Mohamad Riduan Hashim, Zulkhibri Ismail, Ahmad Qushairi Mohamad, Muhammad Atif Akashah, Wan Nura'in Nabilah Noranuar, Lim Yeou Jiann, Sharidan Shafie
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引用次数: 0
摘要
本研究的主要目的是建立加速板对布林克曼型流体通过两个垂直通道的自由对流影响的数学模型并求解。通过使用适当的无量纲变量,在相关初始边界条件的作用下,将有量纲的能量和动量方程简化为无量纲方程。通过拉普拉斯变换法获得解析解。无量纲参数是通过无量纲过程获得的,如格拉肖夫数 Gr、加速度板参数 R、普朗特数 Pr、布林克曼型流体参数和时间 t。观察发现,流体速度随着 Gr 和 t 的增加而增加,而随着 R 和 Pr 的增加而减小。此外,还发现温度曲线随 Prandtl 数(Pr)的高值而减小,同时随时间(t)的高值而增大。为了验证结果,将极限情况下获得的结果与已公布的结果以及 Gaver-Stehfest 数值算法进行了比较。比较结果表明,两者的解法是一致的。
Mathematical Solution for Free Convection Flow of Brinkman Type Fluid in the Channel with the Effect of Accelerated Plate
The main purpose of this research is to formulate the mathematical models and solution for the effect of accelerated plate on free convection flow in Brinkman type fluid through two vertical channels. Using the appropriate dimensionless variables, the dimensional governing energy and momentum equations are reduced to dimensionless equations subjected to the associated initial boundary conditions. The analytical solutions are obtained by using Laplace transform method. Dimensionless parameters are obtained through dimensionless processes such as Grashof number Gr, Acceleration plate parameter, R, Prandtl number Pr, Brinkman type fluid parameter and time, t. The mathematical findings for velocity and temperature are graphically plotted to investigate the influence of dimensionless variables on profiles. It is observed that fluid velocity increases with increasing of Gr and t whereas it decreases with increasing of , R and Pr. Besides that, it is found that temperature profiles decrease with a high value of Prandtl number, Pr while increase with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and also with numerical Gaver-Stehfest algorithm. Both comparisons show that the solution is to be in a mutual agreement.