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This paper evaluates thermal output for the flow of Maxwell nanofluid over an extending sheet with bioconvection of micron size self-motivated organisms. Radiative heat flux and two temperature boundary conditions, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF), are considered. The flow is influenced by a magnetic field and porosity effects of a medium. The motivation pertains to attain an enhancement in thermal transportation via nanoparticle inclusion. The possible settling of the nanoparticles may be avoided by bioconvection of microorganisms. The basic theoretical conservation of mass, concentration, momentum, and energy provides a nonlinear set of partial differential equations which are then transmuted into ordinary differential form. The implementation of Runge-Kutta method with shooting technique in Matlab coding resulted the numerical solution. A deep insight into the problem is inspected by varying the inputs of influential parameters of the dependent functions. It is perceived that the flow speed is hindered by the growing inputs of parameters of buoyancy ratio, magnetic field, Raleigh number, and porosity. The temperature of the fluid attains higher outputs directly with thermophoresis and Brownian movement of nanoparticles. Motile microorganisms 𝜒(𝜂) profile goes down when bioconvection Schmidt number intensified. The current numeric results are validated when compared within existing studies.

In this article, we explore how activation energy and varied transit parameters influence the two-dimensional stagnation point motion of nano-biofilm of Sutterby fluids incorporating gyrotactic microbes across a porous straining/shrinking sheet. Prior investigations implied that fluid viscosity as well as thermal conductance are temperature based. This research proposes that fluid viscosity, heat capacity and nanofluid attributes are all modified by solute concentration. According to some empirical research, the viscosity as well as heat conductivity of nanoparticles are highly based on the concentration of nanoparticles instead of only the temperature. The shooting approach with the RK-4 technique is applied to acquire analytical results. We contrast our outcomes with those in the existing research and examine their consistency and reliability. The graphic performance of relevant factors on heat, velocity, density and motile concentration domains are depicted and discussed. The skin friction factor, Nusselt number, Sherwood number and the motile density are determined. As the concentration-dependent properties are updated, the speed, temperature, concentration and motile density profiles are enhanced, but for all concentration-varying factors, other physical quantities deteriorate.

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The purpose and novelty of our study include the scrutinization of the unsteady flow and heat characteristics of the unsteady Sutterby nano-fluid flow across an elongated cone using slip boundary conditions. The bioconvection of gyrotactic micro-organisms, Cattaneo–Christov, and thermal radiative fluxes with magnetic fields are significant physical aspects of the study. Anisotropic constraints on the cone surface are taken into account. The leading formulation is transmuted into ordinary differential formate via similarity functions. Five coupled equations with nonlinear terms are resolved numerically through the utilization of a MATLAB code for the Runge–Kutta procedure. The parameters of buoyancy ratio, the porosity of medium, and bioconvection Rayleigh number decrease x-direction velocity. The slip parameter retard y-direction velocity. The temperature for Sutterby fluids is at a hotter level, but its velocity is vividly slower compared to those of nanofluids. The temperature profile improves directly with thermophoresis, v-velocity slip, and random motion of nanoentities.