摘要
黏弹性流体的流动和传热特性研究一直是一个备受关注的问题.然而,一些黏弹性流体的行为会偏离由整数阶控制方程描述的经典的流动和传热现象.因此,建立一种新的本构关系来研究复杂黏弹性流体是有必要的.本文研究了霍尔效应作用下具有分布阶特性的广义Maxwell流体在无穷平板上的旋转磁流体流动和传热现象.考虑到广义Maxwell流体流动和传热的多尺度特性和非局部性,引入分数阶微积分理论准确地描述流动和传热机理,导出了由时间分布阶动量方程和时间分数阶能量方程组成的分数阶控制方程.为了计算速度和温度控制方程的数值解,我们基于L1近似公式提出了Crank-Nicolson有限差分格式,然后,验证了数值方法的有效性和可行性,并以图形形式讨论了相关参数对流体速度和温度的影响,给出了一些结论.
Research on the flow and heat transfer characteristics of viscoelastic fluids has been an issue of considerable interest.However,it is gradually found that the behaviors of some viscoelastic fluids deviate from the classical flow and heat transfer phenomena,which are represented by integer order governing equations.Thus,it is necessary to construct a new constitutive relationship to study complex viscoelastic fluids.In this paper,we investigate the rotating magnetohydrodynamics(MHD)flow and heat transfer of generalized Maxwell fluid with distributed order characteristics over an infinite plate,and the Hall effect is considered.In view of the multi-scale characteristics and nonlocality of generalized Maxwell fuid flow and heat transfer,fractional calculus is introduced to accurately depict the flow and heat transfer mechanism.Fractional governing equations consisting of the distributed order time fractional momentum equations and time fractional energy equation are derived.To calculate the numerical solutions of velocities and temperature governing equations,the Crank-Nicolson finite difference schemes are proposed based on the L1 approximation formula.Then,the effectiveness and feasibility of the numerical method are verified,and the effects of relevant parameters on fluid velocities and temperature are discussed,graphically.Finally,some conclusions are summarized.
作者
乔艳丽
续焕英
齐海涛
Yanli Qiao;Huanying Xu;Haitao Qi(School of Mathematics and Statistics,Shandong University,Weihai 264209,China)
基金
This work was supported by the National Natural Science Foundation of China(Grant Nos.12172197,12171284,and 12120101001)
the Natural Science Foundation of Shandong Province(Grant No.ZR2021ZD03).
