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The particle distribution in a fluid is mostly not homogeneous. The inhomogeneous dispersion of solid particles affects the velocity profile as well as the heat transfer of fluid. This study aims to highlight the effects of varying density of particles in a fluid. The fluid flows through a wavy curved passage under an applied magnetic field. Heat transfer is discussed with variable thermal conductivity.

The mathematical model of the problem consists of coupled differential equations, simplified using stream functions. The results of the time flow rate for fluid and solid granules have been derived numerically.

The fluid and dust particle velocity profiles are being presented graphically to analyze the effects of density of solid particles, magnetohydrodynamics, curvature and slip parameters. Heat transfer analysis is also performed for magnetic parameter, density of dust particles, variable thermal conductivity, slip parameter and curvature. As the number of particles in the fluid increases, heat conduction becomes slow through the fluid. Increase in temperature distribution is noticed as variable thermal conductivity parameter grows. The discussion of variable thermal conductivity is of great concern as many biological treatments and optimization of thermal energy storage system’s performance require precise measurement of a heat transfer fluid’s thermal conductivity.

This study of heat transfer with inhomogeneous distribution of the particles in a fluid has not yet been reported.

The purpose of this study is to investigate the entropy generation in different nanofluids flow over a vertically moving rotating disk. Unlike the classical Karman flow, water-based nanofluids have various suspended nanoparticles, namely, Cu, Ag, Al₂O₃ and TiO₂, and the disk is also moving vertically with time-dependent velocity.

The Keller box technique numerically solves the governing equations after reduction by suitable similarity transformations. The shear stress and heat transport features, along with flow and temperature fields, are numerically computed for different concentrations of the nanoparticles.

This study is done comparatively in between different nanofluids and for the cases of vertical movement of the disk. It is found that heat transfer characteristics rely not only on considered nanofluid but also on disk movement. Moreover, the upward movement of the disk diminishes the heat-transfer characteristics of the fluid for considered nanoparticles. In addition, for the same group of nanoparticles, an entropy generation study is also performed, and an increasing trend is found for all nanoparticles, with alumina nanoparticles dominating the others.

This research is a novel work on a vertically moving rotating surface for the water-conveying nanoparticle fluid flow with entropy generation analysis. The results were found to be in good agreement in the case of pure fluid.

The purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.

The governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.

The investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.

This study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.

This paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel.

The treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method.

Analysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances.

Linear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation.

The purpose of this study, thermal radiation and viscous dissipation impacts on double diffusive convection on peristaltic transport of Williamson nanofluid due to induced magnetic field in a tapered channel is examined. The study of propulsion system is on the rise in aerospace research. In spacecraft technology, the propulsion system uses high-temperature heat transmission governed through thermal radiation process. This study will help in assessment of chyme movement in the gastrointestinal tract and also in regulating the intensity of magnetic field of the blood flow during surgery.

The brief mathematical modelling, along with induced magnetic field, of Williamson nanofluid is given. The governing equations are reduced to dimensionless form by using appropriate transformations. Numerical technique is manipulated to solve the highly nonlinear differential equations. The roll of different variables is graphically analyzed in terms of concentration, temperature, volume fraction of nanoparticles, axial-induced magnetic field, magnetic force function, stream functions, pressure rise and pressure gradient.

The key finding from the analysis above can be summed up as follows: the temperature profile decreases and concentration profile increases due to the rising impact of thermal radiation. Brownian motion parameter has a reducing influence on nanoparticle concentration due to massive transfer of nanoparticles from a hot zone to a cool region, which causes a decrease in concentration profile· The pressure rise enhances due to rising values of thermophoresis and thermal Grashof number in retrograde pumping, free pumping and copumping region.

To the best of the authors’ knowledge, a study that integrates double-diffusion convection with thermal radiation, viscous dissipation and induced magnetic field on peristaltic flow of Williamson nanofluid with a channel that is asymmetric has not been carried out so far.

Thermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.

The mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.

The graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.

Such complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.

To the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.

This study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.

The governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.

Graphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.

The reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

The purpose of this paper is to investigate the behavior of a non-Newtonian nanofluid caused by peristaltic waves along an asymmetric channel. Additionally considered is the production of thermal radiation and activation energy.

The equations of momentum, mass and temperature of Sutterby nanofluids are obtained for long wavelength. By taking into account the velocity, temperature and concentration, the formulation is further finished.

Analyses of the physical variables influencing flow features are represented graphically. The present investigation shows that an enhancement in the temperature ratio parameter results in an increase in both the temperature and concentration. The investigation also shows that the dimensionless reaction rate significantly raises the kinetic energy of the reactant, which permits more particle collisions and as a result, raises the temperature field.

Due to their importance in the treatment of cancer, activation energy and thermal radiation as a route of heat transfer are crucial and exciting phenomena for researchers. So, the cancer cells are killed, and tumors are reduced in size with heat and making hyperthermia therapy a cutting-edge cancer treatment.

A parabolic trough solar collector is an advanced concentrated solar power technology that significantly captures radiant energy. Solar power will help different sectors reach their energy needs in areas where traditional fuels are in use. This study aims to examine the sensitivity analysis for optimizing the heat transfer and entropy generation in the Jeffrey magnetohydrodynamic hybrid nanofluid flow under the influence of motile gyrotactic microorganisms with solar radiation in the parabolic trough solar collectors. The influences of viscous dissipation and Ohmic heating are also considered in this investigation.

Governing partial differential equations are derived via boundary layer assumptions and nondimensionalized with the help of suitable similarity transformations. The resulting higher-order coupled ordinary differential equations are numerically investigated using the Runga-Kutta fourth-order numerical approach with the shooting technique in the computational MATLAB tool.

The numerical outcomes of influential parameters are presented graphically for velocity, temperature, entropy generation, Bejan number, drag coefficient and Nusselt number. It is observed that escalating the values of melting heat parameter and the Prandl number enhances the Nusselt number, while reverse effect is observed with an enhancement in the magnetic field parameter and bioconvection Lewis number. Increasing the magnetic field and bioconvection diffusion parameter improves the entropy and Bejan number.

Nanotechnology has captured the interest of researchers due to its engrossing performance and wide range of applications in heat transfer and solar energy storage. There are numerous advantages of hybrid nanofluids over traditional heat transfer fluids. In addition, the upswing suspension of the motile gyrotactic microorganisms improves the hybrid nanofluid stability, enhancing the performance of the solar collector. The use of solar energy reduces the industry’s dependency on fossil fuels.

This study aims to examine the effects of cross-flow and multiple jet impingement on conductive panel cooling performance when subjected to uniform magnetic field effects. The cooling system has double rotating cylinders.

Cross-flow ratios (CFR) ranging from 0.1 to 1, magnetic field strength (Ha) ranging from 0 to 50 and cylinder rotation speed (Rew) ranging from −5,000 to 5,000 are the relevant parameters that are included in the numerical analysis. Finite element method is used as solution technique. Radial basis networks are used for the prediction of average Nusselt number (Nu), average surface temperature of the panel and temperature uniformity effects when varying the impacts of cross-flow, magnetic field and rotations of the double cylinder in the cooling channel.

The effect of CFR on cooling efficiency and temperature uniformity is favorable. By raising the CFR to the highest value under the magnetic field, the average Nu can rise by up to 18.6%, while the temperature drop and temperature difference are obtained as 1.87°C and 3.72°C. Without cylinders, magnetic field improves the cooling performance, while average Nu increases to 4.5% and 8.8% at CR = 0.1 and CR = 1, respectively. When the magnetic field is the strongest with cylinders in channel at CFR = 1, temperature difference (ΔT) is obtained as 2.5 °C. The rotational impacts on thermal performance are more significant when the cross-flow effects are weak (CFR = 0.1) compared to when they are substantial (CFR = 1). Cases without a cylinder have the worst performance for both weak and severe cross-flow effects, whereas using two rotating cylinders increases cooling performance and temperature uniformity for the conductive panel. The average surface temperature lowers by 1.2°C at CFR = 0.1 and 0.5°C at CFR = 1 when the worst and best situations are compared.

The outcomes are relevant in the design and optimization-based studies for electric cooling, photo-voltaic cooling and battery thermal management.