The flow of homogeneous fluids through porous media: analogies with other physical problems

This article reports on the International Nanofluid Property Benchmark Exercise, or INPBE, in which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles or “nanofluids,” was measured by over 30 organizations worldwide, using a variety of experimental approaches, including the transient hot wire method, steady-state methods, and optical methods. The nanofluids tested in the exercise were comprised of aqueous and nonaqueous basefluids, metal and metal oxide particles, near-spherical and elongated particles, at low and high particle concentrations. The data analysis reveals that the data from most organizations lie within a relatively narrow band (±10% or less) about the sample average with only few outliers. The thermal conductivity of the nanofluids was found to increase with particle concentration and aspect ratio, as expected from classical theory. There are (small) systematic differences in the absolute values of the nanofluid thermal conductivity among the various experimental approaches; however, such differences tend to disappear when the data are normalized to the measured thermal conductivity of the basefluid. The effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al. [J. Appl. Phys. 81, 6692 (1997)], was found to be in good agreement with the experimental data, suggesting that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in this exercise.

A Benchmark Study on the Thermal Conductivity of Nanofluids

Impact of Cattaneo–Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface

In this article, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations. On the basis of the homotopy analysis method, a scheme is developed to obtain the approximate solution of the fractional KdV, K(2,2), Burgers, BBM-Burgers, cubic Boussinesq, coupled KdV, and Boussinesq-like B(m,n) equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The homotopy analysis method for partial differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions of the studied models are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Solving nonlinear fractional partial differential equations using the homotopy analysis method

Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature

Entropy optimization in passive and active flow of liquid hydrogen based nanoliquid transport by a curved stretching sheet

Influence of thermal radiation on the laminar two-dimensional incompressible flow of upper-convected Maxwell (UCM) fluid is investigated. An entirely different aspect of Rosseland approximation for thermal radiation is captured. The relevant equations are first modeled and then solved numerically by the shooting method using a fourth-order Runge-Kutta integration technique. The solutions are validated with the built-in solver bvp4c of the software MATLAB. Graphs are sketched to examine the behaviors of interesting parameters entering into the problem.

Effects of Thermal Radiation on the Stagnation-Point Flow of Upper-Convected Maxwell Fluid over a Stretching Sheet

Abstract This paper presents magnetohydrodynamic (MHD) stagnation point flow of second grade fluid over a permeable stretching cylinder. Analysis has been carried out with heat and mass transfer. Viscous dissipation and Joule heating effects are also investigated. Suitable transformations are used to convert non-linear partial differential equations into the non-linear ordinary differential equations. Variation of different parameters on the velocity, temperature and concentration profiles are shown graphically. Numerical values of skin friction coefficient, Nusselt number and Sherwood number are computed. Comparison of f″(0), −θ′(0) and −c′(0) with the previous results are also examined.

MHD Stagnation Point Flow of Second Grade Fluid over a Stretching Cylinder with Heat and Mass Transfer

The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model) with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed.

Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material

A two-dimensional model is used to analyze the unsteady pulsatile flow of blood through a tapered artery with stenosis The rheology of the flowing blood is captured by the constitutive equation of Carreau model The geometry of the time-variant stenosis has been used to carry out the present analysis The flow equations are set up under the assumption that the lumen radius is sufficiently smaller than the wavelength of the pulsatile pressure wave A radial coordinate transformation is employed to immobilize the effect of the vessel wall The resulting partial differential equations along with the boundary and initial conditions are solved using finite difference method The dimensionless radial and axial velocity, volumetric flow rate, resistance impedance and wall shear stress are analyzed for normal and diseased artery with particular focus on variation of these quantities with non-Newtonian parameters

T. Hayat

Papers

Entropy optimization in passive and active flow of liquid hydrogen based nanoliquid transport by a curved stretching sheet

Effects of Thermal Radiation on the Stagnation-Point Flow of Upper-Convected Maxwell Fluid over a Stretching Sheet

MHD Stagnation Point Flow of Second Grade Fluid over a Stretching Cylinder with Heat and Mass Transfer

Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material

Effects of unsteadiness and non-Newtonian rheology on blood flow through a tapered time-variant stenotic artery