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Radiative squeezing flow of unsteady magneto-hydrodynamic Casson fluid between two parallel plates

两平行板间非稳态 Casson 磁流体的辐射挤压流动

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Abstract

Present numerical study examines the heat and mass transfer characteristics of magneto-hydrodynamic Casson fluid flow between two parallel plates under the influence of thermal radiation, internal heat generation or absorption and Joule dissipation effects with homogeneous first order chemical reaction. The non-Newtonian behaviour of Casson fluid is distinguished from those of Newtonian fluids by considering the well-established rheological Casson fluid flow model. The governing partial differential equations for the unsteady two-dimensional squeezing flow with heat and mass transfer of a Casson fluid are highly nonlinear and coupled in nature. The nonlinear ordinary differential equations governing the squeezing flow are obtained by imposing the similarity transformations on the conservation laws. The resulting equations have been solved by using two numerical techniques, namely Runge-Kutta fourth order integration scheme with shooting technique and bvp4c Matlab solver. The comparison between both the techniques is provided. Further, for the different set physical parameters, the numerical results are obtained and presented in the form of graphs and tables. However, in view of industrial use, the power required to generate the movement of the parallel plates is considerably reduced for the negative values of squeezing number. From the present investigation it is noticed that, due to the presence of stronger Lorentz forces, the temperature and velocity fields eventually suppressed for the enhancing values of Hartmann number. Also, higher values of squeezing number diminish the squeezing force on the fluid flow which in turn reduces the thermal field. Further, the destructive nature of the chemical reaction magnifies the concentration field; whereas constructive chemical reaction decreases the concentration field. The present numerical solutions are compared with previously published results and show the good agreement.

摘要

本文通过数值计算, 研究了在均匀一阶化学反应条件下, 受热辐射、内热产生或吸收以及焦耳耗散效应的影响, Casson流体在两平行板间的传热传质特性。建立流变Casson 流体流动模型, 将Casson流体的非牛顿行为与牛顿流体的非牛顿行为进行区分。Casson流体的非稳态二维挤压流动的控制偏微分方程具有高度非线性和耦合性质。对守恒定律进行相似变换, 得到控制挤压流的非线性常微分方程。 分别应用利用龙格库塔四阶积分法和bvp4c Matlab求解法对所得方程进行求解, 并将结果进行比较。 此外, 对于不同的物理参数集, 得到其数值结果, 并以图和表的形式给出计算结果。然而, 考虑到工业应用, 因压缩数为负值, 平行板运动所需的功率大幅度减少。研究发现, 由于存在较强的Lorentz力, Hartmann数的增强值最终会抑制温度场和速度场。此外, 压缩数越大, 流体的压缩力越小, 热场越小。而且化学反应的破坏性放大了浓度场, 而构造性化学反应降低了浓度场。本文给出的数值解与以往的计算结果进行了比较, 显示出较好的一致性。

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Acknowledgements

The authors wish to express their gratitude to the reviewers who highlighted important areas for improvement in this earlier draft of the article. Their suggestions have served specifically to enhance the clarity and depth of the interpretation of results in the revised manuscript. One of the author Usha Shankar wishes to thank Karnataka Power Corporation limited, Raichur Thermal Power Station, Shaktinagar, for their encouragement.

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  1. Department of Mathematics, Gulbarga University, Kalaburagi, 585106, Karnataka, India

    N. B. Naduvinamani & Usha Shankar

  2. Department of Karnataka Power Corporation Limited, Raichur Thermal Power Station, Shaktinagar, 584170, Karnataka, India

    Usha Shankar

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Correspondence to N. B. Naduvinamani.

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Naduvinamani, N.B., Shankar, U. Radiative squeezing flow of unsteady magneto-hydrodynamic Casson fluid between two parallel plates. J. Cent. South Univ. 26, 1184–1204 (2019). https://doi.org/10.1007/s11771-019-4080-0

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