Joule dissipation has an important role in the conversion of mechanical energy to heat within a fluid due to the internal friction and viscosity. Moreover, Darcy friction is a measure of the resistance to flow in a porous medium. In response to the efficient heat transfer performance, a robust statistical approach was established to optimize the heat transfer rate in a two-dimensional flow of a nanofluid over a permeable surface embedded with a porous matrix. The electrically conducive fluid affected the flow phenomena to include a carbon nanotube nanoparticle in the conventional liquid water for the enhanced heat transfer properties; additionally, the power-law heat flux model was considered. Appropriate transformation rules were adopted to obtain a non-dimensional system that brought a developed model equipped with several factors. The traditional numerical technique (i.e., shooting based Runge-Kutta) was proposed to handle the coupled nonlinear system. Furthermore, the statistical response surface methodology (RSM) was adopted to obtain an efficient optimized model for the heat transportation rate of the considered factors. An analysis of variance (ANOVA) was utilized to validate the result of the regression analysis. However, it was evident that the nanoparticle concentrations were useful to augment the fluid velocity and the temperature distributions; the statistical approach adopted for the heat transfer rate displayed an optimized effect as compared to a conventional effect.

Cancer remains a major health concern worldwide, causing high rates of morbidity and mortality. Although chemotherapy with antitumor drugs is the most common treatment for cancer, certain disadvantages limit its usage, such as the damage caused to healthy cells, side effects, and toxicity. Owing to their geometric and mechanical properties, nanotubes are promising nanocarriers of anticancer drugs. Here, the interaction energies of the encapsulation of an anticancer drug by single-walled nanotubes were calculated through the application of the 6–12 Lennard-Jones function with a continuous approach. In particular, the interaction energies of the 5-fluorouracil drug entering three different nanotubes (carbon, silicon and boron nitride) and the offset equilibria inside the nanotubes were obtained. This study aimed at determining the appropriate type and favorable size of nanotubes that can be used to encapsulate the 5-fluorouracil drug. The results showed that the optimal radii of nanotubes for encapsulating the 5-fluorouracil drug were approximately 6.08, 6.05 and 5.98 Å for carbon, boron nitride and silicon nanotubes, corresponding to -16.55, -18.20 and -17.81 kcal/mol, respectively.