Date Published: February 2, 2017
Publisher: Public Library of Science
Author(s): Anum Tanveer, T. Hayat, A. Alsaedi, B. Ahmad, Xiao-Dong Wang.
Main theme of present investigation is to model and analyze the peristaltic activity of Carraeu-Yasuda nanofluid saturating porous space in a curved channel. Unlike the traditional approach, the porous medium effects are characterized by employing modified Darcy’s law for Carreau-Yasuda fluid. To our knowledge this is first attempt in this direction for Carreau-Yasuda fluid. Heat and mass transfer are further considered. Simultaneous effects of heat and mass transfer are examined in presence of mixed convection, viscous dissipation and thermal radiation. The compliant characteristics for channel walls are taken into account. The resulting complex mathematical system has been discussed for small Reynolds number and large wavelength concepts. Numerical approximation to solutions are thus plotted in graphs and the physical description is presented. It is concluded that larger porosity in a medium cause an enhancement in fluid velocity and reduction in concentration.
Nanomaterials are known to posses increase in heat transfer processes like waste heat recovery, automobile radiators, thermal management, heat exchangers and refrigeration. The colloidal suspension of nanometer sized particles (metallic or non-metallic) in traditional fluids give rise to nanofluids. Such fluids with an improvement in thermal conductivity and thermal diffusivity enhance the heat transfer of conventional fluids. Further involvement of nanofluids in heat transfer process reduces the capital costs and upgrade the energy conversion and efficiency. The preparation of nanofluids is due to addition of materials like metals, non-metals, carbides and hybrid etc into water, oil or glycols. Out of existing models of nanofluids the Buongiorno  model emphasizes that heat transfer is mainly due to thermophoresis and Brownian diffusion. Since then extensive literature is available on the topic (see refs. [2–11]).
The mathematical modeling for an incompressible Carreau-Yasuda nanofluid in a channel configured in a circle of inner radius R* and separation 2d¯ is made in this section. The presence of porous medium between the curved walls of the channel is considered. The gravitational effects are taken into account. Here r¯ signifies the radial-direction whereas x¯ denotes the axial direction. The dynamics of fluid inside the channel boundaries is developed through the propagation of peristaltic waves along the channel walls (see Fig 1). Moreover relative to arterial like flow peristalsis the influential aspect of compliance in terms of wall’s stiffness, elasticity and damping is not ignored. The relative positions of the curved channel walls in radial direction can be visualized through the following expression:
where c, a¯, λ denote the peristaltic wave speed, amplitude and length, t¯ and ±η¯ the time and displacements of channel walls.
The above mentioned problem results in the non-linear coupled system of equations whose explicit solution seems difficult to attain. However with the intense algorithmic advancement many built-in solution softwares are available at present. Mathematica is one of these. The exact as well as numerical approximation to solution expressions can be obtained efficiently through mathematica. Mathematica built-in routine NDSolve provides level of numerical computation with its systematic algorithm selection, automatic error tracking and precision arithmetics. Here we solve the above system numerically to skip the complexity of solutions and to obtain the graphical results directly. Thus the graphical description of pertinent parameters towards axial velocity u, temperature θ, concentration ϕ and heat transfer coefficient Z has been made in this section. Particularly the development of u, θ, ϕ and Z with the varying values of heat and mass transfer Grashof numbers Gr and Qr, thermophoresis and Brownian motion parameters Nt and Nb, wall compliant parameters E1, E2, E3, Darcy number Da, viscosity ratio parameter β, fluid parameter n, curvature parameter k, Prandtl number Pr, Brinkman number Br, radiation parameter Rd, Weissenberg number We will be emphasized via physical basis.
Mixed convection flow bounded in curved channel with compliant boundaries is developed for Carreau-Yasuda nanofluid. The observation is made for porous medium using modified Darcy’s law specifically. Such conditions are applicable in blood vessels where small pores allow exchange of water, ions, gases, lymph transport and other small molecules. An increase in porosity signifies disease states where endothelial barrier breaks down and allow large molecules like protein out of the vessel. In addition the thermal radiation and viscous dissipation effects are also examined. The particular points of this study are: