Liancun Zheng

Coupled flow and heat transfer in viscoelastic fluid with Cattaneo–Christov heat flux model

Abstract This letter presents a research for coupled flow and heat transfer of an upper-convected Maxwell fluid above a stretching plate with velocity slip boundary. Unlike most classical works, the new heat flux model, which is recently proposed by Christov, is employed. Analytical solutions are obtained by using the homotopy analysis method (HAM). The effects of elasticity number, slip coefficient, the relaxation time of the heat flux and the Prandtl number on velocity and temperature fields are analyzed. A comparison of Fourier’s Law and the Cattaneo–Christov heat flux model is also presented.

Flow and radiation heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump in porous medium

Abstract In this paper, we present an investigation for the flow and radiation heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump in porous medium. The Brownian motion and thermophoresis are taken into account according to Rosseland’s approximation. The governing coupled partial differential equations are non-dimensionalized and solved both numerically and analytically by local similarity method. The effects of involved parameters (velocity slip, temperature jump, thermal radiation, Prandtl number, Lewis number, Brownian motion, thermophoresis) on velocity, temperature and concentration profiles are presented graphically and analyzed. Moreover, the numerical results are compared with the analytical solutions obtained by Homotopy analysis method with very good agreement to validate the present results.

MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump

Abstract In this paper, the magnetohydrodynamic (MHD) flow and heat transfer over a porous shrinking sheet with velocity slip and temperature jump are investigated. A new technique is proposed to avoid the so called “secular” terms and to improve the computation efficiency of the HAM. The closed form expressions are obtained for the two dimensional flow; two branches of solutions are found first. For the non-slip case, we arrive at the convergence results by a third order iterative, which is better than that of a twenty-fifth order iterative in the literature obtained by classical HAM. Moreover, the effects of pertinent parameters on the axisymmetric flow and heat transfer are analyzed and discussed.

Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative

This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid. The fractional calculus approach is used to establish the constitutive relationship model of a viscoelastic fluid. Exact analytic solutions for the velocity field and shear stress in terms of Fox H-function are obtained by means of the Laplace transform. The influence of the relaxation and retardation times, the orders of the time fractional derivative and the magnetic body force on the velocity and shear stress are analyzed. It is shown that the ordinary Oldroyd-B fluid, generalized second grade fluid and Maxwell fluid are the limiting cases of the presented results.

Marangoni convection of power law fluids driven by power-law temperature gradient

Abstract This paper presents a research for Marangoni convection driven by a power-law temperature gradient. It is assumed that the surface tension is quadratic functions of the temperature and the effects of power law viscosity on temperature field into account by assuming that the temperature field is similar to the velocity field. The Navier–Stokes equations and the heat equation with modified Fouriers law heat conduction (Zhengs Model) for power law fluid media are reduced to two nonlinear ordinary differential equations and the solutions are presented numerically. The effects of the Power-law Number and the Marangoni Number on the interfacial velocity and the interfacial temperature gradient are presented in tabular form and the effects of various parameters on the velocity and temperature fields are analyzed and discussed in detail.

Skin friction and heat transfer in power-law fluid laminar boundary layer along a moving surface

Analytical and numerical solutions are presented for momentum and energy laminar boundary layer along a moving plate in power-law fluids utilizing a similarity transformation and shooting technique. The results indicate that for a given power-law exponent n(0<n⩽1) or velocity ratio parameter ξ, the skin friction σ decreases with the increasing in ξ or n. The shear force decreases with the increasing in dimensionless tangential velocity t. When Prandtl number NPr=1, the dimensionless temperature w(t) is a linear function of t, and the viscous boundary layer is similar to that of thermal boundary layer. In particular, w(t)=t if ξ=0, i.e., the velocity distribution in viscous boundary layer has the same pattern as the temperature distribution in the thermal boundary and δ=δT. For NPr⩾1, the increase of viscous diffusion is larger than that of thermal diffusion with the increasing in NPr, and δT(t)<δ(t). The thermal diffusion ratio increases with the increasing in n(0<n⩽1) and ξ.

Effects of second order velocity slip and nanoparticles migration on flow of Buongiorno nanofluid

Abstract The present work analyzes the effects of second order velocity slip and nanoparticles migration on nanofluids between two rotating parallel plates. The classical Buongiorno model involves Brownian motion and thermophoretic diffusivities is modified by considering nanoparticle volume fraction distribution. Homotopy analysis method is employed to solve the equations, then the accuracy and efficiency of the HAM solutions are verified by h -curves and residual errors curves using package BVPh2.0. Physical interests in Nusselt number and skin friction as well as nanoparticles migration are illustrated by graphs.

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.

Exact solutions for MHD flow of generalized Oldroyd-B fluid due to an infinite accelerating plate

This paper presents a research for the magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid due to an infinite accelerating plate. The motion of the fluid is produced by the infinite plate, which at time t=0^+ begins to slide in its plane with a velocity At. The fractional calculus approach is introduced to establish the constitutive relationship of the Oldroyd-B fluid. The solutions are established by means of Fourier sine and Laplace transforms in terms of the G and R functions written as a direct sum of the Newtonian solution and the corresponding non-Newtonian solutions. When @a=@b=1, M=0, the solutions corresponds to the ordinary Oldroyd-B fluids, while @q=0 and @l=0 describe the Maxwell fluid and the generalized second grade fluid, as limiting cases of present results, respectively.

Unsteady flow and heat transfer of a generalized Maxwell fluid due to a hyperbolic sine accelerating plate

This paper deals with the unsteady flow and heat transfer of a generalized Maxwell fluid over a moving flat plate with variable temperature and hyperbolic sine velocity. Exact solutions are established for the velocity and temperature fields in terms of discrete Fourier sine transform coupled with Laplace transform for the fractional calculus. Graphs are sketched for values of parameters and associated dynamic characteristics are analyzed.