This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual par...This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm.The nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and viscosity.Due to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the flow.The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions.Finally,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.展开更多
In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes eq...In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.展开更多
A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary c...A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical （numerical） solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.展开更多
A heuristic technique is developed for a nonlinear magnetohydrodynamics （MHD） Jeffery-Hamel problem with the help of the feed-forward artificial neural net- work （ANN） optimized with the genetic algorithm （GA） a...A heuristic technique is developed for a nonlinear magnetohydrodynamics （MHD） Jeffery-Hamel problem with the help of the feed-forward artificial neural net- work （ANN） optimized with the genetic algorithm （GA） and the sequential quadratic programming （SQP） method. The twodimensional （2D） MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem （BVP） of ordinary differential equations （ODEs）. The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the an- gles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.展开更多
文摘This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm.The nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and viscosity.Due to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the flow.The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions.Finally,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.
文摘In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.
文摘A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical （numerical） solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.
文摘A heuristic technique is developed for a nonlinear magnetohydrodynamics （MHD） Jeffery-Hamel problem with the help of the feed-forward artificial neural net- work （ANN） optimized with the genetic algorithm （GA） and the sequential quadratic programming （SQP） method. The twodimensional （2D） MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem （BVP） of ordinary differential equations （ODEs）. The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the an- gles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.
