The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The non...The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.展开更多
A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using su...A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.展开更多
This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating （viscous dissipat...This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating （viscous dissipation） and internal heat generation or ab- sorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature （VWT） and variable heat flux （VHF）. The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction pa- rameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.展开更多
Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analy...Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.展开更多
The melting phenomenon plays a critical role in optimizing the performance of power storage, electronic cooling, and semiconductor devices. The present study aims to analyzethe melting effect on the flow of Carreau fl...The melting phenomenon plays a critical role in optimizing the performance of power storage, electronic cooling, and semiconductor devices. The present study aims to analyzethe melting effect on the flow of Carreau fluid over a stretchable cylinder, with special consideration given to the impact of quadratic thermal radiation. Similarity variables and the homotopy analysis method are used to simplify and determine the semi-analytical homotopicsolutions of the governing equations. The present findings reveal that the melting parameter increases the heat transfer rate by more than 10% for both fluids, water (Pr=0.71), and polymer(Pr=10). However, as the temperature ratio due to quadratic radiation increases, the localNusselt number for water has been reduced by 25%, and an even more substantial reductionis observed for the polymer. The present study offers valuable insights into achieving optimalefficiency in electronic devices.展开更多
In the current work,inclined magnetic field,thermal radiation,and the Cattaneo-Christov heat flux are taken into account as we analyze the impact of chemical reaction on magneto-hydrodynamic Casson nanofluid flow on a...In the current work,inclined magnetic field,thermal radiation,and the Cattaneo-Christov heat flux are taken into account as we analyze the impact of chemical reaction on magneto-hydrodynamic Casson nanofluid flow on a stretching sheet.Modified Buongiorno’s nanofluid model has been used to model the flow governing equations.The stretching surface is embedded in a porousmedium.By using similarity transformations,the nonlinear partial differential equations are transformed into a set of dimensionless ordinary differential equations.The numerical solution of transformed dimensionless equations is achieved by applying the shooting procedure together with Rung-Kutta 4th-order method employing MATLAB.The impact of significant parameters on the velocity profile f(ζ),temperature distributionθ(ζ),concentration profileϕ(ζ),skin friction coefficient(Cf),Nusselt number(Nux)and Sherwood number(Shx)are analyzed and displayed in graphical and tabular formats.With an increase in Casson fluid 0.5<β<2,the motion of the Casson fluid decelerates whereas the temperature profile increases.As the thermal relation factor expands 0.1<γ1<0.4,the temperature reduces,and consequently thermal boundary layer shrinks.Additionally,by raising the level of thermal radiation 1<Rd<7,the temperature profile significantly improves,and an abrupt expansion has also been observed in the associated thermal boundary with raise thermal radiation strength.It was observed that higher permeability 0<K<4 hinders the acceleration of Casson fluid.Higher Brownian motion levels 0.2<Nb<0.6 correspond to lower levels of the Casson fluid concentration profile.Moreover,it is observed that chemical reaction 0.2<γ2<0.5 has an inverse relation with the concentration level of Casson fluid.The current model’s significant uses include heat energy enhancement,petroleum recovery,energy devices,food manufacturing processes,and cooling device adjustment,among others.Furthermore,present outcomes have been found in great agreementwith already publishedwork.展开更多
The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal m...The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized flow.The convective boundary assumptions are directed in order to examine the heat and mass transportation of nanofluid.The thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno model.The problem formulated in dimensionless form is solved by NDSolve MATHEMATICA.The graphical analysis for parameters governed by the problem is performed with physical applications.The affiliation of entropy generation and Bejan number for different parameters is inspected in detail.The numerical data for illustrating skin friction,heat and mass transfer rate is also reported.The motion of the fluid is highest for the viscosity ratio parameter.The temperature of the fluid rises via thermal Biot number.Entropy generation rises for greater Brinkman number and diffusion parameter.展开更多
An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. ...An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.展开更多
The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting ...The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.展开更多
The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip fa...The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.展开更多
This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid beh...This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid behavior. The flow is subjected to suction/blowing at the surface. Analysis is carded out in presence of thermal radiation and prescribed surface heat flux. In this study, an exponential order stretching velocity and prescribed exponential order surface heat flux are accorded with each other. The governing partial differential equations are first converted into nonlinear ordinary differential equations by using appropriate transformations and then solved numerically. The effect of increasing values of the Casson parameter is to suppress the velocity field. However the temperature is enhanced when Casson parameter increases. It is found that the skin-friction coefficient increases with increasing values of suction parameter. Temperature also increases for large values of power index n in both suction and blowing cases at the boundary. It is observed that the thermal radiation enhances the effective thermal diffusivity and hence the temperature rises.展开更多
基金supported by the Fundamental Research Grant Scheme (FRGS) of the Ministry of Higher Education (MOHE) of Malaysia (No. UKM-ST-07-FRGS0036-2009)
文摘The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.
基金UGC,New Delhi,India under the Special Assistance Programme DSA Phase-1
文摘A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.
基金Project supported by the Major Research Project of Department of Science and Technology (DST)of New Delhi (No. SR/S4/MS:470/07,25-08-2008)
文摘This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating （viscous dissipation） and internal heat generation or ab- sorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature （VWT） and variable heat flux （VHF）. The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction pa- rameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.
文摘Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.
基金granted under vote numbers Q.J130000.3854.31J28 (UTMER)and Q.J130000.3854.23H22 (UTMFR)。
文摘The melting phenomenon plays a critical role in optimizing the performance of power storage, electronic cooling, and semiconductor devices. The present study aims to analyzethe melting effect on the flow of Carreau fluid over a stretchable cylinder, with special consideration given to the impact of quadratic thermal radiation. Similarity variables and the homotopy analysis method are used to simplify and determine the semi-analytical homotopicsolutions of the governing equations. The present findings reveal that the melting parameter increases the heat transfer rate by more than 10% for both fluids, water (Pr=0.71), and polymer(Pr=10). However, as the temperature ratio due to quadratic radiation increases, the localNusselt number for water has been reduced by 25%, and an even more substantial reductionis observed for the polymer. The present study offers valuable insights into achieving optimalefficiency in electronic devices.
文摘In the current work,inclined magnetic field,thermal radiation,and the Cattaneo-Christov heat flux are taken into account as we analyze the impact of chemical reaction on magneto-hydrodynamic Casson nanofluid flow on a stretching sheet.Modified Buongiorno’s nanofluid model has been used to model the flow governing equations.The stretching surface is embedded in a porousmedium.By using similarity transformations,the nonlinear partial differential equations are transformed into a set of dimensionless ordinary differential equations.The numerical solution of transformed dimensionless equations is achieved by applying the shooting procedure together with Rung-Kutta 4th-order method employing MATLAB.The impact of significant parameters on the velocity profile f(ζ),temperature distributionθ(ζ),concentration profileϕ(ζ),skin friction coefficient(Cf),Nusselt number(Nux)and Sherwood number(Shx)are analyzed and displayed in graphical and tabular formats.With an increase in Casson fluid 0.5<β<2,the motion of the Casson fluid decelerates whereas the temperature profile increases.As the thermal relation factor expands 0.1<γ1<0.4,the temperature reduces,and consequently thermal boundary layer shrinks.Additionally,by raising the level of thermal radiation 1<Rd<7,the temperature profile significantly improves,and an abrupt expansion has also been observed in the associated thermal boundary with raise thermal radiation strength.It was observed that higher permeability 0<K<4 hinders the acceleration of Casson fluid.Higher Brownian motion levels 0.2<Nb<0.6 correspond to lower levels of the Casson fluid concentration profile.Moreover,it is observed that chemical reaction 0.2<γ2<0.5 has an inverse relation with the concentration level of Casson fluid.The current model’s significant uses include heat energy enhancement,petroleum recovery,energy devices,food manufacturing processes,and cooling device adjustment,among others.Furthermore,present outcomes have been found in great agreementwith already publishedwork.
文摘The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized flow.The convective boundary assumptions are directed in order to examine the heat and mass transportation of nanofluid.The thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno model.The problem formulated in dimensionless form is solved by NDSolve MATHEMATICA.The graphical analysis for parameters governed by the problem is performed with physical applications.The affiliation of entropy generation and Bejan number for different parameters is inspected in detail.The numerical data for illustrating skin friction,heat and mass transfer rate is also reported.The motion of the fluid is highest for the viscosity ratio parameter.The temperature of the fluid rises via thermal Biot number.Entropy generation rises for greater Brinkman number and diffusion parameter.
文摘An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.
基金Project supported by the Ministry of Higher Education in Malaysia(No.FRGS/1/2012/SG04/UKM/2001/1)the Universiti Kebangsaan Malaysia(No.DIP-2012-31)
文摘The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.
文摘The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.
文摘This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid behavior. The flow is subjected to suction/blowing at the surface. Analysis is carded out in presence of thermal radiation and prescribed surface heat flux. In this study, an exponential order stretching velocity and prescribed exponential order surface heat flux are accorded with each other. The governing partial differential equations are first converted into nonlinear ordinary differential equations by using appropriate transformations and then solved numerically. The effect of increasing values of the Casson parameter is to suppress the velocity field. However the temperature is enhanced when Casson parameter increases. It is found that the skin-friction coefficient increases with increasing values of suction parameter. Temperature also increases for large values of power index n in both suction and blowing cases at the boundary. It is observed that the thermal radiation enhances the effective thermal diffusivity and hence the temperature rises.
