In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter N _R , and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.

The application of hybrid nanoparticles rather than nanoparticles is one of the greatest critical tasks for enhancing heat transfer. Therefore, the purpose of this article is to analyze the flow and heat transfer resulting from an exponentially decreased sheet of hybrid nanoparticles. The magnetite (Fe₃O₄) and copper (Cu) nanoparticle are suspended in ethylene glycol (EG) to form Fe₃O₄–Cu/EG hybrid nanofluid. The PDEs governing equations of the issue have been solved after conversion to ODEs by using suitable similarity transformations. The resultant system is then solved numerically by the aid of Runge–Kutta–Fehlberg method (RKF45) with the shooting technique. The most important results of this study are the effect of different variable parameters such as permeability of porous media, the stretching/shrinking parameter, heat generation/absorption effect, slip, and nanoparticle volume fraction on the velocity, temperature profiles, skin friction coefficient, and local Nusselt number. Furthermore, the impacts of radiation, magnetohydrodynamic (MHD), suction/injection parameter, and Prandtl number are also taken into consideration. The influence of important physical parameters is discussed through graphs and tables. It is found that the increase of Fe₃O₄ nanoparticle concentration enhances the heat transfer rate of the hybrid nanofluid in a shrinkable case, the opposite happens in a stretchable state.

Parabolic trough solar collectors (PTSCs) are generally utilized to reach high temperatures in solar-thermal applications. The current work investigates entropy production analysis and the influence of nano solid particles on a parabolic trough surface collector (PTSC) installed within a solar powered ship (SPS). For the current investigation, the non-Newtonian Maxwell type, as well as a porous medium and Darcy–Forchheimer effects, were used. The flow in PTSC was produced by a nonlinear stretching surface, and the Cattaneo–Christov approach was used to assess the thermal boundary layer’s heat flux. Similarity transformation approach has been employed to convert partial differential equations into solvable ordinary differential equations allied to boundary conditions. Partial differential and the boundary conditions have been reduced into a group of non-linear ordinary differential equations. A Keller-box scheme applied to solve approximate solutions of the ordinary differential equations. Single-walled carbon nanotubes -engine oil (SWCNT-EO) and Multiwalled carbon nanotubes/engine oil (MWCNT-EO) nanofluids have been utilized as working fluid. According to the findings, the magnetic parameter led to a reduction in the Nusselt number, as well as an increment in skin friction coefficient. Moreover, total entropy variance over the domain enhanced for flow rates through Reynolds number and viscosity fluctuations were monitored by using Brinkman number. Utilizing SWCNT-EO nanofluid increased the thermal efficiency between 1.6–14.9% in comparison to MWCNT-EO.

Heat is absorbed from radiations of the sun by a solar collector, concentrated, and then transmitted to an active nanofluid. The flow of Casson nanofluid is utilized in Parabolic Trough Solar Collector (PTSC) in the present analysis over an infinite and porous sheet. Ordinary differential equations are derived in nonlinear form and solved using suitable similarity transformation reducing into boundary conditions. Keller box method was employed to solve the system of ODEs. Results for nanofluids of Copper-engine oil (Cu-EO), as well as Iron (II, III) oxide-engine oil (Fe₃O₄-EO), were examined and detailed. With the help of the induced magnetic factor, the rate of heat transfer decreased while the parameter of skin resistance increased prominently. While using Cu/Fe₃O₄-EO as base fluid, the rate of heat transfer is an important factor. Total enhancement in the thermal efficiency of Cu-EO on Fe₃O₄-EO has a minimum value of 2.7% while the maximum value is 18.5%.