In this new era of the fluid field, researchers are interested in hybrid nanofluids because of their thermal properties and potential, which are better than those of nanofluids when it comes to increasing the rate at which heat is transferred. Compared to the dynamics of radiative Ethylene Glycol-Zinc Oxide (nanofluid) and Ethylene Glycol-Zinc Oxide-Titanium Dioxide (hybrid nanofluid) flows between two permeable expanding/contracting walls, nothing is known in terms of Lorentz force, heat source, and the activation energy. The thermo-physical characteristics of Ethylene Glycol, Zinc Oxide nanoparticles, and Titanium Dioxide nanoparticles are used in this study to derive the governing equations for the transport of both dynamics. Governing equations are converted as a set of nonlinear ordinary differential equations (with the aid of suitable similarity mutations), and then the MATLAB bvp4c solver is used to solve the equations. This study’s significant findings are that rise in the reaction rate constant increases mass transfer rate, whereas an increase in the activation energy parameter decreases it. The mass transfer rate decreases at a rate of 0.04669 (in the case of hybrid nanofluid) and 0.04721 (in the case of nanofluid) when activation energy ($E$) takes input in the range $0\le E\le 5$. It has been noticed that the velocity profiles are greater when the walls are expanding as opposed to when they are contracting. It is detected that the heat transfer rate reduces as the heat source parameter increases. The heat transfer rate drops at a rate of 0.9734 (in the case of hybrid Nanofluid) and 0.97925 (in the case of nanofluid) when the heat source parameter ($Q$) takes input in the range $0\le Q\le 0.3$. In addition, it has been observed that the entropy generation increases as the Brinkmann number rises.

The effective use of non-Newtonian fluids is vital for situations involving heat and mass transfer. For instance, we employ thermal paste, a non-Newtonian fluid, to cool the CPU. By means of a computational approach, the behaviour of non-Newtonian on the surface of a two-dimensional steady MHD boundary layer flow and melting heat and mass transfer over a micropolar fluid is presented here, in conjunction with a partially slipper sheet at the surface providing heat generation/absorption. Further, heat radiation as well as chemical reactions are considered. Using similarity parameters, the governing nonlinear partial differential equations for heat, mass and flow are converted into a series of coupled nonlinear ordinary differential equations, then solved using the Runge–Kutta fourth order integration scheme and the shooting method. For various parameters defining the flow within the boundary layer, the new findings for velocity, microrotation, temperature and concentration are graphed. Graphic representations of local skin friction, Nusselt number and Sherwood number are provided. Boosting the melting parameter decreases fluid velocity, microrotation and temperature significantly. An intensification in slip near the boundary decreases both fluid velocity and microrotation, but opposite effects are observed on temperature.

The study investigates the flow characteristics of spherical shaped TiO2 –Ag hybrid nanofluid with water as a base fluid passing through a wet porous rectangular moving fin with a focus on understanding the effects of nanoparticle concentration on the heat transfer rate. The fin under consideration are subjected to boundary conditions, insulated and convective tips. Hybrid nanofluid that combine nanoparticles with conventional base fluids have potentially enhanced thermal conductivity and heat transfer properties in engineering applications. The energy balance equation containing the parameters that effect the flow of heat transfer rate is non- dimensionalized and solved numerically using 3-stage Lobatto - IIIa formula with appropriate boundary conditions. The simulation result shows the impact of different parameters on the flow and heat transfer properties of the hybrid nanofluid obtained by mixing spherical shaped TiO2 –Ag hybrid nanoparticles with water as base fluid. It is observed that the fin shows significant heat transfer rate in a convective tip relative to an insulated tip. The findings contribute to the understanding of hybrid nanofluid flow and its potential application in the design and optimization of thermal management system. It also facilitates the ground work for research in the field of nano fluid based cooling system. The observation from the graphical illustration shows that the rise in the thermal conductivity of the base fluid by 23% increases the conduction heat transfer as well as the temperature distribution by 10%. The natural convection and radiation are the key parameters that determines the heat transfer rate from the surface to the surrounding. In our investigation, enhancing the Nc,Nr parameters by 50% and 25%, the temperature distribution profile is reduced by about 13% and 6% respectively. The increase in the Pe number by 100% results in a rise in the temperature distribution by 8%.

The main concern of this paper is to analyze the nonlinearity of the Grashof numbers (thermal and diffusion) on the Williamson fluid flow across a stretching sheet with non-uniform thickness with the consideration of melting heat transfer. The modelled equations are non-dimensionalized with the utilization of similarity transformations. We used shooting technique based on Runge-Kutta 4th order method to unriddle the ensuing equations. Influence of key parameters on the common profiles i.e., velocity, temperature and concentration are deliberated with the support of graphs. And also, we examined friction factor, local Sherwood and Nusselt numbers against the same parameters and displayed the results in tabular form. It is seen that Weissenberg number and wall thickness parameters rise the magnitude of friction factor. It is additionally qualified to specify that the temperature and concentration profiles looking high in the absence of melting parametercontrasted with the presence of melting parameter.

In this paper an examination is completed to explore the influence of variable thickness and variable thermal conductivity on MHD stream. We have considered the governing stream and heat transfer conditions as partial differential equations. These non-linear partial differential equations are changed to non-linear ordinary differential equations at that point explained numerically utilizing fourth order RK strategy with shooting procedure. The influence of governing factors on velocity and temperature is concentrated through diagrams and numerical estimations of skin frictions and wall temperature inclination are determined, classified and examined.