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This paper aims to present a numerical investigation into heat transfer and entropy generation resulting from magnetohydrodynamic laminar flow through a microchannel under asymmetric boundary conditions. Furthermore, the authors consider the effects of viscous dissipation and Joule heating.

The finite difference method is used to obtain the numerical solution. Simulations are conducted across a broad range of Hartmann (Ha = 0 ∼ 40) and Brinkman (Br = 0.01 ∼ 1) numbers, along with various asymmetric isothermal boundaries characterized by a heating ratio denoted as ϕ.

The findings indicate a significant increase in the Nusselt number with increasing Hartmann number, regardless of whether Br equals zero or not. In addition, it is demonstrated that temperature differences between the microchannel walls can lead to substantial distortions in fluid temperature distribution and heat transfer. The results reveal that the maximum entropy generation occurs at the highest values of Ha and η (a dimensionless parameter emerging from the formulation) obtained for ϕ = −1. Moreover, it is observed that local entropy generation rates are highest near the channel wall at the entrance region.

The study provides valuable insights into the complex interactions between magnetic fields, viscous dissipation and Joule heating in microchannel flows, particularly under asymmetric heating conditions. This contributes to a better understanding of heat transfer and entropy generation in advanced microfluidic systems, which is essential for optimizing their design and performance.

The purpose of this study is to explore the impact of Joule heating, slip conditions, Dufour and Soret effects on three-dimensional magneto-convection of nanoliquid over a rotating surface in the existence of thermal radiation, viscous dissipation and internal heat generation/absorption.

The considered physical system is modelled by a set of partial differential equations (PDEs) with conditions at surface. Then, the nonlinear PDEs are altered into a system of ordinary differential equations and they are solved numerically by the Runge−Kutta−Fehlberg method. Plotting the collected velocity, temperature and solute concentration characteristics allows one to see how relevant parameters affect the results. Calculations are made for skin friction and the rate of heat and mass transfer.

The outcomes are portrayed in the form of tables and graphs with a wide range of parameter involved in the study. It is observed that the local thermal energy transfer rate enriches on increasing the value of both thermal and solute slips. The solutal slip parameter suppresses the solute transport rate and thermal slip supports the solute transport.

Combining the Dufour and Soret effects is used in oil reservoirs, binary alloy solidification and isotope separation in mixtures of gases. Heat exchangers, nuclear reactors and thermal engineering can all benefit from the usage of nanofluid with Joule heating.

This study is mainly useful for thermal sciences and chemical engineering.

The investigation of the effects of slip circumstances and Joule heating on magnetohydrodynamic rotating nanoliquid stream with thermal radiation and cross-diffusion makes this work unique. The discoveries produced are valuable and distinctive, and they have applications in many areas of thermal science and technology.

The purpose of this study is to examine the flow and heat transfer performance of titanium oxide/water and copper/water nanofluids with varying nanoparticle morphologies by considering magnetic, Joule heating and viscous dissipation effects. Furthermore, it studies the irreversibility caused by the flow of a hydromagnetic nanofluid past a radiated stretching sheet by considering different shapes of TiO₂ and Cu nanoparticles with water as the base fluid.

In this study, the authors investigated entropy production in an unsteady two-dimensional magneto-hydrodynamic nanofluid regime using water as the base fluid and five unique TiO₂ and Cu nanoparticle morphologies. Using appropriate similarity transformations, the controlling nonlinear system of partial differential equations is transformed into a system of ordinary differential equations. The shooting technique with Runge–Kutta method was then used to solve these equations quantitatively. The findings of this study are depicted graphically, and the skin friction corresponding to various nanoparticle geometries and physical parameter variations is tabulated.

To assess the reliability of the current findings, a tabular representation of the data was compared to that of previously published studies. It is noted that a reduction in thermal energy was detected as a result of the higher levels of Prandtl number (Pr). It is further analysed that the highest heat energy generation of TiO₂ nanoparticles was larger than that of Cu nanoparticles. The most important finding was that the sphere-shaped Cu/H₂O nanofluid had the lowest velocity and greatest temperature. Also, Cu nanoparticles in the shape of platelets generate the most entropy, while TiO₂ nanoparticles in the shape of spheres generate the least.

To the best of the knowledge of the authors, the attempt to investigate the previously unexplored shape effects of TiO₂ and Cu nanoparticles on the heat transfer enhancement and inherent irreversibility caused by hydromagnetic nanofluid flow past a radiated stretching sheet with magnetic, Joule heating and viscous dissipation effects. This study fills this gap in the existing literature and encourages scientists, engineers and businesses to do more research in this area. This model can be used to improve heat transfer in systems that use renewable energy, thermal management in industry and the processing of materials.

This study aims to numerically investigate heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers magnetohydrodynamics, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.

After reducing the system of dimensional equations to dimensionless equations, the authors use the Galerkin finite element method to solve them numerically. Geometric parameters affect heating efficiency; thus, the authors use flow metrics such as the Reynold number Re, magnetic parameter M, volume fraction coefficient, heat absorption and Eckert number Ec. The authors use the finite volume method to solve the governing equations after converting them to dimensionless form. The authors also try the artificial neural network method to predict the innovative cavity’s heat response in future scenarios. Transition state charts, regression analysis, MSE and error histograms accelerate, smooth and accurately converge solutions.

As the magnetic parameter and Eckert number increase, the enclosure emits more heat. As Reynold and volume fraction coefficients rise, the Nusselt number falls. It rose as magnetic, Eckert and heat absorption characteristics increased. The average Nusselt number rises with Reynolds and volume fraction coefficients. The magnetic, Eckert and heat absorption characteristics have inverse values.

This study numerically investigates heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers MHD, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.

Microfluidics is one of the extensive elaborated technologies in thermal and engineering fields due to its wide range of applications, such as micro heat exchangers, micro mixture and microchannel heat sinks, which is used to develop a large number of microscopic devices and systems. Enhancement of thermal energy using verity of nanoliquids is one of the challenges in these applications of microfluidics. Therefore, using single wall carbon nanotubes for enhancement of thermal energy in microchannel is the main purpose of this study. Hall effect of natural convection flow in a vertical channel with slip and temperature jump condition is considered. The impacts of radiative heat flux, uniform heat source/sink, viscous dissipation and joule heating are also taken into account.

Suitable non-dimension variables are applied to the governing equations to reduce the system into ordinary differential equations. The reduced nonlinear system is then solved numerically using Runge–Kutta–Fehlberg fourth–fifth-order method along with shooting technique. The impact of different pertinent parameters on numerical solutions of primary velocity, secondary velocity, temperature, entropy generation and Bejan number is comprehensively discussed in detail. Also, the obtained numerical results are compared with existing one which perfectly found to be in good agreement.

It is established that, with the aspects of Joule heating, viscous dissipation, radiative heat flux and uniform heat source/sink, the production in the entropy can be improved. Further, it is found that the increasing ratio of wall ambient temperature difference and nanoparticle volume fraction leads to enhance the entropy generation. The same effect reverses with increasing values of fluid wall interaction parameter (FWIP) and rare faction. The irreversibility ratio enhances with larger values of nanoparticle volume fraction and decelerates with increment values of FWIP.

The impact of single wall carbon nanoliquid in a vertical channel flow by using radiative heat flux, heat source/sink, joule heating and viscous dissipation is first time investigated. Further, the influence of Hall current is explored in detail.

Outstanding features such as superior electrical conductivity and thermal conductivity of alloy nanoparticles with working fluids make them ideal materials to be used as coolants in microelectromechanical systems (MEMSs). This paper aims to investigate the effects of different alloy nanoparticles such as AA7075 and Ti6Al4V on microchannel flow of magneto-nanoliquids with partial slip and convective boundary conditions. Flow features are explored with the effects of magnetism and nanoparticle shape. Heat transport of fluid includes radiative heat, internal heat source/sink, viscous and Joule heating phenomena.

Suitable dimensionless variables are used to reduce dimensional governing equations into dimensionless ordinary differential equations. The relevant dimensionless ordinary differential systems are computed numerically by using Runge–Kutta–Fehlberg-based shooting approach. Pertinent results of velocity, temperature, entropy number and Bejan number for assorted values of physical parameters are comprehensively discussed. Also, a closed-form solution is obtained for momentum equation for a particular case. Analytical results agree perfectly with numerical results.

It is established that the entropy production can be improved with radiative heat, Joule heating, convective heating and viscous dissipation aspects. The entropy production is higher in the case of Ti6Al4V-H₂O nanofluid than AA7075-H₂O. Further, the inequality Ns(ξ)_Sphere > Ns(ξ)_Hexahedran > Ns(ξ)_Tetrahydran > Ns(ξ)_Column > Ns(ξ)_Lamina holds true.

Effects of aluminium and titanium alloy nanoparticles in microchannel flows by using viscous dissipation and Joule heating are investigated for the first time. Flow features are explored with the effects of magnetism and nanoparticle shape. The results for different alloy nanoparticles such as AA7075 and Ti6Al4V have been compared.

Fully developed Casson fluid flow through vertical microchannel is deliberated in the presence of thermal radiation. The two predominant features of micro scale phenomenon such as velocity slip and temperature jump are considered. The paper aims to discuss this issue.

The governing equations of the physical phenomenon are solved using Runge–Kutta–Fehlberg fourth fifth order method.

The outcome of the present work is discussed through graphs. This computation shows that entropy generation rate decreases with enhancing wall ambient temperature difference ratio and fluid wall interaction parameter. Also, it is found that Bejan number is fully retarded with rise in fluid wall interaction parameter. Enhancement in heat transfer or Nusselt number is achieved by increasing the wall ambient temperature ratio and fluid wall interaction parameter.

Casson liquid flow through microchannel is analyzed by considering temperature jump and velocity slip. This computation shows that entropy generation rate decreases with enhancing wall ambient temperature difference ratio.

Microfluidics is one of the interesting areas of the research in thermal and engineering fields due to its wide range of applications in a variety of heat transport problems such as micromixers, micropumps, cooling systems for microelectromechanical systems (MEMS) micro heat exchangers, etc. Lower cost with better thermal performance is the main objective of these devices. Therefore, in this study, the entropy generation in an electrically conducting Casson fluid flow through an inclined microchannel with hydraulic slip and the convective condition hves been numerically investigated. Aspects of viscous dissipation, natural convection, joule heating, magnetic field and uniform heat source/sink are used

Suitable non-dimensional variables are used to reduce the non-linear system of ordinary differential equations, and then this system is solved numerically using Runge-Kutta-Fehlberg fourth fifth order method along with shooting technique. The obtained numerical solutions of the fluid velocity and temperature are used to characterize the entropy generation and Bejan number. Also, the Nusselt number and skin friction coefficient for various values of parameters are examined in detail through graphs. The obtained present results are compared with the existing one which is perfectly found to be in good agreement.

It is established that the production of the entropy can be improved with the aspects of joule heating, viscous dissipation and internal heat source/sink. The entropy generation enhances for increasing values of Casson Parameter (β) and Biot number (Bi). Furthermore, it is interestingly noticed that the enhancement of Reynolds number and uniform heat source/sink shows the dual behaviour of the entropy generation due to significant influence of the viscous forces in the region close to the channel walls. It was observed that increasing behaviour of the heat transfer rate for enhancement values of the Eckert number and heat source/sink ratio parameter and the drag force are retarded with higher estimations of Reynolds number.

Entropy generation analysis on MHD Casson fluid flow through an inclined microchannel with the aspects of convective, Joule heating, viscous dissipation, magnetism, hydraulic slip and internal heat source/sink has been numerically investigated.

The main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.

The non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.

AI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

This study aims to expose the flow phenomena and entropy generation during a; magnetohydrodynamic (MHD) Poiseuille flow of water-based nanofluids (NFs) in a porous channel subject to hydrodynamic slip and convective heating boundary conditions. The flow caused by the uniform pressure; gradient between infinite parallel plates is considered steady and fully developed. The nanoparticles; namely, copper, alumina and titanium oxide are taken with pure water as the base fluid. Viscous dissipation and Joule heating impacts are also incorporated in this investigation.

The reduced governing equations are solved analytically in closed form. The physical insights of noteworthy parameters on the important flow quantities are demonstrated through graphs and analyzed elaborately. The thermodynamic analysis is performed by calculating entropy generation; rate and Bejan number. A graphical comparison between solutions corresponding to NFs and regular fluid in the channel is also provided.

The analysis of the results divulges that entropy generation minimization can be achieved by an appropriate combination of the geometrical and physical parameters of thermomechanical systems. It is reported that ascent in magnetic parameter number declines the velocity profiles, while the inverse pattern is witnessed with augmentation in hydrodynamic slip parameters. The temperature dissemination declines with the growth of Biot numbers. It is perceived that the entropy generation rate lessens with an upgrade in magnetic parameter, whereas the reverse trend of Bejan number is perceived with expansion in magnetic parameter and Biot number. The important contribution of the result is that the entropy generation rate is controlled with an appropriate composition of thermo-physical parameter values. Moreover, in the presence of a magnetic field and suction/injection at the channel walls, the shear stresses at the channel walls are reduced about two times.

In various industrial applications, minimizing entropy generation plays a significant role. Miniaturization of entropy is the utilization of the energy of thermal devices such as micro heat exchangers, micromixers, micropumps and cooling microelectromechanical devices.

An attentive review of the literature discloses that quite a few studies have been conducted on entropy generation analysis of a fully developed MHD Poiseuille flow of NFs through a permeable channel subject to the velocity slip and convective heating conditions at the walls.