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This paper aims to numerically examine the impact of gyrotactic microorganisms and radiation on heat transport features of magnetic nanoliquid within a closed cavity. Thermophoresis, chemical reaction and Brownian motion are also considered in flow geometry for the moment of nanoparticles.

Finite element method (FEM) was depleted to numerically approximate the temperature, momentum, concentration and microorganisms concentration of the nanoliquid. The present simulation was unsteady state, and the resulting transformed equations are simulated by FEM-based Mathematica algorithm.

It has been found that isotherm patterns get larger with increasing values of the magnetic field parameter. Additionally, numerical codes for rate of heat transport impedance inside the cavity with an increasing Brownian motion parameter values.

To the best of the authors’ knowledge, the research work carried out in this paper is new, and no part is copied from others’ works.

The investigation has appraised the problem of an incompressible laminar steady magnetohydrodynamic (MHD) nanofluid stream over three distinct slendering thin isothermal needles of paraboloid, cylindrical and cone shapes. Water as a base liquid is assumed in this flow model. The influences of the Hall current and variable sorts of magnetic forces have enriched our investigation. Energy and concentration expressions consist of thermophoresis and Brownian migration phenomena. The analysis of thermal and mass slips of the presumed model has also been performed.

A relevant transformation is implemented for the alteration of the leading partial differential equations (PDEs) to the equations with nonlinear ordinary form. Due to the strong nonlinearity of the foremost equations, the problem is solved numerically by embedding the well-known RK-4 shooting practice. The software MAPLE 2017 has been exploited in reckoning the entire computation. To enunciate the investigated upshots, some graphical diagrams have been regarded here. According to technological interest, we measured the engineering quantities like the Sherwood number, the coefficient of drag friction and the Nusselt number in tabular customs.

The obtained consequences support that Hall current intensifies fluid movement when the needle is in a cone shape, while the superior velocity is noticed for cylindrical-shaped needles. The transference of heat responds inversely along with the growths of thermal and mass slip factors.

No work has been performed on the flow model of radiated nanofluid over a variable-shaped thin needle under Hall current, the variable magnetic field and different slip factors.

Recent advancements in technology have led to the exploration of solar-based thermal radiation and nanotechnology in the field of fluid dynamics. Solar energy is captured through sunlight absorption, acting as the primary source of heat. Various solar technologies, such as solar water heating and photovoltaic cells, rely on solar energy for heat generation. This study focuses on investigating heat transfer mechanisms by utilizing a hybrid nanofluid within a parabolic trough solar collector (PTSC) to advance research in solar ship technology. The model incorporates multiple effects that are detailed in the formulation.

The mathematical model is transformed using suitable similarity transformations into a system of higher-order nonlinear differential equations. The model was solved by implementing a numerical procedure based on the Wavelets and Chebyshev wavelet method for simulating the outcome.

The velocity profile is reduced by Deborah's number and velocity slip parameter. The Ag-EG nanoparticles mixture demonstrates less smooth fluid flow compared to the significantly smoother fluid flow of the Ag-Fe3O4/EG hybrid nanofluids (HNFs). Additionally, the Ag-Ethylene Glycol nanofluids (NFs) exhibit higher radiative performance compared to the Ag-Fe3O4/Ethylene Glycol hybrid nanofluids (HNFs).

Additionally, the Oldroyd-B hybrid nanofluid demonstrates improved thermal conductivity compared to traditional fluids, making it suitable for use in cooling systems and energy applications in the maritime industry.

The originality of the study lies in the exploration of the thermal transport enhancement in sun-powered energy ships through the incorporation of silver-magnetite hybrid nanoparticles within the heat transfer fluid circulating in parabolic trough solar collectors. This particular aspect has not been thoroughly researched previously. The findings have been validated and provide a highly positive comparison with the research papers.

This study is to examine the impact of viscous dissipation, thermal radiation and Ohmic heating on the magnetohydrodynamic (MHD) flow with thermal and mass transport over a horizontally stretching surface. Cattaneo–Christov heat flux model on a non-Newtonian viscous fluid along with two viscosity models and convective boundary condition has been employed. Tri-hybrid nanofluid has been used to increase thermal performance.

Governing mathematical model has been transposed into a dimensionless system of ordinary differential equations (ODEs) by applying suitable similarity transformation. Numerical solution has been found by applying the bvp4c shooting method in MATLAB software.

Velocity and thermal profiles of Model-I dominate the profiles of Model-II whereas opposite behavior is noticed for concentration profiles. It is concluded that there is an increase in temperature due to thermal radiation, viscous dissipation and convective boundary condition.

The novelty of presented work is to examine the impact of Ohmic heating, viscous dissipation, thermal radiation, chemical reaction and two models of viscosity on Cattaneo–Christov heat flux model of tri-hybrid non-Newtonian nanofluid with convective boundary constraint. The accuracy and effectiveness of presented model have been compared with already published research.

The main purpose of this study is to analyze the heat transfer phenomena in a dynamically bulging enclosure filled with Cu-water nanofluid. This study examines the convective heat transfer process induced by a bulging area considered a heat source, with the enclosure's side walls having a low temperature and top and bottom walls being treated as adiabatic. Various factors, such as the Rayleigh number (Ra), nanoparticle volume fraction, Darcy effects, Hartmann number (Ha) and effects of magnetic inclination, are analyzed for their impact on the flow behavior and temperature distribution.

The finite element method (FEM) is employed for simulating variations in flow and temperature after validating the results. Solving the non-linear partial differential equations while incorporating the modified Darcy number (10⁻³ ≤ Da ≤ 10⁻¹), Ra (10³ ≤ Ra ≤ 10⁵) and Ha (0 ≤ Ha ≤ 100) as the dimensionless operational parameters.

This study demonstrates that in enclosures with dynamically positioned bulges filled with Cu-water nanofluid, heat transfer is significantly influenced by the bulge location and nanoparticle volume fraction, which alter flow and heat patterns. The varying impact of magnetic fields on heat transfer depends on the Rayleigh and Has.

The geometry configurations employed in this research have broad applications in various engineering disciplines, including heat exchangers, energy storage, biomedical systems and food processing.

This research provides insights into how different shapes of the heated bulging area impact the hydromagnetic convection of Cu-water nanofluid flow in a dynamically bulging-shaped porous system, encompassing curved surfaces and various multi-physical conditions.

This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe₃O₄ and MoS₂-Fe₃O₄.

The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios.

Results obtained show that the Cu-Fe₃O₄ hybrid nanofluid exhibits higher entropy generation than the MoS₂-Fe₃O₄ hybrid nanofluid when comparing them at a Rayleigh number of 10⁶ and a Darcy number of 10^–1. The MoS₂ hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10^–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 10⁴are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS₂ nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 10⁵ and a Darcy number of 10^–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature.

The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

This research focuses on the controlling irreversibilities in a radiative, chemically reactive electromagnetohydrodynamics (EMHD) flow of a nanofluid toward a stagnation point. Key considerations include the presence of Ohmic dissipation, linear thermal radiation, second-order chemical reaction with the multiple slips. With these factors, this study aims to provide insights for practical applications where thermal management and energy efficiency are paramount.

Lie group transformation is used to revert the leading partial differential equations into nonlinear ODE form. Hence, the solutions are attained analytically through differential transformation method-Padé and numerically using the Runge–Kutta–Fehlberg method with shooting procedure, to ensure the precise and reliable determination of the solution. This dual approach highlights the robustness and versatility of the methods.

The system’s entropy generation is enhanced by incrementing the magnetic field parameter (M), while the electric field (E) and velocity slip parameters (ξ) control its growth. Mass transportation irreversibility and the Bejan number (Be) are significantly increased by the chemical reaction rate (C_r). In addition, there is a boost in the rate of heat transportation by 3.66% while 0.05⩽ξ⩽0.2; meanwhile for 0.2⩽ξ⩽1.1, the rate of mass transportation gets enhanced by 12.87%.

This paper presents a novel approach to analyzing the entropy optimization in a radiative, chemically reactive EMHD nanofluid flow near a stagnation point. Moreover, this research represents a significant advancement in the application of analytical techniques, complemented by numerical approaches to study boundary layer equations.

The purpose of this paper is to study the two-dimensional micropolar fluid flow with conjugate heat transfer and mass transpiration. The considered nanofluid has graphene nanoparticles.

Governing nonlinear partial differential equations are converted to nonlinear ordinary differential equations by similarity transformation. Then, to analyze the flow, the authors derive the dual solutions to the flow problem. Biot number and radiation effect are included in the energy equation. The momentum equation was solved by using boundary conditions, and the temperature equation solved by using hypergeometric series solutions. Nusselt numbers and skin friction coefficients are calculated as functions of the Reynolds number. Further, the problem is governed by other parameters, namely, the magnetic parameter, radiation parameter, Prandtl number and mass transpiration. Graphene nanofluids have shown promising thermal conductivity enhancements due to the high thermal conductivity of graphene and have a wide range of applications affecting the thermal boundary layer and serve as coolants and thermal management systems in electronics or as heat transfer fluids in various industrial processes.

Results show that increasing the magnetic field decreases the momentum and increases thermal radiation. The heat source/sink parameter increases the thermal boundary layer. Increasing the volume fraction decreases the velocity profile and increases the temperature. Increasing the Eringen parameter increases the momentum of the fluid flow. Applications are found in the extrusion of polymer sheets, films and sheets, the manufacturing of plastic wires, the fabrication of fibers and the growth of crystals, among others. Heat sources/sinks are commonly used in electronic devices to transfer the heat generated by high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes to a fluid medium, thermal radiation on the fluid flow used in spectroscopy to study the properties of materials and also used in thermal imaging to capture and display the infrared radiation emitted by objects.

Micropolar fluid flow across stretching/shrinking surfaces is examined. Biot number and radiation effects are included in the energy equation. An increase in the volume fraction decreases the momentum boundary layer thickness. Nusselt numbers and skin friction coefficients are presented versus Reynolds numbers. A dual solution is obtained for a shrinking surface.

This study aims to investigate the heat and mass transfer characteristics of a temperature-sensitive ternary nanofluid in a porous medium with magnetic field and the Soret–Dufour effect through a tapered asymmetric channel. The ternary nanofluid consists of Boron Nitride Nanotubes (BNNT), silver (Ag) and copper (Cu) nanoparticles, with a focus on understanding the thermal behaviour and performance across mono, hybrid and tri-hybrid nanofluids. This paper also examines the thermal behaviour of MHD oscillatory nanofluid flow and carries out an uncertainty analysis of the model using the Taguchi method.

The governing equations for this system are transformed into coupled linear partial differential equations using non-similarity transformations and solved numerically with the Crank–Nicolson scheme. The impact of temperature sensitivity at three distinct temperatures (5°C, 20°C and 60°C) is incorporated to analyse variations in viscosity and Prandtl number. The study also examines the combined effects of Soret–Dufour numbers and thermal radiation on heat and mass transfer within the nanofluid.

The results demonstrate that the inclusion of BNNT, Ag and Cu nanoparticles significantly enhances heat and mass transfer rate, with copper nanoparticles showing superior performance in terms of skin friction and heat transfer rates. The Soret and Dufour effects play critical roles in modulating heat and mass diffusion within tri-hybrid nanofluids. The study reveals that temperature sensitivity alters heat and mass transfer characteristics depending on the temperature range, with pronounced variations at elevated temperatures. The influence of thermal radiation and the Peclet number is found to significantly impact temperature distribution and overall heat transfer performance within the asymmetric channel.

To the best of the authors’ knowledge, this study is the first to analyse the heat and mass diffusion in a ternary nanofluid composed of BNNT, Ag and Cu nanoparticles, considering porous media, oscillatory flow and thermal radiation within a tapered asymmetric channel. The research extends to a novel examination of temperature sensitivity in mono, hybrid and tri-hybrid nanofluids at varying temperature gradients. Furthermore, a comparative analysis of skin friction and heat transfer rates between copper, alumina and ferro composites is presented for optimising the nanofluid performance.