A pressure driven axisymmetric flow in a circular tube, having a non- Newtonian Oldroyd 8-constan... more A pressure driven axisymmetric flow in a circular tube, having a non- Newtonian Oldroyd 8-constant fluid in the core, is considered in this paper. The Oldroyd 8-constant fluid is surrounded by a Newtonian fluid in the present study. The exact solution of the governing equation is obtained in the form of an integral which is evaluated using Gaussian quadrature. The expression for the apparent viscosity is obtained. The graphical results are presented for the pro les of apparent viscosity for different values of the material parameters plotted against tube radius. It is found that for all the values of the material parameters, the apparent viscosity decreases as the tube radius decreases which is the Fahraeus-Lindqvist eff ect. The results for the case, when there is no Newtonian fluid present in the periphery, are also deduced.
This article presented an analysis of the pulsatile flow of non-Newtonian micropolar (MP) fluid u... more This article presented an analysis of the pulsatile flow of non-Newtonian micropolar (MP) fluid under Lorentz force’s effect in a channel with symmetrical constrictions on the walls. The governing equations were first converted into the vorticity–stream function form, and a finite difference-based solver was used to solve it numerically on a Cartesian grid. The impacts of different flow controlling parameters, including the Hartman number, Strouhal number, Reynolds number, and MP parameter on the flow profiles, were studied. The wall shear stress (WSS), axial, and micro-rotation velocity profiles were depicted visually. The streamlines and vorticity patterns of the flow were also sketched. It is evident from the numerical results that the flow separation region near constriction as well as flattening of the axial velocity component is effectively controlled by the Hartmann number. At the maximum flow rate, the WSS attained its peak. The WSS increased in both the Hartmann number and ...
The present paper examines the flow behavior and separation region of a non-Newtonian electricall... more The present paper examines the flow behavior and separation region of a non-Newtonian electrically conducting Casson fluid through a two-dimensional porous channel by using Darcy’s law for the steady and pulsatile flows. The vorticity-stream function approach is employed for the numerical solution of the flow equations. The effects of various emerging parameters on wall shear stress and stream-wise velocity are displayed through graphs and discussed in detail. It is noticed the increasing values of the magnetic field parameter (Hartman number) cause vanishing of the flow separation region and flattening of the stream-wise velocity component. The study also reveals that the non-Newtonian character of Casson fluid bears the potential of controlling the flow separation region in both steady and pulsating flow conditions.
The study depicts the variations in the hydromagnetics flow of a Careau fluid in a semi permeable... more The study depicts the variations in the hydromagnetics flow of a Careau fluid in a semi permeable curved channel with convective boundary condition. Furthermore, Rosseland approximation is also considered to analyze the non-linear thermal radiation effects. Curvilinear co-ordinates system has been adopted for the mathematical modeling of the flow equations. The attained set of governing equation are then converted into non-linear dimensionless differential equations, by making use of similarity variables which are later treated by shooting method. In addition, the Newton?s Raphson method is also incepted to improve the accuracy of the obtained numerical result. The velocity field and temperature distributions are affected by various involved parameter which are presented in graphs and in table form. It is noticed that the velocity profiles are influenced by the change in the Weissenberg number.
Abstract.In this analysis, we have discussed the Blasius flow of a nanofluid over a curved surfac... more Abstract.In this analysis, we have discussed the Blasius flow of a nanofluid over a curved surface coiled in a circle of radius R . The physical situation is formulated in a mathematical model using a curvilinear coordinates system. The model is considered for the nanofluid including the effects of Brownian motion and thermophoresis in the presence of thermal radiation. A similarity solution of the developed ordinary differential equations is obtained numerically using the shooting method. The influence of the various involved parameters on the flow phenomena are analyzed through graphs and tables.
Journal of Mechanics in Medicine and Biology, 2017
Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical un... more Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the pro...
This study investigates the heat transfer characteristics for Blasius and Sakiadis flows over a c... more This study investigates the heat transfer characteristics for Blasius and Sakiadis flows over a curved surface coiled in a circle of radius R having constant curvature. Effects of thermal radiation are also analyzed for nonlinear Rosseland approximation which is valid for all values of the temperature difference between the fluid and the surface. The considered physical situation is represented by a mathematical model using curvilinear coordinates. Similar solutions of the developed partial differential equations are evaluated numerically using a shooting algorithm. Fluid velocity, skin-friction coefficient, temperature and local Nusselt number are the quantities of interest interpreted for the influence of pertinent parameters. A comparison of the present and the published data for a flat surface validates the obtained numerical solution for the curved geometry.
The boundary layer flow of a third grade fluid and mass transfer near a stagnation-point with dif... more The boundary layer flow of a third grade fluid and mass transfer near a stagnation-point with diffusion of chemically reacting species on a porous plate is investigated. Due to a porous plate the suction is taken into an account. Using suitable transformations, the momentum and concentration equations are first transformed into nonlinear ordinary ones and then solved using a hybrid numerical method. This method combines the features of finite difference and shooting methods. The effects of various controlling parameters on the flow velocity, concentration profile, skin friction and rate of mass transfer on surface are analyzed graphically and in tabular form. Comparison of the present results with the previous reported results has been found in excellent agreement.
International Communications in Heat and Mass Transfer
In this communication we address a recent article by Olajuwon [B.I. Olajuwon, Convection heat and... more In this communication we address a recent article by Olajuwon [B.I. Olajuwon, Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion, International Communications in Heat and Mass Transfer 38 (2011) 377–382]. We point out some errors in the mathematical formulation, numerical solution and the discussion of the results. It is believed that the readers of International Communications in Heat and Mass Transfer will gain better insight into the problem.
Little information is available on the impact of hemodialysis on cerebral water homeostasis and i... more Little information is available on the impact of hemodialysis on cerebral water homeostasis and its distribution in chronic kidney disease. We used a neuropsychological test battery, structural magnetic resonance imaging (MRI) and a novel technique for quantitative measurement of localized water content using 3T MRI to investigate ten hemodialysis patients (HD) on a dialysis-free day and after hemodialysis (2.4±2.2 hours), and a matched healthy control group with the same time interval. Neuropsychological testing revealed mainly attentional and executive cognitive dysfunction in HD. Voxel-based-morphometry showed only marginal alterations in the right inferior medial temporal lobe white matter in HD compared to controls. Marked increases in global brain water content were found in the white matter, specifically in parietal areas, in HD patients compared to controls. Although the global water content in the gray matter did not differ between the two groups, regional increases of brain water content in particular in parieto-temporal gray matter areas were observed in HD patients. No relevant brain hydration changes were revealed before and after hemodialysis. Whereas longer duration of dialysis vintage was associated with increased water content in parieto-temporal-occipital regions, lower intradialytic weight changes were negatively correlated with brain water content in these areas in HD patients. Worse cognitive performance on an attention task correlated with increased hydration in frontal white matter. In conclusion, long-term HD is associated with altered brain tissue water homeostasis mainly in parietal white matter regions, whereas the attentional domain in the cognitive dysfunction profile in HD could be linked to increased frontal white matter water content.
International Journal of Numerical Methods for Heat & Fluid Flow, 2011
PurposeThis paper looks into the rotating flow of an incompressible viscous fluid over an exponen... more PurposeThis paper looks into the rotating flow of an incompressible viscous fluid over an exponentially stretching continuous surface. The flow is governed by non‐linear partial differential equations. A non‐similar solution is developed after transforming the governing equations using two different numerical techniques namely Keller‐box and shooting methods. The influence of the non‐dimensional local rotating parameter Ω on the velocity fields and skin friction coefficients is analyzed and discussed.Design/methodology/approachIn this paper, the authors have used the well‐known numerical methods, Keller‐box and shooting.FindingsIt is observed that for the increase in the rotation velocity of the frame there is a reduction in the boundary layer thickness and an increase in the drag force at the surface.Originality/valueThe present study is concerned with the boundary layer flow of a rotating viscous fluid over an exponentially stretching sheet. Numerical solutions are found. To the b...
Journal of the Taiwan Institute of Chemical Engineers, 2010
This study deals the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer ana... more This study deals the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer analysis in an incompressible rotating viscous fluid over a stretching continuous sheet. A similar solution is developed numerically using the Keller-box method. The effects of the involving physical parameters on the velocity field, the temperature distribution, the local skin friction coefficients and the local Nusselt number are graphically shown and discussed. Comparison of the present results for hydrodynamic flow (M = 0) is given and found in excellent agreement with the existing results in the literature.
This Letter looks at the peristaltic flow of a micropolar fluid in a channel. Five illustrative w... more This Letter looks at the peristaltic flow of a micropolar fluid in a channel. Five illustrative wave forms are considered. Exact analytic solutions of the flow quantities are developed under long wavelength and low Reynolds number assumptions. Besides that the phenomena of pumping and trapping are analyzed. The comparison of the various considered wave forms on the flow is delineated.
The unsteady flow of a Maxwell fluid caused by a suddenly moved plane wall between two side walls... more The unsteady flow of a Maxwell fluid caused by a suddenly moved plane wall between two side walls perpendicular to the plane is considered. Closed form solution is developed employing the Fourier sine transforms. The solution obtained for large values of time is similar to the steady solution of a Newtonian fluid. The unsteady solution for a Newtonian fluid have been recovered as a limiting case by choosing → 0. The physical interpretation of the solution is presented through the graph and tables.
We deal with the study of momentum and heat transfer characteristics in a second-grade rotating f... more We deal with the study of momentum and heat transfer characteristics in a second-grade rotating flow past a porous plate. The analysis is performed when the suction velocity normal to the plate, as well as the external flow velocity, varies periodically with time. The plate is assumed at a higher temperature than the fluid. Analytic solutions for velocity, skin friction, and temperature are derived. The effects of various parameters of physical interest on the velocity, skin friction, and temperature are shown and discussed in detail.
The development of two-dimensional or axisymmetric stagnation flow of an incompressible viscous f... more The development of two-dimensional or axisymmetric stagnation flow of an incompressible viscous fluid over a moving plate with partial slip has been investigated. The effects of partial slip on the flow and heat transfer characteristics are considered. The equations of conservation of mass, momentum, and energy, which govern the flow and heat transfer, are solved analytically using homotopy analysis method. The convergence of the series solution is analyzed explicitly. Comparison of the present homotopy results is made with the existing numerical and asymptotic solution (Wang, 2006, “Stagnation Slip Flow and Heat Transfer on a Moving Plate,” Chem. Eng. Sci., 23, pp. 7668–7672) and an excellent agreement is achieved.
In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer... more In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer flow of a second grade fluid over a shrinking sheet. Both exact and series solutions have been determined. For the series solution, the governing nonlinear problem is solved using the homotopy analysis method. The convergence of the obtained solution is analyzed explicitly. Graphical results have been presented and discussed for the pertinent parameters.
International Journal of Heat and Mass Transfer, 2008
This paper deals with the study of the radiation effects on the magnetohydrodynamic (MHD) flow of... more This paper deals with the study of the radiation effects on the magnetohydrodynamic (MHD) flow of an incompressible viscous fluid in a porous space. The flow is induced due to a non-linear stretching sheet. Two cases of heat transfer analysis are discussed. These are: (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case). By means of similarity transformation, the governing partial differential equations are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using a very efficient technique namely homotopy analysis method (HAM). Expressions for velocity and temperature fields are developed in series form. Convergence of the series solution is shown explicitly. The influence of various pertinent parameters is also seen on the velocity and temperature fields. The tabulated values of the wall shear stress and the Nusselt number show good agreement with the existing results.
International Journal of Heat and Mass Transfer, 2008
An analytic technique, namely the homotopy analysis method (HAM), is applied to study the steady ... more An analytic technique, namely the homotopy analysis method (HAM), is applied to study the steady mixed convection in two-dimensional stagnation flows of a viscoelastic fluid around heated surfaces for the case when the temperature of the wall varies linearly with the distance from the stagnation point. The two-dimensional boundary layer equations governing the flow and thermal fields are reduced by appropriate transformations to a set of two ordinary differential equations. These equations are solved analytically using the HAM in the buoyancy assisting and opposing regions. It is found that, as for the Newtonian flow case, a reverse flow region develops in the buoyancy opposing flow region, and dual solutions are found to exist in that flow regime for a certain ranges of the buoyancy and viscoelastic parameters.
A pressure driven axisymmetric flow in a circular tube, having a non- Newtonian Oldroyd 8-constan... more A pressure driven axisymmetric flow in a circular tube, having a non- Newtonian Oldroyd 8-constant fluid in the core, is considered in this paper. The Oldroyd 8-constant fluid is surrounded by a Newtonian fluid in the present study. The exact solution of the governing equation is obtained in the form of an integral which is evaluated using Gaussian quadrature. The expression for the apparent viscosity is obtained. The graphical results are presented for the pro les of apparent viscosity for different values of the material parameters plotted against tube radius. It is found that for all the values of the material parameters, the apparent viscosity decreases as the tube radius decreases which is the Fahraeus-Lindqvist eff ect. The results for the case, when there is no Newtonian fluid present in the periphery, are also deduced.
This article presented an analysis of the pulsatile flow of non-Newtonian micropolar (MP) fluid u... more This article presented an analysis of the pulsatile flow of non-Newtonian micropolar (MP) fluid under Lorentz force’s effect in a channel with symmetrical constrictions on the walls. The governing equations were first converted into the vorticity–stream function form, and a finite difference-based solver was used to solve it numerically on a Cartesian grid. The impacts of different flow controlling parameters, including the Hartman number, Strouhal number, Reynolds number, and MP parameter on the flow profiles, were studied. The wall shear stress (WSS), axial, and micro-rotation velocity profiles were depicted visually. The streamlines and vorticity patterns of the flow were also sketched. It is evident from the numerical results that the flow separation region near constriction as well as flattening of the axial velocity component is effectively controlled by the Hartmann number. At the maximum flow rate, the WSS attained its peak. The WSS increased in both the Hartmann number and ...
The present paper examines the flow behavior and separation region of a non-Newtonian electricall... more The present paper examines the flow behavior and separation region of a non-Newtonian electrically conducting Casson fluid through a two-dimensional porous channel by using Darcy’s law for the steady and pulsatile flows. The vorticity-stream function approach is employed for the numerical solution of the flow equations. The effects of various emerging parameters on wall shear stress and stream-wise velocity are displayed through graphs and discussed in detail. It is noticed the increasing values of the magnetic field parameter (Hartman number) cause vanishing of the flow separation region and flattening of the stream-wise velocity component. The study also reveals that the non-Newtonian character of Casson fluid bears the potential of controlling the flow separation region in both steady and pulsating flow conditions.
The study depicts the variations in the hydromagnetics flow of a Careau fluid in a semi permeable... more The study depicts the variations in the hydromagnetics flow of a Careau fluid in a semi permeable curved channel with convective boundary condition. Furthermore, Rosseland approximation is also considered to analyze the non-linear thermal radiation effects. Curvilinear co-ordinates system has been adopted for the mathematical modeling of the flow equations. The attained set of governing equation are then converted into non-linear dimensionless differential equations, by making use of similarity variables which are later treated by shooting method. In addition, the Newton?s Raphson method is also incepted to improve the accuracy of the obtained numerical result. The velocity field and temperature distributions are affected by various involved parameter which are presented in graphs and in table form. It is noticed that the velocity profiles are influenced by the change in the Weissenberg number.
Abstract.In this analysis, we have discussed the Blasius flow of a nanofluid over a curved surfac... more Abstract.In this analysis, we have discussed the Blasius flow of a nanofluid over a curved surface coiled in a circle of radius R . The physical situation is formulated in a mathematical model using a curvilinear coordinates system. The model is considered for the nanofluid including the effects of Brownian motion and thermophoresis in the presence of thermal radiation. A similarity solution of the developed ordinary differential equations is obtained numerically using the shooting method. The influence of the various involved parameters on the flow phenomena are analyzed through graphs and tables.
Journal of Mechanics in Medicine and Biology, 2017
Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical un... more Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the pro...
This study investigates the heat transfer characteristics for Blasius and Sakiadis flows over a c... more This study investigates the heat transfer characteristics for Blasius and Sakiadis flows over a curved surface coiled in a circle of radius R having constant curvature. Effects of thermal radiation are also analyzed for nonlinear Rosseland approximation which is valid for all values of the temperature difference between the fluid and the surface. The considered physical situation is represented by a mathematical model using curvilinear coordinates. Similar solutions of the developed partial differential equations are evaluated numerically using a shooting algorithm. Fluid velocity, skin-friction coefficient, temperature and local Nusselt number are the quantities of interest interpreted for the influence of pertinent parameters. A comparison of the present and the published data for a flat surface validates the obtained numerical solution for the curved geometry.
The boundary layer flow of a third grade fluid and mass transfer near a stagnation-point with dif... more The boundary layer flow of a third grade fluid and mass transfer near a stagnation-point with diffusion of chemically reacting species on a porous plate is investigated. Due to a porous plate the suction is taken into an account. Using suitable transformations, the momentum and concentration equations are first transformed into nonlinear ordinary ones and then solved using a hybrid numerical method. This method combines the features of finite difference and shooting methods. The effects of various controlling parameters on the flow velocity, concentration profile, skin friction and rate of mass transfer on surface are analyzed graphically and in tabular form. Comparison of the present results with the previous reported results has been found in excellent agreement.
International Communications in Heat and Mass Transfer
In this communication we address a recent article by Olajuwon [B.I. Olajuwon, Convection heat and... more In this communication we address a recent article by Olajuwon [B.I. Olajuwon, Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion, International Communications in Heat and Mass Transfer 38 (2011) 377–382]. We point out some errors in the mathematical formulation, numerical solution and the discussion of the results. It is believed that the readers of International Communications in Heat and Mass Transfer will gain better insight into the problem.
Little information is available on the impact of hemodialysis on cerebral water homeostasis and i... more Little information is available on the impact of hemodialysis on cerebral water homeostasis and its distribution in chronic kidney disease. We used a neuropsychological test battery, structural magnetic resonance imaging (MRI) and a novel technique for quantitative measurement of localized water content using 3T MRI to investigate ten hemodialysis patients (HD) on a dialysis-free day and after hemodialysis (2.4±2.2 hours), and a matched healthy control group with the same time interval. Neuropsychological testing revealed mainly attentional and executive cognitive dysfunction in HD. Voxel-based-morphometry showed only marginal alterations in the right inferior medial temporal lobe white matter in HD compared to controls. Marked increases in global brain water content were found in the white matter, specifically in parietal areas, in HD patients compared to controls. Although the global water content in the gray matter did not differ between the two groups, regional increases of brain water content in particular in parieto-temporal gray matter areas were observed in HD patients. No relevant brain hydration changes were revealed before and after hemodialysis. Whereas longer duration of dialysis vintage was associated with increased water content in parieto-temporal-occipital regions, lower intradialytic weight changes were negatively correlated with brain water content in these areas in HD patients. Worse cognitive performance on an attention task correlated with increased hydration in frontal white matter. In conclusion, long-term HD is associated with altered brain tissue water homeostasis mainly in parietal white matter regions, whereas the attentional domain in the cognitive dysfunction profile in HD could be linked to increased frontal white matter water content.
International Journal of Numerical Methods for Heat & Fluid Flow, 2011
PurposeThis paper looks into the rotating flow of an incompressible viscous fluid over an exponen... more PurposeThis paper looks into the rotating flow of an incompressible viscous fluid over an exponentially stretching continuous surface. The flow is governed by non‐linear partial differential equations. A non‐similar solution is developed after transforming the governing equations using two different numerical techniques namely Keller‐box and shooting methods. The influence of the non‐dimensional local rotating parameter Ω on the velocity fields and skin friction coefficients is analyzed and discussed.Design/methodology/approachIn this paper, the authors have used the well‐known numerical methods, Keller‐box and shooting.FindingsIt is observed that for the increase in the rotation velocity of the frame there is a reduction in the boundary layer thickness and an increase in the drag force at the surface.Originality/valueThe present study is concerned with the boundary layer flow of a rotating viscous fluid over an exponentially stretching sheet. Numerical solutions are found. To the b...
Journal of the Taiwan Institute of Chemical Engineers, 2010
This study deals the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer ana... more This study deals the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer analysis in an incompressible rotating viscous fluid over a stretching continuous sheet. A similar solution is developed numerically using the Keller-box method. The effects of the involving physical parameters on the velocity field, the temperature distribution, the local skin friction coefficients and the local Nusselt number are graphically shown and discussed. Comparison of the present results for hydrodynamic flow (M = 0) is given and found in excellent agreement with the existing results in the literature.
This Letter looks at the peristaltic flow of a micropolar fluid in a channel. Five illustrative w... more This Letter looks at the peristaltic flow of a micropolar fluid in a channel. Five illustrative wave forms are considered. Exact analytic solutions of the flow quantities are developed under long wavelength and low Reynolds number assumptions. Besides that the phenomena of pumping and trapping are analyzed. The comparison of the various considered wave forms on the flow is delineated.
The unsteady flow of a Maxwell fluid caused by a suddenly moved plane wall between two side walls... more The unsteady flow of a Maxwell fluid caused by a suddenly moved plane wall between two side walls perpendicular to the plane is considered. Closed form solution is developed employing the Fourier sine transforms. The solution obtained for large values of time is similar to the steady solution of a Newtonian fluid. The unsteady solution for a Newtonian fluid have been recovered as a limiting case by choosing → 0. The physical interpretation of the solution is presented through the graph and tables.
We deal with the study of momentum and heat transfer characteristics in a second-grade rotating f... more We deal with the study of momentum and heat transfer characteristics in a second-grade rotating flow past a porous plate. The analysis is performed when the suction velocity normal to the plate, as well as the external flow velocity, varies periodically with time. The plate is assumed at a higher temperature than the fluid. Analytic solutions for velocity, skin friction, and temperature are derived. The effects of various parameters of physical interest on the velocity, skin friction, and temperature are shown and discussed in detail.
The development of two-dimensional or axisymmetric stagnation flow of an incompressible viscous f... more The development of two-dimensional or axisymmetric stagnation flow of an incompressible viscous fluid over a moving plate with partial slip has been investigated. The effects of partial slip on the flow and heat transfer characteristics are considered. The equations of conservation of mass, momentum, and energy, which govern the flow and heat transfer, are solved analytically using homotopy analysis method. The convergence of the series solution is analyzed explicitly. Comparison of the present homotopy results is made with the existing numerical and asymptotic solution (Wang, 2006, “Stagnation Slip Flow and Heat Transfer on a Moving Plate,” Chem. Eng. Sci., 23, pp. 7668–7672) and an excellent agreement is achieved.
In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer... more In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer flow of a second grade fluid over a shrinking sheet. Both exact and series solutions have been determined. For the series solution, the governing nonlinear problem is solved using the homotopy analysis method. The convergence of the obtained solution is analyzed explicitly. Graphical results have been presented and discussed for the pertinent parameters.
International Journal of Heat and Mass Transfer, 2008
This paper deals with the study of the radiation effects on the magnetohydrodynamic (MHD) flow of... more This paper deals with the study of the radiation effects on the magnetohydrodynamic (MHD) flow of an incompressible viscous fluid in a porous space. The flow is induced due to a non-linear stretching sheet. Two cases of heat transfer analysis are discussed. These are: (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case). By means of similarity transformation, the governing partial differential equations are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using a very efficient technique namely homotopy analysis method (HAM). Expressions for velocity and temperature fields are developed in series form. Convergence of the series solution is shown explicitly. The influence of various pertinent parameters is also seen on the velocity and temperature fields. The tabulated values of the wall shear stress and the Nusselt number show good agreement with the existing results.
International Journal of Heat and Mass Transfer, 2008
An analytic technique, namely the homotopy analysis method (HAM), is applied to study the steady ... more An analytic technique, namely the homotopy analysis method (HAM), is applied to study the steady mixed convection in two-dimensional stagnation flows of a viscoelastic fluid around heated surfaces for the case when the temperature of the wall varies linearly with the distance from the stagnation point. The two-dimensional boundary layer equations governing the flow and thermal fields are reduced by appropriate transformations to a set of two ordinary differential equations. These equations are solved analytically using the HAM in the buoyancy assisting and opposing regions. It is found that, as for the Newtonian flow case, a reverse flow region develops in the buoyancy opposing flow region, and dual solutions are found to exist in that flow regime for a certain ranges of the buoyancy and viscoelastic parameters.
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