (DTM)-Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials. Findings -Graphical results are presented to investigate influence of the slip parameter and the suction parameter on the normal velocity and on the lateral velocity. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. It is predicted that the DTM-Padé can have wide application in engineering problems especially for boundary-layer problems. Originality/value -The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method, namely the DTM-Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

A coupled system of nonlinear ordinary differential equations that models the three-dimensional f... more A coupled system of nonlinear ordinary differential equations that models the three-dimensional flow of a nanofluid in a rotating channel on a lower permeable stretching porous wall is derived. The mathematical equations are derived from the Navier-Stokes equations where the governing equations are normalized by suitable similarity transformations. The fluid in the rotating channel is water that contains different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The differential transform method (DTM) is employed to solve the coupled system of nonlinear ordinary differential equations. The effects of the following physical parameters on the flow are investigated: characteristic parameter of the flow, rotation parameter, the magnetic parameter, nanoparticle volume fraction, the suction parameter, and different types of nanoparticles. Results are illustrated graphically and discussed in detail.

In this study combined heat and mass transfer by mixed convective flow along a moving vertical fl... more In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, C f x x , local Nusselt number, Nu x x , and local Sherwood number Sh x x are shown and explained through tables.

Physical Science International Journal, 2015

The main concern of present study is to investigate the MHD stagnation flow past a porous rotatin... more The main concern of present study is to investigate the MHD stagnation flow past a porous rotating disk in the presence of the velocity slip condition. The boundary-layer governing partial differential equations (PDEs) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) consist of the momentum and energy equations using similarity solution. The velocity profiles in radial, tangential and axial directions and temperature distribution are obtained via a semi analytical/numerical method, called Homotopy Analysis Method (HAM). An excellent agreement is observed between some of the obtained results of the current study and those of previously published studies. The influences of physical flow parameters such as magnetic interaction parameter , slip factor ( ) γ , rotation strength parameter ( ) ω , and suction parameter ( ) s W on the all fluid velocity components, temperature distribution as well as the skin friction coefficients and the rate of heat transfer are examined and analyzed. This simulation presents the feasibility of using magnetic rotating disk drives in novel nuclear space propulsion engines.

Asian Journal on Quality, 2011

... Baki, B., Cigdem, SB, Zuhal, C., Ilker, MAR (2009), "An application of integrati... more ... Baki, B., Cigdem, SB, Zuhal, C., Ilker, MAR (2009), "An application of integrating SERVQUAL and Kano's model into QFD for logistics services: a case study from Turkey", Asia Pacific Journal of Marketing and Logistics., Vol. 21 No.1, pp.106-26. ...

Bioimpacts, 2014

Introduction: A number of assays have so far been exploited for detection of cancer biomarkers in... more Introduction: A number of assays have so far been exploited for detection of cancer biomarkers in various malignancies. However, the expression of cancer biomarker(s) appears to be extremely low, therefore accurate detection demands sensitive optical imaging probes. While optical detection using conventional fluorophores often fail due to photobleaching problems, quantum dots (QDs) offer stable optical imaging in vitro and in vivo. Methods: In this review, we briefly overview the impacts of QDs in biology and its applications in bioimaging of malignancies. We will also delineate the existing obstacles for early detection of cancer and the intensifying use of QDs in advancement of diagnostic devices. Results: Of the QDs, unlike the II-VI type QDs (e.g., cadmium (Cd), selenium (Se) or tellurium (Te)) that possess inherent cytotoxicity, the I-III-VI 2 type QDs (e.g., AgInS 2 , CuInS 2 , ZnS-AgInS 2 ) appear to be less toxic bioimaging agents with better control of band-gap energies. As highly-sensitive bioimaging probes, advanced hybrid QDs (e.g., QD-QD, fluorochrome-QD conjugates used for sensing through fluorescence resonance energy transfer (FRET), quenching, and barcoding techniques) have also been harnessed for the detection of biomarkers and the monitoring of delivery of drugs/genes to the target sites. Antibody-QD (Ab-QD) and aptamer-QD (Ap-QD) bioconjugates, once target the relevant biomarker, can provide highly stable photoluminescence (PL) at the target sites. In addition to their potential as nanobiosensors, the bioconjugates of QDs with homing devices have successfully been used for the development of smart nanosystems (NSs) providing targeted bioimaging and photodynamic therapy (PDT). Conclusion: Having possessed great deal of photonic characteristics, QDs can be used for development of seamless multifunctional nanomedicines, theranostics and nanobiosensors.

Numerical Methods for Partial Differential Equations, 2009

... Correspondence to: MM Rashidi, Mechanical Engineering Department, Engineering Faculty, Bu-Ali... more ... Correspondence to: MM Rashidi, Mechanical Engineering Department, Engineering Faculty, Bu-Ali Sina University, Hamedan, Iran (e-mail: mm_rashidi@yahoo.com ... equations by Ganji and Sadighi [19], to the Helmholtz equation and fifth-order KdV equation by Rafei and Ganji ...

Numerical Methods for Partial Differential Equations, 2009

... Three-Dimensional Navier-Stokes Equations of Flow Between Two Stretchable Disks Saeed Dinarva... more ... Three-Dimensional Navier-Stokes Equations of Flow Between Two Stretchable Disks Saeed Dinarvand, Mohammad Mehdi Rashidi, Hamed Shahmohamadi Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran ...

Numerical Methods for Partial Differential Equations, 2009

In this work, the homotopy analysis method (HAM) is applied to obtain the explicit analytical sol... more In this work, the homotopy analysis method (HAM) is applied to obtain the explicit analytical solutions for system of the Jaulent-Miodek equations. The validity of the method is verified by comparing the approximation series solutions with the exact solutions. Unlike perturbation methods, the HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniques, the HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter . Briefly speaking, this work verifies the validity and the potential of the HAM for the study of nonlinear systems.

Nonlinear Analysis: Real World Applications, 2009

The similarity transform for the steady three-dimensional problem of a condensation film on an in... more The similarity transform for the steady three-dimensional problem of a condensation film on an inclined rotating disk gives a system of nonlinear ordinary differential equations which are analytically solved by applying a newly developed method namely the homotopy analysis method ...

Nonlinear Analysis: Real World Applications, 2010

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous ... more The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial ...

Mathematical Problems in Engineering, 2008

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion o... more The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourthorder differential equation by using similarity solutions. Homotopy analysis method HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

Mathematical Problems in Engineering, 2014

International Journal of Thermal Sciences, 2010

In this study, the problem of mixed convection about an inclined flat plate embedded in a porous ... more In this study, the problem of mixed convection about an inclined flat plate embedded in a porous medium is performed. The similarity transformations are applied to reduce governing partial differential equations (PDEs) to a set of nonlinear coupled ordinary differential equations (ODEs) in dimensionless form. An efficient mathematical technique, called the differential transform method (DTM), is used to solve the nonlinear differential equations governing the problem in the form of series with easily computable terms. Then, Padé approximant is applied to the solutions to increase the convergence of given series. It has been attempted to show the reliability and performance of the DTM in comparison with the numerical method (fourth-order RungeeKutta) in solving this problem. The obtained solutions, in comparison with the numerical solutions admit a remarkable accuracy.

International Journal for Computational Methods in Engineering Science and Mechanics, 2012

In this study, the problem of unsteady squeezing flow between Q1 circular parallel plates is perf... more In this study, the problem of unsteady squeezing flow between Q1 circular parallel plates is performed. The similarity transformation is applied to reduce a governing partial differential equation (PDE) to a nonlinear ordinary differential equation ODE) in dimension-10 less form. A new method, called the homotopy analytical method (HAM), is applied to obtain approximate analytical solution of this nonlinear equation. The obtained solutions, in comparison with the numerical solutions (fourth-order Runge-Kutta scheme), admit a remarkable accuracy. 15

International Journal for Computational Methods in Engineering Science and Mechanics, 2011

A new analytical method was developed for solving two-dimensional viscous flow. The flow is incom... more A new analytical method was developed for solving two-dimensional viscous flow. The flow is incompressible, laminar, and isothermal in a rectangular domain bounded by two moving porous walls. An efficient mathematical technique (differential transform method (DTM)) was used to solve the governing equation in the form of a series with easily computable terms. Graphical results were presented to investigate the

In this paper, performance analysis one of the EG methods i.e. 2-Point Explicit Group Successive ... more In this paper, performance analysis one of the EG methods i.e. 2-Point Explicit Group Successive Over-Relaxation (2-EGSOR) will be investigated. The 2-EGSOR method will be applied sequentially in solving first order composite closed Newton-Cotes (1-CCNC) algebraic equations associated with the numerical solutions of the linear Fredholm integral equations of the second kind. Numerical results are included in order to verify the performance of the method compared with the 2-Point Explicit Group Gauss-Seidel (2-EGGS) method. Based on the numerical results obtained, the results show that 2-EGSOR method is better than 2-EGGS method in terms of number of iterations and CPU time.

Advanced Powder Technology, 2015

The nano-fluids in view of the fabulous thermal conductivity enhancement have been recognized use... more The nano-fluids in view of the fabulous thermal conductivity enhancement have been recognized useful in several industrial and engineering applications. Present study provides an analytical investigation of the fluid flow, heat and mass transfer and entropy generation for the steady laminar non-Newtonian nano-fluid flow induced by a stretching sheet in the presence of velocity slip and convective surface boundary conditions using Optimal Homotopy Analysis Method (OHAM). In contrast to the conventional no-slip condition at the surface, Navier's slip condition is applied. The governing partial differential equations (PDEs) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) consist of the momentum, energy and concentration equations via appropriate similarity transformations. Entropy generation equations, for the first time in this problem, are derived as a function of velocity, temperature and concentration gradients. The current OHAM solution demonstrates very good correlation with those of the previously published studies in the especial cases. The influences of different flow physical parameters on fluid velocity component, temperature distribution and concentration profile as well as the entropy generation number are discussed in details. Increasing the Brownian motion parameter and thermophoresis parameter, Biot number, Reynolds number, and Brinkman number or decreasing the Casson parameter and velocity slip parameter cause an increase in the entropy generation number. (M.H. Abolbashari). Advanced Powder Technology xxx (2015) xxx-xxx Contents lists available at ScienceDirect Advanced Powder Technology j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p t Please cite this article in press as: M.H. Abolbashari et al., Analytical modeling of entropy generation for Casson nano-fluid flow induced by a stretching surface, Advanced Powder Technology (2015), http://dx.

In this paper, a novel analytical method (DTM-Padé) is proposed for solving nonlinear differentia... more In this paper, a novel analytical method (DTM-Padé) is proposed for solving nonlinear differential equations, especially for boundary-layer and natural convection problems. This method is based on combination of the differential transform method and the Padé approximant that we use for solve the thermal boundary-layer over a flat plate with a convective surface boundary condition. This technique is extended to give solutions for nonlinear differential equations whit boundary conditions at the infinity. In order to show the effectiveness of the DTM-Padé, the results obtained from the DTM-Padé is compared with available solutions obtained using Runge-Kutta-Fehlberg fourth-fifth order (RFK45) method to generate the numerical solution. Numerical comparisons between the DTM-Padé and the RFK45 reveal that the new technique introduced here is a promising tool for solving nonlinear differential equations whit infinity boundary conditions.

I. INTRODUCTION Magnetohydrodynamics (MHD) is the study of the interaction of conducting fluids w... more I. INTRODUCTION Magnetohydrodynamics (MHD) is the study of the interaction of conducting fluids with electromagnetic phenomena. The flow of an electrically conducting fluid in the presence of a magnetic field is of importance in various areas of technology and engineering such ...

Purpose -The purpose of this paper is to investigate the nano boundary-layer flows over stretchin... more Purpose -The purpose of this paper is to investigate the nano boundary-layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary differential equation by presented similarity transformation. The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method. The authors consider two types of flows: viscous flows over a two-dimensional stretching surface; and viscous flows over an axisymmetric stretching surface. Design/methodology/approach -The governing equation is solved analytically by applying a newly developed method, namely the differential transform method (DTM)-Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials. Findings -Graphical results are presented to investigate influence of the slip parameter and the suction parameter on the normal velocity and on the lateral velocity. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. It is predicted that the DTM-Padé can have wide application in engineering problems especially for boundary-layer problems. Originality/value -The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method, namely the DTM-Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

A coupled system of nonlinear ordinary differential equations that models the three-dimensional f... more A coupled system of nonlinear ordinary differential equations that models the three-dimensional flow of a nanofluid in a rotating channel on a lower permeable stretching porous wall is derived. The mathematical equations are derived from the Navier-Stokes equations where the governing equations are normalized by suitable similarity transformations. The fluid in the rotating channel is water that contains different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The differential transform method (DTM) is employed to solve the coupled system of nonlinear ordinary differential equations. The effects of the following physical parameters on the flow are investigated: characteristic parameter of the flow, rotation parameter, the magnetic parameter, nanoparticle volume fraction, the suction parameter, and different types of nanoparticles. Results are illustrated graphically and discussed in detail.

In this study combined heat and mass transfer by mixed convective flow along a moving vertical fl... more In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, C f x x , local Nusselt number, Nu x x , and local Sherwood number Sh x x are shown and explained through tables.

Physical Science International Journal, 2015

The main concern of present study is to investigate the MHD stagnation flow past a porous rotatin... more The main concern of present study is to investigate the MHD stagnation flow past a porous rotating disk in the presence of the velocity slip condition. The boundary-layer governing partial differential equations (PDEs) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) consist of the momentum and energy equations using similarity solution. The velocity profiles in radial, tangential and axial directions and temperature distribution are obtained via a semi analytical/numerical method, called Homotopy Analysis Method (HAM). An excellent agreement is observed between some of the obtained results of the current study and those of previously published studies. The influences of physical flow parameters such as magnetic interaction parameter , slip factor ( ) γ , rotation strength parameter ( ) ω , and suction parameter ( ) s W on the all fluid velocity components, temperature distribution as well as the skin friction coefficients and the rate of heat transfer are examined and analyzed. This simulation presents the feasibility of using magnetic rotating disk drives in novel nuclear space propulsion engines.

Asian Journal on Quality, 2011

... Baki, B., Cigdem, SB, Zuhal, C., Ilker, MAR (2009), "An application of integrati... more ... Baki, B., Cigdem, SB, Zuhal, C., Ilker, MAR (2009), "An application of integrating SERVQUAL and Kano's model into QFD for logistics services: a case study from Turkey", Asia Pacific Journal of Marketing and Logistics., Vol. 21 No.1, pp.106-26. ...

Bioimpacts, 2014

Introduction: A number of assays have so far been exploited for detection of cancer biomarkers in... more Introduction: A number of assays have so far been exploited for detection of cancer biomarkers in various malignancies. However, the expression of cancer biomarker(s) appears to be extremely low, therefore accurate detection demands sensitive optical imaging probes. While optical detection using conventional fluorophores often fail due to photobleaching problems, quantum dots (QDs) offer stable optical imaging in vitro and in vivo. Methods: In this review, we briefly overview the impacts of QDs in biology and its applications in bioimaging of malignancies. We will also delineate the existing obstacles for early detection of cancer and the intensifying use of QDs in advancement of diagnostic devices. Results: Of the QDs, unlike the II-VI type QDs (e.g., cadmium (Cd), selenium (Se) or tellurium (Te)) that possess inherent cytotoxicity, the I-III-VI 2 type QDs (e.g., AgInS 2 , CuInS 2 , ZnS-AgInS 2 ) appear to be less toxic bioimaging agents with better control of band-gap energies. As highly-sensitive bioimaging probes, advanced hybrid QDs (e.g., QD-QD, fluorochrome-QD conjugates used for sensing through fluorescence resonance energy transfer (FRET), quenching, and barcoding techniques) have also been harnessed for the detection of biomarkers and the monitoring of delivery of drugs/genes to the target sites. Antibody-QD (Ab-QD) and aptamer-QD (Ap-QD) bioconjugates, once target the relevant biomarker, can provide highly stable photoluminescence (PL) at the target sites. In addition to their potential as nanobiosensors, the bioconjugates of QDs with homing devices have successfully been used for the development of smart nanosystems (NSs) providing targeted bioimaging and photodynamic therapy (PDT). Conclusion: Having possessed great deal of photonic characteristics, QDs can be used for development of seamless multifunctional nanomedicines, theranostics and nanobiosensors.

Numerical Methods for Partial Differential Equations, 2009

... Correspondence to: MM Rashidi, Mechanical Engineering Department, Engineering Faculty, Bu-Ali... more ... Correspondence to: MM Rashidi, Mechanical Engineering Department, Engineering Faculty, Bu-Ali Sina University, Hamedan, Iran (e-mail: mm_rashidi@yahoo.com ... equations by Ganji and Sadighi [19], to the Helmholtz equation and fifth-order KdV equation by Rafei and Ganji ...

Numerical Methods for Partial Differential Equations, 2009

... Three-Dimensional Navier-Stokes Equations of Flow Between Two Stretchable Disks Saeed Dinarva... more ... Three-Dimensional Navier-Stokes Equations of Flow Between Two Stretchable Disks Saeed Dinarvand, Mohammad Mehdi Rashidi, Hamed Shahmohamadi Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran ...

Numerical Methods for Partial Differential Equations, 2009

In this work, the homotopy analysis method (HAM) is applied to obtain the explicit analytical sol... more In this work, the homotopy analysis method (HAM) is applied to obtain the explicit analytical solutions for system of the Jaulent-Miodek equations. The validity of the method is verified by comparing the approximation series solutions with the exact solutions. Unlike perturbation methods, the HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniques, the HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter . Briefly speaking, this work verifies the validity and the potential of the HAM for the study of nonlinear systems.

Nonlinear Analysis: Real World Applications, 2009

The similarity transform for the steady three-dimensional problem of a condensation film on an in... more The similarity transform for the steady three-dimensional problem of a condensation film on an inclined rotating disk gives a system of nonlinear ordinary differential equations which are analytically solved by applying a newly developed method namely the homotopy analysis method ...

Nonlinear Analysis: Real World Applications, 2010

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous ... more The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial ...

Mathematical Problems in Engineering, 2008

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion o... more The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourthorder differential equation by using similarity solutions. Homotopy analysis method HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

Mathematical Problems in Engineering, 2014

International Journal of Thermal Sciences, 2010

In this study, the problem of mixed convection about an inclined flat plate embedded in a porous ... more In this study, the problem of mixed convection about an inclined flat plate embedded in a porous medium is performed. The similarity transformations are applied to reduce governing partial differential equations (PDEs) to a set of nonlinear coupled ordinary differential equations (ODEs) in dimensionless form. An efficient mathematical technique, called the differential transform method (DTM), is used to solve the nonlinear differential equations governing the problem in the form of series with easily computable terms. Then, Padé approximant is applied to the solutions to increase the convergence of given series. It has been attempted to show the reliability and performance of the DTM in comparison with the numerical method (fourth-order RungeeKutta) in solving this problem. The obtained solutions, in comparison with the numerical solutions admit a remarkable accuracy.

International Journal for Computational Methods in Engineering Science and Mechanics, 2012

In this study, the problem of unsteady squeezing flow between Q1 circular parallel plates is perf... more In this study, the problem of unsteady squeezing flow between Q1 circular parallel plates is performed. The similarity transformation is applied to reduce a governing partial differential equation (PDE) to a nonlinear ordinary differential equation ODE) in dimension-10 less form. A new method, called the homotopy analytical method (HAM), is applied to obtain approximate analytical solution of this nonlinear equation. The obtained solutions, in comparison with the numerical solutions (fourth-order Runge-Kutta scheme), admit a remarkable accuracy. 15

International Journal for Computational Methods in Engineering Science and Mechanics, 2011

A new analytical method was developed for solving two-dimensional viscous flow. The flow is incom... more A new analytical method was developed for solving two-dimensional viscous flow. The flow is incompressible, laminar, and isothermal in a rectangular domain bounded by two moving porous walls. An efficient mathematical technique (differential transform method (DTM)) was used to solve the governing equation in the form of a series with easily computable terms. Graphical results were presented to investigate the