Homotopy Simulation of Two-Phase Thermo-Hemodynamic Filtration in a High Permeability Blood Purification Device

Abstract

A two-phase thermo-hydrodynamic model is presented for transport in the vertical chamber of a porous media blood filtration device. A non-Darcy drag force formulation was employed. The MarbleÀDrew fluidÀparticle suspension model was used to simulate the plasma phase and the suspension (erythrocyte) particle phase. The non-dimensional transport equations were solved using a semi-computational procedure known as the homotopy analysis method (HAM). With the judicious use of the auxiliary parameter }, HAM affords a powerful mechanism to adjust and control the convergence region of solution series. This method provides an efficient approximate analytical solution with high accuracy, minimal calculation and avoidance of physically unrealistic assumptions. Detailed computations are presented for the effects of Grashof number (Gr), momentum inverse Stokes number (Sk m ), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (P L ), buoyancy parameter (B) and temperature inverse Stokes number (Sk T ) on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity (U p ), dimensionless fluid phase temperature (È) and the dimensionless temperature of particle phase (È p ). A Prandtl number of 25 was used to simulate blood at room temperature. Excellent correlation was obtained between the HAM and numerical shooting quadrature solutions. The results indicated that there is a strong decrease in fluid phase velocities with increasing Darcian (first order) drag and second-order Forchheimer drag, and a weaker reduction in particle phase velocity field. Applications of the study include porous media bio-filtration devices and dialysis simulations.

Homotopy Semi-Numerical Modeling of Non-Newtonian Nanofluid Transport External to Multiple Geometries Using a Revised Buongiorno Model

“…Hayat et al [49] examined the non-Fourier thermal convection of carbon nanotube fluids over a curved stretching surface. Other applications of HAM in biological fluid dynamics and nanoscale transport include [50][51][52]. To extract the solutions of Equations (7)-(9) subject to the boundary conditions (10) using HAM, we have considered initial guesses f 0 , θ 0 and φ 0 of f , θ and φ in the following form:…”

Numerical study of time dependent flow of immiscible Saffman dusty (fluid-particle suspension) and Eringen micropolar fluids in a duct with a modified cubic B-spline Differential Quadrature method

“…The current study has demonstrated the excellent accuracy and stability characteristics of the modified cubic B-spine differential quadrature method (MCB-DQM) in numerical simulations of interfacial two-fluid (dusty-micropolar) duct flows. However, heat transfer and electromagnetic effects [54], [55] have been neglected. These may be considered in future studies and are also of relevance in biomedical and materials processing systems.…”

Magneto-bioconvection flow of a casson thin film with nanoparticles over an unsteady stretching sheet

“…Vasu and Ray (2019) applied HAM to discuss the non-similarity solution for the flow of Carreau nanofluid past vertical plate with Cattaneo–Christov heat flux model. Other applications in biological fluid dynamics and nanoscale transport include (Bég et al , 2012; Bég, et al , 2013; Tripathi and Bég, 2015; Srinivas and Bég, 2018). To extract the solutions of the equations (15) to (18) subjected to the boundary conditions in equation (19) using HAM, we take the initial guesses f 0 , θ 0 , ϕ 0 and χ 0 of f , θ , ϕ and χ in the following form: …”