The present work discusses the 2D unsteady flow of second grade hybrid nanofluid in terms of heat transfer and MHD effects over a stretchable moving flat horizontal porous plate. The entropy of system is taken into account. The magnetic field and the Joule heating effects are also considered. Tiny-sized nanoparticles of silicon carbide and titanium oxide dispersed in a base fluid, kerosene oil. Furthermore, the shape factors of tiny-sized particles (sphere, bricks, tetrahedron, and platelets) are explored and discussed in detail. The mathematical representation in expressions of PDEs is built by considering the heat transfer mechanism owing to the effects of Joule heating and viscous dissipation. The present set of PDEs (partial differential equations) are converted into ODEs (ordinary differential equations) by introducing suitable transformations, which are then resolved with the bvp4c (shooting) scheme in MATLAB. Graphical expressions and numerical data are obtained to scrutinize the variations of momentum and temperature fields versus different physical constraints.

The bioconvection effects with nanofluid are major application in biofuels. This analysis aimed to observe the bioconvection effect in unsteady two-dimensional Maxwell nanofluid flow containing gyrotactic motile microorganisms across a stretching/shrinking cylinder evaluating the consequences of thermal radiation and activation energy. The Cattaneo-Christov double diffusion theory is also observed. Nanofluids are quickly perceptive into many solicitations in the latest technology. The current research has noteworthy implementations in the modern nanotechnology, microelectronics, nano-biopolymer field, biomedicine, biotechnology, treatment of cancer therapy, cooling of atomic reactors, fuel cells, and power generation. By using the proper similarity transformation, the partial differential equations that serve as the basis for the current study are gradually reduced to a set of highly nonlinear forms of ordinary differential equations, which are then numerically, approached using a well-known shooting scheme and the bvp4c tool of the MATLAB software. Investigated is the profile behavior of the flow regulating parameters for the velocity field, thermal field, and volumetric concentration of nanoparticles and microorganisms. From the results, it is concluded that velocity is reduced with a larger bioconvection Rayleigh number. The thermal field is increased with a larger amount of thermal Biot number and thermal radiation. The concentration of nanoparticles increases with an increment in the thermophoresis parameter. Furthermore, the microorganism’s field is decreased with a larger Lewis number. The findings demonstrate that by optimizing the concentration of nanoparticles and microorganisms, the thermal efficiency of biofuels can be significantly improved. This leads to more sustainable and efficient energy production. By optimizing the concentration of nanoparticles and microorganisms in biofuels, the thermal properties can be significantly improved, leading to more efficient combustion processes. This can reduce the overall cost and increase the yield of biofuels. Improved cooling systems for medical imaging devices such as MRI machines can be developed using nanofluids, ensuring better performance and patient safety.