Purpose This paper aims to investigate a mathematical model with numerical simulation for bacterial growth in the heart valve. Design/methodology/approach For antibacterial activities and antibodies properties, nanoparticles have been used. As antibiotics are commonly thought to be homogeneously dispersed through the blood, therefore, non-Newtonian fluid of Casson micropolar blood flow in the heart valve for two dimensional with variable properties is used. The heat transfer with induced magnetic field translational attraction under the influence of slip is considered for the resemblance of the heart valve prosthesis. The numeral results have been obtained by using the Chebyshev pseudospectral method. Findings It is proven that vascular resistance decreases for increasing blood velocity. It is noted that when the magnetic field will be induced from the heart valve prosthesis then it may cause a decrease in vascular resistance. The unbounded molecules and antibiotic concentration that are able to penetrate the bacteria are increased by increasing values of vascular resistance. The bacterial growth density cultivates for upswing values of magnetic permeability and magnetic parameters. Originality/value To the best of the authors’ knowledge, this is the first study to investigate a mathematical model with numerical simulation for bacterial growth in the heart valve.

This study deals with the mass transport phenomena on the particle-fluid motion through an annulus. The non-Newtonian fluid propagates through a ciliated annulus in the presence of two phenomenon, namely (i) endoscopy, and (ii) blood clot. The outer tube is ciliated. To examine the flow behavior we consider the bi-viscosity fluid model. The mathematical modeling has been formulated for small Reynolds number to examine the inertia free flow. The purpose of this assumption is that wavelength-to-diameter is maximal, and the pressure could be considerably uniform throughout the entire cross-section. The resulting equations are analytically solved, and exact solutions are given for particle- and fluid-phase profiles. Computational software Mathematica has been used to evaluate both the closed-form and numerical results. The graphical behavior across each parameter has been discussed in detail and presented with graphs. The trapping mechanism is also shown across each parameter. It is noticed clearly that particle volume fraction and the blood clot reveal converse behavior on fluid velocity; however, the velocity of the fluid reduced significantly when the fluid behaves as a Newtonian fluid. Schmidt and Soret numbers enhance the concentration mechanism. Furthermore, more pressure is required to pass the fluid when the blood clot appears.

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Purpose The study aims to determine an efficiency of external magnetic field on the bacteria surrounded by thousands of magnetic magnetite nanoparticles. The interstitial nanoliquid in which an artificial bacteria swims in biological cell is utilized with variable thermal conductivity. Two dimensions unsteady motion of second grade fluid are considered. The stretching wall is taken as a curved surface pattern. Design/methodology/approach The mathematical results have been obtained by Chebyshev pseudospectral method. Findings The impact of the various governing parameters is described by numerical tables and diagrams. It is proven that the pure blood velocity curves are higher when compared with the magnetite/blood. It is demonstrated from clinical disease that dangerous tumors show diminished blood flow. This study concludes that the blood velocity profile increases by increasing the values of fluid parameters. This implies that the medication conveyance therapy lessens the tumor volume and helps in annihilating malignancy cells. The blood temperature distribution raises as the magnetite nanoparticles concentration increases. Consequently, the physical properties of the blood can be enhanced by immersing the magnetite nanoparticles. Further, the present outcomes cleared the thermal conductivity as, a variable function of the temperature, has an important role to enhance the heat transfer rate. Originality/value To the best of authors’ knowledge, this study is reported for the first time.