Comparison Between Thermal Conductivity Models on Heat Transfer in Power-Law Non-Newtonian Fluids (with Liancun Zheng and Xinxin Zhang) ASME Journal of heat transfer, 134(4), 041702.


This paper endeavors to complete a numerical research on forced convection steady heat transfer in power-law non-Newtonian fluids in a circle duct. Incompressible, laminar fluids are to be studied with a uniform wall temperature. A hydrodynamic entrance length is neglected which allows establishing a fully developed flow. The energy equation is solved by using a LU decomposition coupled with control volume technique based on finite difference method. Four thermal conductivity models are adopted in this paper, that is, constant thermal conductivity model, linear thermal conductivity varying with temperature, thermal conductivity varying as a function of velocity gradient, and thermal conductivity varying as a function of temperature gradient. The results are compared with each other and the physical characteristics for values of parameters are also discussed in details. It is shown that the heat transfer behaviors are strongly depending on the power-law index in all models. Comparisons of temperature and local Nusselt number between models are made. It reveals the increasing values of thermal conductivity parameter result in increasing the local Nusselt number when the thermal conductivity is a linear one. Furthermore, there is obvious difference in the local Nusselt number between the constant model and the power-law velocity-dependent model, but Nusselt number varies little from the constant model to the power-law temperature-dependent model.


Multiple Solutions of Laminar Flow in Channels with a Transverse Magnetic Field (with Liancun Zheng and Xinxin Zhang) Chinese Physics Letters, Vol. 26, No. 9 (2009) 094101.


We present a numerical investigation for steady laminar flow of a viscous incompressible electrically conducting fluid through a channel of a rectangular cross-section with a transverse magnetic field and suction or injection walls. Multiple solutions are presented for values of suction Reynolds number R and velocity coefficients of accelerating walls. Additionally, the associated transfer characteristics are discussed in detail.


Precipitation phenomenon of nanoparticles in power-law fluids over a rotating disk(with Chen Xi, Zheng Liancun, Zhu Liangliang, Zhou Jialv, and Wang Tongtong) Microfluidics and Nanofluidics. DOI 10.1007/s10404-013-1298-2.


The steady flow and mass transfer of nanofluids with power-law type base fluids over a free-rotating disk are investigated. Previously, we have modeled the volume fraction of nanoparticles and verified the experimental conclusion through the numerical simulation of particle distribution in nanofluid in a Petri dish under the influence of movement using a power-law model of mass diffusivity. We further this study by a similar model of the mass diffusivity following a power-law type to consider the laminar non-Newtonian power-law flow in a rotating infinite disk with angular velocity about the z-axis. The coupled governing equations are transformed into ODEs. Homotopy analysis method (HAM) is applied to solve the ODEs while special attention is paid to deal with the nonlinear items in the ODEs. In the last section, we provide images of nanoparticles suspended in power-law fluids in a rotating disk as obtained using the laser speckle method. When they are compared with the analytical results gained by the HAM, they qualitatively matched the solutions of the concentration equation of nanofluids.