In this work, an effective thermal conductivity (ETC) for living tissues, which directly affects the energy transport process, is determined. The fractal scaling and Monte Carlo methods are used to describe the tissue as a porous medium, and blood is considered a Newtonian and non-Newtonian fluid for comparative and analytical purposes. The effect of the principal variables—such as fractal dimensions $D_T$ and $D_f$, porosity, and the power-law index, n—on the temperature profiles as a function of time and tissue depth, for one- and three-layer tissues, besides temperature distribution, are presented. ETC was improved by considering high tissue porosity, low tortuosity, and shear-thinning fluids. In three-layer tissues with different porosities, perfusion with a non-Newtonian fluid contributes to the understanding of the heat transfer process in some parts of the human body.

In this work, the dynamics of the bioconvection process of gravitactic microorganisms enclosed in a rectangular cavity, is analyzed. The dimensionless cell and energy conservation equations are coupled with the vorticity-stream function formulation. Then, the effects of the bioconvection Rayleigh number and the heating source on the dynamics of microorganisms are discussed. The results based in streamlines, concentration and temperature contours are obtained through numerical simulations considering eight different configurations of symmetrical and asymmetrical heat sources. It is concluded that microorganisms accumulate in the warmer regions and swim through the cooler regions to reach the surface. They form cells for each heat source, but at high concentrations, they form a single stable cell. The results presented here can be applied to control and to understand the dynamics of microorganisms with discrete heat sources.

The multiscale modeling of complex fluids under small and large amplitude oscillatory shear flow using non-linear kinetic and transient network models is presented. The kinetics of microstates is analogous to chemical kinetics, which defines the physical macromolecule interaction in a Newtonian fluid, and the concentration of microstates defines a variable maximum length of extension for each microstate. The effect of important parameters like viscosity ratio, chain length, viscoelasticity, kinetic rate constants, for different initial entanglement scenarios (entangled, disentangled and aleatory) are analyzed. The Lissajous curves for the shear stress and the first normal stress difference versus the instantaneous strain or strain-rate are shown. The self-intersection of the Lissajous curves or secondary loops is shown to depend on the kinetic rate constants, the maximum extension length, and the elasticity.

The results of numerical simulations of gravitactic bioconvection influenced by nanoparticles suspended in water are analyzed. In this work, two cases are established which consider the removal of nanometric particles suspended in wastewater. The competence among the bioconvection of Paramecium caudatum, natural convection and buoyancy of nanoparticles phenomena in an aqueous suspension is presented. The position of a thermal source to control the orientation of microorganisms when swimming is analyzed. Numerical simulations are carried out using the finite difference method in an ADI scheme, employing stream-vorticity formulations and equations for microorganisms, nanoparticle concentration, and energy. The percentage of nanoparticles is considered using the Rayleigh number, which includes the effect of Brownian and thermophoretic parameters. At low values of the Brownian parameter ${\delta }_{Bm}=0.1$, thermophoretic parameter ${\delta }_{Tm}=0.1$, and the nanoparticles Rayleigh number $0.005<R{a}_n<0.015$, the swimming of microorganisms contributed to streamlines across which nanoparticles traveled in response to a thermal control source. Thus, the results obtained suggest an alternative approach to the removal of solids such as heavy metals in polluting waters. The development of this type of technology will help in the bioremediation of wastewater.

The scale-up and control of the acrylamide polymerization process in solution is presented. The viscosity is modeled as a function of temperature and monomer concentration. Four cases are analyzed: (i) Keeping the similarity principles to carry out the polymerization using water to heat and cool the process, (ii) using water with nanoparticles to heat and cool the process, (iii) adding the initiator at different temperatures to start the polymerization, and (iv) modifying the heat-transfer area by changing the aspect ratio $L/D_r$. The reactor and jacket temperature profiles, the reaction conversion, and the average molecular weight are presented. The main finding is that increasing the heat-transfer area by modifying the $L/D_r$ ratio also increases the efficiency of the polymerization process. Futhermore, the numerical results indicate that the addition of the initiator at low temperatures increases the molecular weight of the final product.

This paper presents a novel implementation of a numerical scheme for predicting complex flows of viscoelastic fluids using a finitely extensible nonlinear elastic (FENE) transient network model. This model extends the FENE model by incorporating chain interactions and accounting for the way in which the maximum chain length, drag, and relaxation time are influenced by entanglement and disentanglement processes. Three different initial networks are considered (disentanglement, entanglement, and aleatory), and the influence of variables such as the kinetic rate constants, elasticity, and chain length on the microstate concentration, stresses, and drag force is investigated. It is shown that although the concentrations of the microstates are independent of the Weissenberg number and the maximum extension length, the stresses and hence the drag are influenced by them.