Hamza Muhammed Murtala, Shuaibu Abdulsalam, Kamba Ahmad Samaila
Department of Mathematics, Usmanu Danfodiyo University Sokoto, P.M.B 2346, Sokoto, Nigeria.
Department of Mathematics, Federal University of Agriculture Zuru, P.M.B 28, Zuru, Nigeria.
Sci Rep. 2022 Jul 14;12(1):11989. doi: 10.1038/s41598-022-16064-y.
Utilizing porous media in a new mathematical model to improve convective heat transfer characteristics in a variety of applications, such as radiation nuclear disposal storing, evaporation cooling, sieving, geological extraction, crude petroleum refining, and building heating and cooling, is becoming increasingly important. This study proposed a numerical analysis of the unsteady magnetohydrodynamic free convection flow of an exothermic fluid with Newtonian heating. This discovery reveals two types of solutions: steady state and unsteady state. After transforming the governing equation from dimensional form to dimensionless form, the steady state governing equation was solved by the Homotopy Perturbation Method. However, the implicit finite difference approach is used to solve the time-dependent governing equations numerically. The impact of various emerging parameters, namely the Hartmann number, Boit number, Darcy number, Navier slip parameter, and the Frank-Kamenetskii parameter, was discussed and graphically analyzed. During the computations and analysis, it was discovered that a minor rise in the Hartman number results in the Lorentz force, which streamlines the momentum barrier layer and hence slows the fluid flow. The fluid velocity, on the other hand, rose as the porous medium, thermal Biot number, slip parameter, and temperature field increased as the viscous reactive fluid parameter and Newtonian heating increased. The skin friction and Nusselt number were also examined and reported. By comparing the finding to an existing work, a great agreement was revealed.
在各种应用中，如辐射核废料储存、蒸发冷却、筛分、地质开采、原油精炼以及建筑供热和制冷等，利用多孔介质建立新的数学模型来改善对流换热特性变得越来越重要。本研究提出了一种对具有牛顿加热的放热流体的非稳态磁流体动力学自由对流流动进行数值分析的方法。这一发现揭示了两种类型的解：稳态和非稳态。将控制方程从有量纲形式转换为无量纲形式后，采用同伦摄动法求解稳态控制方程。然而，对于与时间相关的控制方程，则使用隐式有限差分法进行数值求解。讨论并以图形方式分析了各种新出现的参数的影响，即哈特曼数、毕奥数、达西数、纳维滑移参数和弗兰克 - 卡门涅茨基参数。在计算和分析过程中发现，哈特曼数的小幅增加会导致洛伦兹力，该力使动量边界层流线化，从而减缓流体流动。另一方面，随着多孔介质、热毕奥数、滑移参数以及温度场随粘性反应流体参数和牛顿加热的增加而增加，流体速度也随之上升。还对表面摩擦和努塞尔数进行了研究并给出报告。通过将该研究结果与现有工作进行比较，发现二者具有高度一致性。
