The present study investigates the impacts of thermal radiation and inclined magnetic field on th... more The present study investigates the impacts of thermal radiation and inclined magnetic field on the Sutterby fluid by capitalizing Cattaneo-Christov heat flux system. The suitable transformations from partial differential equations (PDEs) into ordinary differential equations (ODEs) are achieved by capitalizing the strength of similarity conversion system. Well known numerical shooting technique is used along with integrated strength Runge Kutta method of fourth order. The proposed results are compared with Lobatto 111A method which strengthen the convergence and accuracy of present fluidic system. The skin friction coefficients and Nusselt number are numerically exhibited in tabular form, while the parameter of interests in terms of velocity ratio parameter, power law index, the thermal radiation parameter, Prandtl number, Deborah number, magnetic parameter. Here in this contemporary investigation, the phenomenon of thermal radiation on an inclined magnetic field using Sutterby capit...
In this paper, some higher order algorithms have been introduced for solving fixed point problems... more In this paper, some higher order algorithms have been introduced for solving fixed point problems. These algorithms have been developed by Homotopy Perturbation Method. New algorithms are tested on diversified nonlinear problems. The results are very promising and useful. Comparison of numerical results along with existing proficient techniques explicitly reflects the very high level of accuracy of developed iterative schemes.
In this paper, we present two versions of the Hadamard inequality forα,mconvex functions via Capu... more In this paper, we present two versions of the Hadamard inequality forα,mconvex functions via Caputo fractional derivatives. Several related results are analyzed for convex andm-convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are established by applying some known identities.
This work deals with the bounds of a unified integral operator with which several fractional and ... more This work deals with the bounds of a unified integral operator with which several fractional and conformable integral operators are directly associated. By using quasiconvex and monotone functions we establish bounds of these integral operators. We prove their boundedness and continuity. The results of this paper generalize already published results and have direct consequences for fractional and conformable integrals
This paper considers a theoretical study on steady incompressible flow of co-rotational Maxwell f... more This paper considers a theoretical study on steady incompressible flow of co-rotational Maxwell fluid in helical screw rheometer (HSR). The rheological constitutive equation for co-rotational Maxwell fluid model gives the second order nonlinear coupled differential equations which could not be solved explicitly. An iterative procedure, Adomian decomposition method (ADM) is used to obtain the analytical solution. Expressions for velocity components in θ and − z direction are obtained. The volume flow rates are calculated for the azimuthal and axial components of velocity field by introducing the effect of flights. The results have been discussed with the help of graphs as well. We observe that the velocity profiles are strongly depend on non-dimensional parameter α ~ , with the increase in α ~ , progressive increase seen in the flow profiles. We also noted that the parabolicity of flow profiles increase with increase in the magnitude of pressure gradients. Thus the profound conclusio...
This work solves the problem of thin-film withdrawal and drainage of a steady incompressible coup... more This work solves the problem of thin-film withdrawal and drainage of a steady incompressible couple stress fluid on the outer surface of a vertical cylinder. The governing equations for velocity and temperature distributions are subjected to the boundary conditions and solved with the help of homotopy analysis method. The obtained expressions for flow profile, temperature profile, average velocity, volume flow rate, and shear stress confirmed that the thin-film flow of couple stress fluid highly depends on involved parameters say Stokes number St , vorticity parameter λ, couple stress parameter η, and Brinkman number Br presented in the graphical description as well.
The aim of this paper is to study approximate analytical unsteady flow and heat transfer analysis... more The aim of this paper is to study approximate analytical unsteady flow and heat transfer analysis of CNTs nanofluid over stretching sheet for the improvement of heat assignment ratio. The present work has some important application in industry and engineering because the heat transfer ratio of nanofluid is larger compared to other fluid. With the help of defined similarity transformation, the nonlinear partial differential equations is converted to nonlinear ordinary differential equations. The model of nonlinear ordinary differential equations are then solved by Optimal Homotopy Asymptotic Method. The impact of different parameters are then interpreted using graphs in the form of velocity and temperature profiles. The influence of skin friction coefficient and Nusselt number is presented in the table form.
In this paper, the steady flow of an incompressible, co-rotational Maxwell fluid in a helical scr... more In this paper, the steady flow of an incompressible, co-rotational Maxwell fluid in a helical screw rheometer is studied by 'unwrapping or flattening' the channel, lands, and the outside rotating barrel. The geometry is approximated as a shallow infinite channel, by assuming the width of the channel large as compared to the depth. The developed second order nonlinear coupled differential equations are transformed to a single differential equation. Using perturbation methods, analytical expressions are obtained for the velocity components in the x-and z-directions and the resultant velocity in the direction of the screw axis. Volume flow rates, shear and normal stresses, shear at wall, and forces exerted on fluid and average velocity are also calculated. The behavior of the velocity profiles are discussed with the help of graphs. We observe that the velocity profiles are strongly dependent on the non-dimensional parameter (Wi) 2 , the flight angle φ and the pressure gradients.
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
This paper provides a theoretical study of steady flow of an incompressible third grade fluid in he... more This paper provides a theoretical study of steady flow of an incompressible third grade fluid in helical screw rheometer. The model developed in cylindrical coordinates pertains to second order nonlinear coupled differential equations that are solved using homotopy perturbation method. Expressions for velocity components in � and zdirection are obtained. The volume flow rates are calculated for the azimuthal and axial components of velocity profiles by introducing the effect of flights. The results have been discussed with the help of graphs. It is noticed that extrusion process depends on the involved non-Newtonian parameter and pressure gradients.
The steady flow of an incompressible, third-grade fluid in helical screw rheometer (HSR) is studi... more The steady flow of an incompressible, third-grade fluid in helical screw rheometer (HSR) is studied by "unwrapping or flattening" the channel, lands, and the outside rotating barrel. The geometry is approximated as a shallow infinite channel, by assuming that the width of the channel is large as compared to the depth. The developed second-order nonlinear coupled differential equations are reduced to single differential equation by using a transformation. Using Adomian decomposition method, analytical expressions are calculated for the the velocity profiles and volume flow rates. The results have been discussed with the help of graphs as well. We observed that the velocity profiles are strongly dependant on non-Newtonian parameter (̃), and with the increase iñ, the velocity profiles increase progressively, which conclude that extrusion process increases with the increase iñ. We also observed that the increase in pressure gradients in x-and z-direction increases the net flow inside the helical screw rheometer, which increases the extrusion process. We noticed that the flow increases as the flight angle increase.
This paper aims to study the flow of an incompressible, isothermal Eyring-Powell fluid in a helic... more This paper aims to study the flow of an incompressible, isothermal Eyring-Powell fluid in a helical screw rheometer. The complicated geometry of the helical screw rheometer is simplified by “unwrapping or flattening” the channel, lands, and the outside rotating barrel, assuming the width of the channel is larger as compared to the depth. The developed second order nonlinear differential equations are solved by using Adomian decomposition method. Analytical expressions are obtained for the velocity profiles, shear stresses, shear at wall, force exerted on fluid, volume flow rates, and average velocity. The effect of non-Newtonian parameters, pressure gradients, and flight angle on the velocity profiles is noticed with the help of graphical representation. The observation confirmed the vital role of involved parameters during the extrusion process.
This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids ... more This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids though a cylindrical pipe. The flow is assumed to be steady, incompressible, and stable and the fluid layers do not mix with each other. The fluid flow and heat transfer equations are modeled using the linear PTT fluid model. Exact solutions for the velocity, flow rates, temperature profiles, and stress distributions are obtained. It has also been shown that one can recover the Newtonian fluid results from the obtained results by putting the non-Newtonian parameters to zero. These results match with the corresponding results for Newtonian fluids already present in the literature. Graphical analysis of the behavior of the fluid velocities, temperatures, and stresses is also presented at the end. It is also shown that maximum velocity occurs in the inner fluid layer.
The present study investigates the impacts of thermal radiation and inclined magnetic field on th... more The present study investigates the impacts of thermal radiation and inclined magnetic field on the Sutterby fluid by capitalizing Cattaneo-Christov heat flux system. The suitable transformations from partial differential equations (PDEs) into ordinary differential equations (ODEs) are achieved by capitalizing the strength of similarity conversion system. Well known numerical shooting technique is used along with integrated strength Runge Kutta method of fourth order. The proposed results are compared with Lobatto 111A method which strengthen the convergence and accuracy of present fluidic system. The skin friction coefficients and Nusselt number are numerically exhibited in tabular form, while the parameter of interests in terms of velocity ratio parameter, power law index, the thermal radiation parameter, Prandtl number, Deborah number, magnetic parameter. Here in this contemporary investigation, the phenomenon of thermal radiation on an inclined magnetic field using Sutterby capit...
In this paper, some higher order algorithms have been introduced for solving fixed point problems... more In this paper, some higher order algorithms have been introduced for solving fixed point problems. These algorithms have been developed by Homotopy Perturbation Method. New algorithms are tested on diversified nonlinear problems. The results are very promising and useful. Comparison of numerical results along with existing proficient techniques explicitly reflects the very high level of accuracy of developed iterative schemes.
In this paper, we present two versions of the Hadamard inequality forα,mconvex functions via Capu... more In this paper, we present two versions of the Hadamard inequality forα,mconvex functions via Caputo fractional derivatives. Several related results are analyzed for convex andm-convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are established by applying some known identities.
This work deals with the bounds of a unified integral operator with which several fractional and ... more This work deals with the bounds of a unified integral operator with which several fractional and conformable integral operators are directly associated. By using quasiconvex and monotone functions we establish bounds of these integral operators. We prove their boundedness and continuity. The results of this paper generalize already published results and have direct consequences for fractional and conformable integrals
This paper considers a theoretical study on steady incompressible flow of co-rotational Maxwell f... more This paper considers a theoretical study on steady incompressible flow of co-rotational Maxwell fluid in helical screw rheometer (HSR). The rheological constitutive equation for co-rotational Maxwell fluid model gives the second order nonlinear coupled differential equations which could not be solved explicitly. An iterative procedure, Adomian decomposition method (ADM) is used to obtain the analytical solution. Expressions for velocity components in θ and − z direction are obtained. The volume flow rates are calculated for the azimuthal and axial components of velocity field by introducing the effect of flights. The results have been discussed with the help of graphs as well. We observe that the velocity profiles are strongly depend on non-dimensional parameter α ~ , with the increase in α ~ , progressive increase seen in the flow profiles. We also noted that the parabolicity of flow profiles increase with increase in the magnitude of pressure gradients. Thus the profound conclusio...
This work solves the problem of thin-film withdrawal and drainage of a steady incompressible coup... more This work solves the problem of thin-film withdrawal and drainage of a steady incompressible couple stress fluid on the outer surface of a vertical cylinder. The governing equations for velocity and temperature distributions are subjected to the boundary conditions and solved with the help of homotopy analysis method. The obtained expressions for flow profile, temperature profile, average velocity, volume flow rate, and shear stress confirmed that the thin-film flow of couple stress fluid highly depends on involved parameters say Stokes number St , vorticity parameter λ, couple stress parameter η, and Brinkman number Br presented in the graphical description as well.
The aim of this paper is to study approximate analytical unsteady flow and heat transfer analysis... more The aim of this paper is to study approximate analytical unsteady flow and heat transfer analysis of CNTs nanofluid over stretching sheet for the improvement of heat assignment ratio. The present work has some important application in industry and engineering because the heat transfer ratio of nanofluid is larger compared to other fluid. With the help of defined similarity transformation, the nonlinear partial differential equations is converted to nonlinear ordinary differential equations. The model of nonlinear ordinary differential equations are then solved by Optimal Homotopy Asymptotic Method. The impact of different parameters are then interpreted using graphs in the form of velocity and temperature profiles. The influence of skin friction coefficient and Nusselt number is presented in the table form.
In this paper, the steady flow of an incompressible, co-rotational Maxwell fluid in a helical scr... more In this paper, the steady flow of an incompressible, co-rotational Maxwell fluid in a helical screw rheometer is studied by 'unwrapping or flattening' the channel, lands, and the outside rotating barrel. The geometry is approximated as a shallow infinite channel, by assuming the width of the channel large as compared to the depth. The developed second order nonlinear coupled differential equations are transformed to a single differential equation. Using perturbation methods, analytical expressions are obtained for the velocity components in the x-and z-directions and the resultant velocity in the direction of the screw axis. Volume flow rates, shear and normal stresses, shear at wall, and forces exerted on fluid and average velocity are also calculated. The behavior of the velocity profiles are discussed with the help of graphs. We observe that the velocity profiles are strongly dependent on the non-dimensional parameter (Wi) 2 , the flight angle φ and the pressure gradients.
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
This paper provides a theoretical study of steady flow of an incompressible third grade fluid in he... more This paper provides a theoretical study of steady flow of an incompressible third grade fluid in helical screw rheometer. The model developed in cylindrical coordinates pertains to second order nonlinear coupled differential equations that are solved using homotopy perturbation method. Expressions for velocity components in � and zdirection are obtained. The volume flow rates are calculated for the azimuthal and axial components of velocity profiles by introducing the effect of flights. The results have been discussed with the help of graphs. It is noticed that extrusion process depends on the involved non-Newtonian parameter and pressure gradients.
The steady flow of an incompressible, third-grade fluid in helical screw rheometer (HSR) is studi... more The steady flow of an incompressible, third-grade fluid in helical screw rheometer (HSR) is studied by "unwrapping or flattening" the channel, lands, and the outside rotating barrel. The geometry is approximated as a shallow infinite channel, by assuming that the width of the channel is large as compared to the depth. The developed second-order nonlinear coupled differential equations are reduced to single differential equation by using a transformation. Using Adomian decomposition method, analytical expressions are calculated for the the velocity profiles and volume flow rates. The results have been discussed with the help of graphs as well. We observed that the velocity profiles are strongly dependant on non-Newtonian parameter (̃), and with the increase iñ, the velocity profiles increase progressively, which conclude that extrusion process increases with the increase iñ. We also observed that the increase in pressure gradients in x-and z-direction increases the net flow inside the helical screw rheometer, which increases the extrusion process. We noticed that the flow increases as the flight angle increase.
This paper aims to study the flow of an incompressible, isothermal Eyring-Powell fluid in a helic... more This paper aims to study the flow of an incompressible, isothermal Eyring-Powell fluid in a helical screw rheometer. The complicated geometry of the helical screw rheometer is simplified by “unwrapping or flattening” the channel, lands, and the outside rotating barrel, assuming the width of the channel is larger as compared to the depth. The developed second order nonlinear differential equations are solved by using Adomian decomposition method. Analytical expressions are obtained for the velocity profiles, shear stresses, shear at wall, force exerted on fluid, volume flow rates, and average velocity. The effect of non-Newtonian parameters, pressure gradients, and flight angle on the velocity profiles is noticed with the help of graphical representation. The observation confirmed the vital role of involved parameters during the extrusion process.
This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids ... more This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids though a cylindrical pipe. The flow is assumed to be steady, incompressible, and stable and the fluid layers do not mix with each other. The fluid flow and heat transfer equations are modeled using the linear PTT fluid model. Exact solutions for the velocity, flow rates, temperature profiles, and stress distributions are obtained. It has also been shown that one can recover the Newtonian fluid results from the obtained results by putting the non-Newtonian parameters to zero. These results match with the corresponding results for Newtonian fluids already present in the literature. Graphical analysis of the behavior of the fluid velocities, temperatures, and stresses is also presented at the end. It is also shown that maximum velocity occurs in the inner fluid layer.
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