Effects of Hall current on heat transfer and magnetohydrodynamic (MHD) boundary layer flow induced by a continuous surface in a parallel free stream of a second-order viscoelastic fluid are studied for uniform suction...Effects of Hall current on heat transfer and magnetohydrodynamic (MHD) boundary layer flow induced by a continuous surface in a parallel free stream of a second-order viscoelastic fluid are studied for uniform suction/injection by taking viscous dissipation into account. Complex nonsimilar solutions to the stream function and temperature are developed by means of an elegant technique, known as homotopy analysis method (HAM). Convergence of the solutions is ensured with the help of -curves. Graphical and tabular results for the effects of Hall current reveal that it has a significant influence on: complex velocity, complex temperature, magnitude of the shear stress at the surface, magnitude of the rate of heat transfer at the surface and on boundary layer thickness.展开更多
Tumor invasion follows a complex mechanism which involves cell migration and proliferation.To study the processes in which primary and secondary metastases invade and damage the normal cells,mathematical models are of...Tumor invasion follows a complex mechanism which involves cell migration and proliferation.To study the processes in which primary and secondary metastases invade and damage the normal cells,mathematical models are often extremely useful.In this paper,we present a mathematical model of acid-mediated tumor growth consisting of radially symmetric reaction-diffusion equations.The assumption on the radial symmetry of the solutions is imposed here in view that tumors present spherical symmetry at the microscopic level.Moreover,we consider various empirical mechanisms which describe the propagation of tumors by considering cancer cells,normal cells,and the concentration of H+ions.Among other assumptions,we suppose that these components follow logistictype growth rates.Evidently,this is an important difference with respect to various other mathematical models for tumor growth available in the literature.Moreover,we also add competition terms of normal and tumor cells growth.We carry out a balancing study of the equations of the model,and a numerical model is proposed to produce simulations.Various practical remarks derived from our assumptions are provided in the discussion of our simulations.展开更多
文摘Effects of Hall current on heat transfer and magnetohydrodynamic (MHD) boundary layer flow induced by a continuous surface in a parallel free stream of a second-order viscoelastic fluid are studied for uniform suction/injection by taking viscous dissipation into account. Complex nonsimilar solutions to the stream function and temperature are developed by means of an elegant technique, known as homotopy analysis method (HAM). Convergence of the solutions is ensured with the help of -curves. Graphical and tabular results for the effects of Hall current reveal that it has a significant influence on: complex velocity, complex temperature, magnitude of the shear stress at the surface, magnitude of the rate of heat transfer at the surface and on boundary layer thickness.
基金wishes to acknowledge the financial support from the National Council of Science and Technology of Mexico(CONACYT)through grant A1-S-45928.
文摘Tumor invasion follows a complex mechanism which involves cell migration and proliferation.To study the processes in which primary and secondary metastases invade and damage the normal cells,mathematical models are often extremely useful.In this paper,we present a mathematical model of acid-mediated tumor growth consisting of radially symmetric reaction-diffusion equations.The assumption on the radial symmetry of the solutions is imposed here in view that tumors present spherical symmetry at the microscopic level.Moreover,we consider various empirical mechanisms which describe the propagation of tumors by considering cancer cells,normal cells,and the concentration of H+ions.Among other assumptions,we suppose that these components follow logistictype growth rates.Evidently,this is an important difference with respect to various other mathematical models for tumor growth available in the literature.Moreover,we also add competition terms of normal and tumor cells growth.We carry out a balancing study of the equations of the model,and a numerical model is proposed to produce simulations.Various practical remarks derived from our assumptions are provided in the discussion of our simulations.
