变热导率的幂律流体在水平波面上的传热问题研究  

Heat transfer of power-law fluids with variable thermal conductivities on a horizontal rough surface

作　　者：刘芳芳 张爱莉 司新辉[1] 曹丽梅[1] LIU Fangfang;ZHANG Aili;SI Xinhui;CAO Limei(School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China)

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《工程科学学报》2023年第11期1977-1984,共8页Chinese Journal of Engineering

基　　金：国家自然科学基金面上资助项目(12072024)。

摘　　要：根据泰勒展开式和边界层理论,推导了变热导率的Oswad-de Waele幂律流体沿水平波面上的边界层方程.假设热传导系数是依赖于温度梯度的幂律函数,构建了变热导率的能量方程模型.引入一系列变换,把变量量纲为一化和坐标变换,将原始问题转换为偏微分方程组,并用Keller-box方法进行数值求解.讨论了某些参数如波幅与波长的比值、幂律指数以及广义普朗特数对壁面摩擦和流体传热的影响.计算结果显示:表面速度和压力梯度沿波面呈周期性变化,而且它们的变化周期与波面的变化周期完全一致.而对于壁面的摩擦系数和局部Nusselt数,在靠近零点的地方会有剧烈震荡,沿轴向会呈现波形分布状态,随着波长比率的增大而减小,且会随着振幅的增大,壁面摩擦系数也会震荡加剧.随着幂律指数的增加,局部Nusselt数呈现递减的分布状态.对于问题的特殊情况,当壁面是光滑平板时,尽管壁面的摩擦系数和局部Nusselt数沿轴向在初始位置会有波动,但会在很短的距离达到稳定的状态.从不同参数对周期的影响来看,周期性波动的壁面摩擦系数和局部Nusselt数与波面曲线的峰顶和波谷并不保持一致.Power-law fluids have recently received increasing attention because of their applications in different industrial fields.In previous works,the energy and momentum equations for power-law fluids were considered the same as those for Newtonian fluids.However,as the heat transfer of fluids results from thermomolecular motions,the heat-transfer behavior of non-Newtonian power-law fluids should be different from that of Newtonian fluids.The flow of fluids on a smooth plate is a classical problem.In most situations,the plates are rough.In particular,in industrial fields,many plates are deliberately designed to be rough to enhance heat transfer.Herein,according to the Taylor expansion and boundary-layer theory,the boundary-layer equations for the Ostwald–de Waele power-law fluids with a variable thermal conductivity along a horizontal wavy surface are reduced to partial differential equations.An energy equation with a variable thermal conductivity is constructed,where the heat-conduction coefficient is assumed to be a power-law function dependent on the temperature gradient.Through the introduction of a series of transformations,including nondimensional and coordinate transformations,the original wavy-surface problem is transformed into a system of partial differential equations describing the flow problem with boundary conditions on a flat plate,which is solved numerically using the Keller-box method.The effects of someαn Nzhparameters,such as the amplitude–wavelength ratio,power-law index,and generalized Prandtl number,on the local friction coefficient and heat-transfer coefficient are discussed.Numerical results show that the velocity of power-law fluids on the surface and pressure gradient varies periodically along the wavy plate.Furthermore,the cycles of the velocity and pressure gradients are the same as the one of the wavy-shape plate.The results show that the local Nusselt number and the friction coefficient vary periodically in a wavelike manner and increase gradually with the amplitude–wavelength ratio

关 键 词：幂律流体 正弦波面 变热导率 泰勒展式 边界层理论 

分 类 号：O29[理学—应用数学]