Typical liquids aren't great for engineering because of their low heat conductivity. To enhance heat transfer capabilities in industries as diverse as computers, pharmaceuticals, and molten metals, researchers and scientists have developed nanofluids, which are composed of nanoparticles distributed in a base fluid. Mathematical modeling of micropolar C u - H 2 O nanofluid driven by a deformable sheet in the stagnation area with nanoparticle aggregation, thermal radiation, and the mass suction action has been investigated in this paper. In this case, copper ( C u ) nanoparticles make up the nanofluid. ology: We have used suitable transformations to arrive at a system of nonlinear ODEs, which we then solve numerically in MATHEMATICA using Runge-Kutta methods of the fourth order coupled with shooting approaches. Tables and graphs are used to examine the effects of immersed flow and display profiles of physical parameters of interest. This includes velocities, temperatures, skin friction, and Nusselt numbers. The average heat transfer rate increased to 17 . 725 % as the volume percentage of copper nanoparticles in micropolar nanofluid increased from 0.0 to 0.01 . Additionally, the results showed that the local Nusselt number of the micropolar nanofluid increased along with an increase in the unsteady and radiation parameters. However, its value is reduced in an undeniable fashion if a material parameter is present. The impact of radiation on the aggregation of nanoparticles is compared and contrasted with the effects of a non-radiative scenario, and the resulting fluctuations in Nusselt numbers are provided in tables. When the results of this study were compared to data that had already been published about some cases, a lot of agreement was found.

Nanofluids with aggregation effects mediated by nanoparticles, like geothermal panels and crossflow heat exchangers, ignite new industrial interests. Polymer and conversion processes have transport phenomena in the stagnation zone that must be continuously improved to raise the process quality standard. Hence, the current computational study examines a $Ti{O}_2-C_2{H}_6{O}_2$ nanofluid's unsteady stagnation-point flow performance via a shrinking horizontal cylinder. In addition, the effects of a magnetic field, joule-heating viscous dissipation, nanoparticles aggregation and mass suction on the boundary layer flow are reflected. ology: The RK-IV with shooting method is applied to resolve the simplified mathematical model numerically in computing software MATHEMATICA. In certain circumstances, comparing the current and prior findings indicates good agreement with a relative error of around 0%. The implementation of a heat transfer operation may be improved by increasing suction settings. Unsteadiness, nanoparticle volume fraction, magnetic, curvature, and Eckert number (implies the operating Joule heating and viscous dissipation) all influence heat transfer rate. The velocity and temperature profiles both increase as the unsteadiness, magnetic field, and nanoparticle volume fraction parameters increase, whereas the curvature and suction parameters show the opposite behavior. When the values of the suction parameters were changed from 2.0 to 2.5 with $\phi$ = 0.01, the heat transfer rates rose by 4.751%. A comparison shows that the model with aggregation has a better velocity profile, while the model without aggregation has a better temperature profile.

In this article, we investigate the bioconvection flow of Casson nanofluid by a rotating disk under the impacts of Joule heating, convective conditions, heat source/sink and gyrotactic microorganisms. When Brownian diffusion and thermophoretic effects exist, the Casson fluid is examined. The existing physical problem of Casson nanofluid flow with energy transports is demonstrated under the above considerations in the form of partial differential equations (PDEs). Using the appropriate transformations, the PDEs are converted into non-linear ordinary differential equations (ODEs). The mathematical results are calculated through MATLAB by using the function bvp4c. The problem's results are rigorously examined graphically and described with physical justifications. Velocity fields decrease as the bioconvection Rayleigh parameter rises. The thermal profile and soluteal field of species also magnify with an upsurge in thermophoresis number estimations. The microorganism's fields are decayed by larger microbes Biot number.

To aid in the prevention of reaction explosions, chemical engineers and scientists must analyze the Arrhenius kinetics and activation energies of chemical reactions involving binary chemical mixtures. Nanofluids with an Arrhenius kinetic are crucial for a broad variety of uses in the industrial sector, involving the manufacture of chemicals, thermoelectric sciences, biomedical devices, polymer extrusion, and the enhancement of thermal systems via technology. The goal of this study is to determine how the presence of thermal radiation influences heat and mass transfer during free convective unsteady stagnation point flow across extending/shrinking vertical Riga plate in the presence of a binary chemical reaction where the activation energy of the reaction is known in advance. For the purpose of obtaining numerical solutions to the mathematical model of the present issue the Runge-Kutta (RK-IV) with shooting technique in Mathematica was used. Heat and mass transfer processes, as well as interrupted flow phenomena, are characterized and explained by diagrams in the suggested suction variables along boundary surface in the stagnation point flow approaching a permeable stretching/shrinking Riga Plate. Graphs illustrated the effects of many other factors on temperature, velocity, concentration, Sherwood and Nusselt number as well as skin friction in detail. Velocity profile increased with Z , λ and S and decreased with ε . Increasing values of ε , λ and S decline the temperature profile. The concentration profile boosts up with Z , α and slow down with ε , S c , β , δ and n 1 parameters. Skin friction profile increased with Z and S and decreased with ε . Nusselt number profile increased with S , Z , ε and radiation. Sherwood number profile shows upsurges with ε , Z , α , S c , β , S and n 1 whereas slow down with δ . So that the verdicts could be confirmed, a study was done to compare the most recent research with the results that had already been published for a certain case. The outcomes demonstrated strong concordance between the two sets of results.

It is still not quite apparent how suspended nanoparticles improve heat transmission. Multiple investigations have demonstrated that the aggregation of nanoparticles is a critical step in improving the thermal conductivity of nanofluids. However, the thermal conductivity of the nanofluid would be greatly affected by the fractal dimension of the nanoparticle aggregation. The purpose of this research is to learn how nanoparticle aggregation, joule heating, and a heat source affect the behavior of an ethylene glycol-based nanofluid as it flows over a permeable, heated, stretched vertical Riga plate and through a porous medium. Numerical solutions to the present mathematical model were obtained using Mathematica's Runge-Kutta (RK-IV) with shooting technique. In the stagnation point flow next to a permeable, heated, extending Riga plate, heat transfer processes and interrupted flow phenomena are defined and illustrated by diagrams in the proposed mixed convection, joule heating, and suction variables along a boundary surface. Data visualizations showed how different variables affected temperature and velocity distributions, skin friction coefficient, and the local Nusselt number. The rates of heat transmission and skin friction increased when the values of the suction parameters were raised. The temperature profile and the Nusselt number both rose because of the heat source setting. The increase in skin friction caused by changing the nanoparticle volume fraction from $\phi =0.0$ to $\phi =0.01$ for the without aggregation model was about 7.2% for the case of opposing flow area $\left(\lambda =-1.0\right)$ and 7.5% for the case of aiding flow region $\left(\lambda =1.0\right)$. With the aggregation model, the heat transfer rate decreases by approximately 3.6% for cases with opposing flow regions $\left(\lambda =-1.0\right)$ and 3.7% for cases with assisting flow regions $\left(\lambda =1.0\right)$, depending on the nanoparticle volume fraction and ranging from $\phi =0.0$ to $\phi =0.01$, respectively. Recent findings were validated by comparing them to previously published findings for the same setting. There was substantial agreement between the two sets finding.