Analytical solutions of dissipative heat transfer on the peristaltic flow of non-newtonian fluids in asymmetric channels

Peristalsis is a natural mechanism responsible for the propulsion and the segmentation of biofluids in living structures, and this mechanism is important due to its efficient pumping characteristics. An essential feature of peristalsis is dissipation, thus dissipative heat transfer must be considered in the propulsion of biofluids. Most biofluids exist with different non-Newtonian fluid characteristics and experimental investigations reveal that the physiological structures are non-uniform with asymmetric peristaltic waves. This research focuses on the development of mathematical models which take into account the dissipative heat transfer on the peristaltic flow of non-Newtonian fluids. The non-Newtonian fluids include Walter’s B, fourth grade and Sisko fluids and the flow have been considered in the horizontal and inclined asymmetric channels. Governing equations are first modeled in the laboratory frame and then transformed into the wave frame. Resulting equations are non-dimensionalized and the nonlinearity has been reduced by adopting the long wavelength and small Reynolds number approximations. Explicit forms of the analytical solutions have been obtained using the regular perturbation method. Influences of various parameters such as velocity slip parameter, Sisko fluid parameter, Brinkman, Eckert, Deborah, Soret and Schmidt numbers on the flow quantities namely velocity, shear stress, pumping, trapping, temperature, concentration and heat transfer coefficients have been investigated. Results show that pumping, trapping and temperature are reduced for increasing velocity slip parameter. Temperature and heat transfer coefficients are increased with the increase of Brinkman, Eckert and Deborah numbers. Concentration decreases with the increase of Brinkman, Soret and Schmidt numbers. Comparative study amongst viscous, shear thinning and shear thickening fluids has also been presented

Partial slip effect on heat and mass transfer of MHD peristaltic transport in a porous medium

This research looks at the effects of partial slip on heat and mass transfer of peristaltic transport. The magnetohydrodynamic (MHD) flow of viscous fluid in a porous asymmetric channel has been considered. The exact solutions for the stream function, longitudinal pressure gradient, longitudinal velocity, shear stress, temperature and concentration fields are derived by adopting long wavelength and small Reynolds number approximations. The results showed that peristaltic pumping and trapping are reduced with increasing velocity slip parameter. Furthermore, temperature increases with increasing thermal slip parameter. Moreover, the concentration profile decreases with increasing porosity parameter, Schmidt number and concentration slip parameter. Comparisons with published results are found to be in good agreement

Application of caputo-fabrizio fractional order derivative (NFDt) in simulating the MHD flow of the third grade non-newtonian fluid in the porous artery

In this paper, the third grade non-Newtonian MHD blood flow in the porous arteries subjected to the periodic pressure gradient was studied using the Caputo-Fabrizio (NFDt ) time fractional order derivative. The time fractional model was solved by taking the Laplace and the finite Hankel transforms. Results were compared with those reported in the previous studies and good agreement was found. The Mathematica software was used to simulate the velocity profile and the Bessel functions with zero order and first order of first kind. The correlations between the flow velocity and the third grade non-Newtonian fluid parameter, the magnetic field and the porosity were negative. Nevertheless, the flow velocity increased with respect to the Womersely number

Pulsatile blood flow through a constricted porous artery

In this paper a speculative study of an incompressible Newtonian blood flow through a constricted porous channel and pulsatile nature is inspected. Porosity parameter λ is incorporated in the momentum equation. Governing nonlinear differential equations are numerically evaluated by employing the perturbation method technique for a very small perturbation parameter ε 1 such that ε ≠ 0 and with conformable boundary conditions. Numerical results of the flow velocity profile and volumetric flow rate have been derived numerically and detailed graphical analysis for different physical parameters porosity, Reynolds number and stenosis has been presented. It is found that arterial blood velocity is dependent upon all of these factors and that the relationship of fluid velocity and flow is more complex and nonlinear than heretofore generally believe. Furthermore the flow velocity enhanced with Reynolds number, porosity parameter and at maximum position of the stenosis/constriction

Caputo-fabrizio time fractional derivative applied to visco elastic MHD fluid flow in the porous medium

In this paper the laminar fluid flow in the axially symmetric porous cylindrical channel subjected to the magnetic field was studied. Fluid model was non-Newtonian and visco elastic. The effects of magnetic field and pressure gradient on the fluid velocity were studied by using a new trend of fractional derivative without singular kernel. The governing equations consisted of fractional partial differential equations based on the Caputo-Fabrizio new time-fractional derivatives NFDt. Velocity profiles for various fractional parameter a, Hartmann number, permeability parameter and elasticity were reported. The fluid velocity inside the cylindrical artery decreased with respect to Hartmann number, permeability parameter and elasticity. The results obtained from the fractional derivative model are significantly different from those of the ordinary model

A Note on Radiative Heat Transfer to Peristaltic Flow of Sisko Fluid

This paper looks at the effects of radiative heat transfer on the peristaltic transport of a Sisko fluid in an asymmetric channel with nonuniform wall temperatures. Adopting the lubrication theory, highly nonlinear coupled governing equations involving power law index as an exponent have been linearized and perturbation solutions are obtained about the Sisko fluid parameter. Analytical solutions for the stream function, axial pressure gradient, axial velocity, skin friction, and Nusselt number are derived for three different cases (i.e., shear thinning fluid, viscous fluid, and shear thickening fluid). The effects of Grashof number, radiation parameter, and other configuration parameters on pumping, trapping, temperature, Nusselt number, and skin friction have been examined in detail. A good agreement has been found for the case of viscous fluid with existing results

Non-linear peristaltic flow of Walter's B fluid in an asymmetric channel with heat transfer and chemical reactions

In this paper, effects of heat and mass transfer on peristaltic transport of Walter's B fluid in an asymmetric channel are investigated. The governing equations are solved using regular perturbation method by taking wave number as a small parameter. Expressions for the stream function, temperature distribution, heat transfer coefficient, and mass concentration are presented in explicit form. Solutions are analyzed graphically for different values of arising parameters such as viscoelastic parameter, Prandtl, Eckert, Soret, Schmidt and Reynolds number. It has been found that these parameters considerably affect the considered flow characteristics. Results show that with an increase in Eckert and Prandtl number temperature and heat transfer coefficient increase while mass concentration decreases. Further, Mass concentration also decreases with increasing Soret and Schmidt numbe

Unsteady two-dimensional blood flow in porous artery with multi-irregular stenosis

The flow characteristics of an unsteady axisymmetric two-dimensional (2D) blood flow in a diseased porous arterial segment with flexible walls are investigated. The arterial walls mimic the irregular constrictions whereas the lumen containing the thrombus, cholesterol, and fatty plaques represents the porous medium. The governing equations with appropriate initial and boundary conditions are solved numerically using MAC method. The discretization is done on staggered grid with non-uniform grid size and pressure-poisson equation is solved following SOR method. The pressure and velocity corrections are made cyclically until the steady state is achieved. It is observed that for decreasing permeability, flow is highly decelerated while pressure drop and wall shear stress increases. The separation zones and re-circulation regions are found for severe stenoses. Flow separation and re-circulation diminishes for decreasing permeability of the porous medium. Comparisons are provided with published experimental and numerical result