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Keywords = quasi-Newtonian flows problem

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20 pages, 9213 KiB  
Article
A Posteriori Error Estimators for the Quasi-Newtonian Stokes Problem with a General Boundary Condition
by Omar El Moutea, Lahcen El Ouadefli, Abdeslam El Akkad, Nadia Nakbi, Ahmed Elkhalfi, Maria Luminita Scutaru and Sorin Vlase
Mathematics 2023, 11(8), 1943; https://doi.org/10.3390/math11081943 - 20 Apr 2023
Cited by 2 | Viewed by 1421
Abstract
In this paper, we approach two nonlinear differential equations applied in fluid mechanics by finite element methods (FEM). Our objective is to approach the solution to these problems; the first one is the “p-Laplacian” problem and the second one is the [...] Read more.
In this paper, we approach two nonlinear differential equations applied in fluid mechanics by finite element methods (FEM). Our objective is to approach the solution to these problems; the first one is the “p-Laplacian” problem and the second one is the “Quasi-Newtonian Stokes” problem with a general boundary condition. To study and analyze our solutions, we introduce the a posteriori error indicator; this technique allows us to control the error, and each is shown the equivalent between the true and the a posterior errors estimators. The performance of the finite element method by this type of general boundary condition is presented via different numerical simulations. Full article
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14 pages, 794 KiB  
Article
Effect of Chemical Reaction and Heat Absorption on MHD Nanoliquid Flow Past a Stretching Sheet in the Presence of a Transverse Magnetic Field
by Raj Nandkeolyar, Bhupesh Kumar Mahatha, Goutam Kumar Mahato and Precious Sibanda
Magnetochemistry 2018, 4(1), 18; https://doi.org/10.3390/magnetochemistry4010018 - 27 Feb 2018
Cited by 19 | Viewed by 4172
Abstract
In this paper, authors investigate homogeneous-heterogeneous chemical reaction and heat absorption effects on a two-dimensional steady hydromagnetic Newtonian nanoliquid flow along a continuously stretching sheet. The flow field is subjected to a uniform magnetic field acting in a direction perpendicular to the direction [...] Read more.
In this paper, authors investigate homogeneous-heterogeneous chemical reaction and heat absorption effects on a two-dimensional steady hydromagnetic Newtonian nanoliquid flow along a continuously stretching sheet. The flow field is subjected to a uniform magnetic field acting in a direction perpendicular to the direction of nanoliquid flow. A mathematical model of the physical problem is presented involving nonlinear partial differential equations with appropriate boundary conditions. These equations are then transformed into nonlinear ordinary differential equations using a suitable similarity transformation. Finally, approximate solutions of the transformed equations are obtained using the spectral quasi-linearization method. Results of fluid velocity, fluid temperature, and species concentration are depicted graphically, while the values of skin friction and Nusselt number are presented in tabular form. Fluid flow models of this kind find applications in catalytic reactors involving chemical reactions, insulation systems, and in heat exchangers. The applied magnetic field has a retarding influence on the nanofluid velocity and species concentration, while it does not have any significant effect on the nanofluid temperature. The homogeneous and heterogeneous reactions tend to decrease the species concentration. Full article
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