This study looks at the natural convections of Cu + Al₂O₃/H₂O nanofluid into a permeable chamber. The magnetic field is also executed on the flow field and the analysis has been approached numerically by the control volume method. The study of hybrid nanofluid heat in terms of the transfer flux was supplemented with a wide range of parameters of hybrid nanofluid fractions, Rayleigh numbers Hartmann numbers and porosity factor. It's also determined that the flow and thermal distribution are heavily affected by the concentration of the nanoparticles. The concentration of nanoparticles increases the transport of convective energy inside the enclosure. The primary findings demonstrate that a rise in both the Rayleigh number and Darcy number leads to an improvement in convective heat transfer within the enclosure. However, the porosity has a negligible effect. Additionally, the rotation in a clockwise direction has a beneficial impact on the dispersion of heat transfer throughout the cavity. Furthermore, it is concluded that hybrid nanofluids are more reliable than conventional fluids in improving thermal properties.

Heat and mass transfer are crucial to numerous technical and commercial operations, including air conditioning, machinery power collectors, crop damage, processing food, heat transfer mechanisms, and cooling, among numerous others. The fundamental purpose of this research is to use the Cattaneo-Christov heat flux model to disclose an MHD flow of ternary hybrid nanofluid through double discs. The results of a heat source and a magnetic field are therefore included in a system of PDEs that model the occurrences. These are transformed into an ODE system using similarity replacements. The first-order differential equations that emerge are then handled using the computational technique Bvp4c shooting scheme. The Bvp4c function in MATLAB is used to numerically solve the governing equations. The influence of the key important factors on velocity, temperature, nanoparticles concentration, and is illustrated visually. Furthermore, increasing the volume fraction of nanoparticles improves thermal conduction, increasing the heat transfer rate at the top disc. The graph indicates that a slight increase in melting parameter rapidly declines the velocity distribution profile of nanofluid. The temperature profile was boosted due to the growing outcomes of the Prandtl number. The increasing variations of the thermal relaxation parameter decline the thermal distribution profile. Furthermore, for some exceptional instances, the obtained numerical answers were compared to previously disclosed data, yielding a satisfactory compromise. We believe that this discovery will have far-reaching ramifications in engineering, medicine, and the field of biomedical technology. Additionally, this model can be used to examine biological mechanisms, surgical techniques, nano-pharmacological drug delivery systems, and the therapy of diseases like cholesterol using nanotechnology.

In present times modern electronic devices often come across thermal difficulties as an outcome of excessive heat production or reduction in surface area for heat exclusion. The current study is aimed to inspect the role of iron (III) oxide in heat transfer enhancement over the rotating disk in an axisymmetric flow. Water is utilized as base fluid conveying nano-particle over the revolving axisymmetric flow mechanism. Additionally, the computational fluid dynamics (CFD) approach is taken into consideration to design and compute the present problem. For our convenience, two-dimensional axisymmetric flow configurations are considered to illustrate the different flow profiles. For radial, axial, and tangential velocity profiles, the magnitude of the velocity, streamlines, and surface graphs are evaluated with the similarity solution in the computational fluid dynamics module. The solution of dimensionless equations and the outcomes of direct simulations in the CFD module show a comparable solution of the velocity profile. It is observed that with an increment in nanoparticle volumetric concentration the radial velocity decline where a tangential motion of flow enhances. Streamlines stretch around the circular surface with the passage of time. The high magnetization force $$0 \le {{\mathrm{m}}_{1}}\le 6$$0≤m1≤6 resist the free motion of the nanofluid around the rotating disk. Such research has never been done, to the best of the researchers’ knowledge. The outcomes of this numerical analysis could be used for the design, control, and optimization of numerous thermal engineering systems, as described above, due to the intricate physics of nanofluid under the influences of magnetic field and the inclusion of complex geometry. Ferrofluids are metallic nanoparticle colloidal solutions. These kinds of fluids do not exist in nature. Depending on their purpose, ferrofluids are produced using a variety of processes. One of the most essential characteristics of ferrofluids is that they operate in a zero-gravity environment. Ferrofluids have a wide range of uses in engineering and medicine. Ferrofluids have several uses, including heat control loudspeakers and frictionless sealing. In the sphere of medicine, however, ferrofluid is employed in the treatment of cancer via magneto hyperthermia.

In this paper, we study linear and nonlinear mixed convection, activation energy, and heat radiation effects caused by nanoparticles. This study aims to improve the understanding of how nanofluids behave in the presence of rotating disks and develop more efficient and effective cooling technologies. The flow problem consisted of partial differential equations (PDE). It is challenging to calculate these equations as a result of these nonlinear PDEs. Consequently, we use appropriate similarities to transform them into ordinary differential equations (ODEs). The bvp4c Matlab built-in technique is then used to resolve these ODEs. The velocities, temperature, and concentration outcomes with the various factors are examined graphically. Additionally, tables are employed to analyze the skin friction and Nusselt number values. It is analyzed that increasing the linear and linear mixed convection parameters enhances the velocity profiles of nanofluid. Enhancements in heat are analyzed by increasing nonlinear thermal radiation and enhancement in concentration is examined by increasing activation energy. Furthermore, as the variables for thermophoresis and Brownian motion are increased, the Nusselt number falls. The heat transfer rate is 27.16% for $$Rd=0.6$$R d = 0.6 and 39.28% for $$Rd=1.4$$R d = 1.4 . Thus, the heat transfer rate is enhanced 12.12%. This study’s practical applications include improving the behavior of fluids and the transfer of heat in rotating frameworks, which may affect energy systems, heat exchangers, and cooling advances in technology.

In this work, the novel iterative transformation technique and homotopy perturbation transformation technique are used to calculate the fractional-order gas dynamics equation. In this technique, the novel iteration method and homotopy perturbation method are combined with the Elzaki transformation. The current methods are implemented with four examples to show the efficacy and validation of the techniques. The approximate solutions obtained by the given techniques show that the methods are accurate and easy to apply to other linear and nonlinear problems.

This study investigates the impact of heat radiation on magnetically-induced forced convection of nanofluid in a semi-porous channel. The research employs Akbari-Ganji's and Homotopy perturbation methods to analyze the effects of multiple parameters, including Hartmann number, Reynolds number, Eckert number, radiation parameter, and suction parameter, on the flow and heat transfer characteristics. The results demonstrate that increasing Reynolds number, suction, and radiation parameters increases temperature gradient, providing valuable insights into improving heat transfer in semi-porous channels. The study validates the proposed methods by comparing the results with those obtained from other established methods in the literature. The main focus of this work is to understand the behavior of nanofluids in semi-porous channels under the influence of magnetic fields and heat radiation, which is essential for various industrial and engineering applications. The future direction of this research includes exploring the effects of different nanoparticle shapes and materials on heat transfer performance and investigating the influence of other parameters, such as buoyancy forces and variable properties, on the flow and heat transfer characteristics. The findings of this study are expected to contribute to the development of more efficient thermal management systems in the future.