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The problem of Rayleigh-Bénard convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law is studied by the method of small perturbation. Modified Darcy-Brinkman model is used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an isothermal boundary condition is imposed at the lower boundary. The non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary conditions and the thresholds for the marginal stability are determined. Some of the known cases are derived as special cases. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection has been analyzed. It is found that the Bénard problem for a Maxwell-Cattaneo ferromagnetic fluid is always less stable than the classical ferroconvection problem. It is shown that the destabilizing influence of the Cattaneo number is not attenuated by that of magnetic forces and vice versa, and that the aspect ratio of the convection cells changes when the parameters involved in the study vary with the porous structure bringing out considerable influence.
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In this action research study, where the subjects are our undergraduate grade mathematics students, w e try to investigate the impact of direct ‘inquisition’ instruction on their communication and achievement. We will strategically implement the addition of ‘replication’ study into each concept of limit over a four-month time period and thus conclusion can be making for the rest of the Mathemat ics . The students practiced using inquiry in verbal discussions, review activities, and in mathematical problem explanations. We discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data we collected. We also found that in general, students felt that knowing the definition of mathematical words are important and that it increased their achievement when they understood the concept as a whole. In addition, students will be more exact in their communication after receiving inquiry instructions. As a result of this research, we plan to continue to implement inquisition into daily lessons and keep replication communication as a focus of the mathematics class
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The problem of Rayleigh-Bénard convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law is studied by the method of small perturbation. Modified Darcy-Brinkman model is used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an isothermal boundary condition is imposed at the lower boundary. The non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary conditions and the thresholds for the marginal stability are determined. Some of the known cases are derived as special cases. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection has been analyzed. It is found that the Bénard problem for a Maxwell-Cattaneo ferromagnetic fluid is always less stable than the classical ferroconvection problem. It is shown that the destabilizing influence of the Cattaneo number is not attenuated by that of magnetic forces and vice versa, and that the aspect ratio of the convection cells changes when the parameters involved in the study vary with the porous structure bringing out considerable influence.
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In this action research study, where the subjects are our undergraduate grade mathematics students, w e try to investigate the impact of direct ‘inquisition’ instruction on their communication and achievement. We will strategically implement the addition of ‘replication’ study into each concept of limit over a four-month time period and thus conclusion can be making for the rest of the Mathemat ics . The students practiced using inquiry in verbal discussions, review activities, and in mathematical problem explanations. We discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data we collected. We also found that in general, students felt that knowing the definition of mathematical words are important and that it increased their achievement when they understood the concept as a whole. In addition, students will be more exact in their communication after receiving inquiry instructions. As a result of this research, we plan to continue to implement inquisition into daily lessons and keep replication communication as a focus of the mathematics class
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