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 Marble–Drew fluid–particle 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 ℏ, 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 (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (PL), buoyancy parameter (B) and temperature inverse Stokes number (SkT) on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity (Up), dimensionless fluid phase temperature (Φ) and the dimensionless temperature of particle phase (Φp). 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.