Analytical solution for MHD nanofluid flow over a porous wedge with melting heat transfer.

This study employs the Hybrid Analytical-Numerical (HAN) method to investigate steady two-dimensional magnetohydrodynamic (MHD) nanofluid flow over a permeable wedge. Analyzing hyperbolic tangent nanofluid flow, the governing time-independent partial differential equations (PDEs) for continuity, momentum, energy, and concentration transform into a set of nonlinear third-order coupled ordinary differential equations (ODEs) through similarity transformations. These ODEs encompass critical parameters such as Lewis and Prandtl numbers, Brownian diffusion, Weissenberg number, thermophoresis, Dufour and Soret numbers, magnetic field strength, thermal radiation, power law index, and medium permeability. The study explores how variations in these parameters impact the velocity field, skin friction coefficient, Nusselt, and Sherwood numbers. Noteworthy findings include the sensitivity of fluid velocity to parameters like Weissenberg number, power law index, wedge angle, magnetic field strength, permeability, and melting heat transfer. The skin friction coefficient experiences a significant increase with specific parameter changes, while Nusselt and Sherwood numbers remain relatively constant. The local Reynolds number significantly affects Nusselt and Sherwood numbers, with a less pronounced impact on the skin friction coefficient. The study's uniqueness lies in employing the analytical HAN method and extracting recent insights from the results.

Free convection in a square wavy porous cavity with partly magnetic field: a numerical investigation.

Natural convection in a square porous cavity with a partial magnetic field is investigated in this work. The magnetic field enters a part of the left wall horizontally. The horizontal walls of the cavity are thermally insulated. The wave vertical wall on the right side is at a low temperature, while the left wall is at a high temperature. The Brinkman-Forchheimer-extended Darcy equation of motion is utilized in the construction of the fluid flow model for the porous media. The Finite Element Method (FEM) was used to solve the problem's governing equations, and the current study was validated by comparing it to earlier research. On streamlines, isotherms, and Nusselt numbers, changes in the partial magnetic field length, Hartmann number, Rayleigh number, Darcy number, and number of wall waves have been examined. This paper will show that the magnetic field negatively impacts heat transmission. This suggests that the magnetic field can control heat transfer and fluid movement. Additionally, it was shown that heat transfer improved when the number of wall waves increased.

Investigating double-diffusive natural convection in a sloped dual-layered homogenous porous-fluid square cavity.

This article investigates natural convection with double-diffusive properties numerically in a vertical bi-layered square enclosure. The cavity has two parts: one part is an isotropic and homogeneous porous along the wall, and an adjacent part is an aqueous fluid. Adiabatic, impermeable horizontal walls and constant and uniform temperatures and concentrations on other walls are maintained. To solve the governing equations, the finite element method (FEM) employed and predicted results shows the impact of typical elements of convection on double diffusion, namely the porosity thickness, cavity rotation angle, and thermal conductivity ratio. Different Darcy and Rayleigh numbers effects on heat transfer conditions were investigated, and the Nusselt number in the border of two layers was obtained. The expected results, presented as temperature field (isothermal lines) and velocity behavior in X and Y directions, show the different effects of the aforementioned parameters on double diffusion convective heat transfer. Also results show that with the increase in the thickness of the porous layer, the Nusselt number decreases, but at a thickness higher than 0.8, we will see an increase in the Nusselt number. Increasing the thermal conductivity ratio in values less than one leads to a decrease in the average Nusselt number, and by increasing that parameter from 1 to 10, the Nusselt values increase. A higher rotational angle of the cavity reduces the thermosolutal convective heat transfer, and increasing the Rayleigh and Darcy numbers, increases Nusselt. These results confirm that the findings obtained from the Finite Element Method (FEM), which is the main idea of this research, are in good agreement with previous studies that have been done with other numerical methods.

A comprehensive review of microbial fuel cells considering materials, methods, structures, and microorganisms.

Microbial fuel cells (MFCs) are promising for generating renewable energy from organic matter and efficient wastewater treatment. Ensuring their practical viability requires meticulous optimization and precise design. Among the critical components of MFCs, the membrane separator plays a pivotal role in segregating the anode and cathode chambers. Recent investigations have shed light on the potential benefits of membrane-less MFCs in enhancing power generation. However, it is crucial to recognize that such configurations can adversely impact the electrocatalytic activity of anode microorganisms due to increased substrate and oxygen penetration, leading to decreased coulombic efficiency. Therefore, when selecting a membrane for MFCs, it is essential to consider key factors such as internal resistance, substrate loss, biofouling, and oxygen diffusion. Addressing these considerations carefully allows researchers to advance the performance and efficiency of MFCs, facilitating their practical application in sustainable energy production and wastewater treatment. Accelerated substrate penetration could also lead to cathode clogging and bacterial inactivation, reducing the MFC's efficiency. Overall, the design and optimization of MFCs, including the selection and use of membranes, are vital for their practical application in renewable energy generation and wastewater treatment. Further research is necessary to overcome the challenges of MFCs without a membrane and to develop improved membrane materials for MFCs. This review article aims to compile comprehensive information about all constituents of the microbial fuel cell, providing practical insights for researchers examining various variables in microbial fuel cell research.

Analytical and numerical investigation of heat transfer of porous fin in a local thermal non-equilibrium state.

This research employs a local thermal non-equilibrium (LTNE) model to analyze the heat transfer phenomenon through a porous fin, considering natural convection and radiation effects. The infiltration velocity within the porous medium is evaluated using the Darcy model, and buoyancy effects are accounted for using the Boussinesq approximation. The Akbari-Ganji method (AGM) is applied to address the governing energy equations. The accuracy of the proposed solution is verified by comparing it with numerical results obtained from the finite difference method (FDM), the finite element method (FEM), and earlier investigations. The results are presented regarding the total average Nusselt number and temperature profiles. These results shed light on the influence of several important parameters, such as the thermal conductivity ratio, dimensionless thickness, convectional heat transfer, and external and internal radiation. The analysis reveals that decreasing Rayleigh and Biot numbers reduces the temperature profiles of the solid phase. Additionally, when the Rayleigh number is low but the assigned Biot number is high, the temperature difference between the solid and fluid phases diminishes. Furthermore, increased thermal conductivity ratio and dimensionless thickness for assigned Biot and Rayleigh numbers lead to higher solid phase temperatures. The Nusselt number exhibits a decreasing trend with a decreasing thermal conductivity ratio but increases with higher Rayleigh and Biot numbers and increased external radiation.

Investigating the effect of structural changes of two stretching disks on the dynamics of the MHD model.

The purpose of this theoretical study is to explore the behavior of an electrically conducting micropolar fluid when subjected to a uniform magnetic field along the vertical axis between two stretching disks as the structure of the problem changes. In this context, structural changes refer to alterations in the distance between the two discs or the stretching rate of the two discs. The governing equations of this problem are a set of nonlinear coupled partial differential equations, which are transformed into a nonlinear coupled ordinary differential equation set by a similarity transformation. The transformation results in four dimensionless quantities and their derivatives that appear in the equations. Nine dimensionless parameters are derived via similarity variables, including stretching Reynolds number, magnetic parameter, radiation parameter, Prandtl number, Eckert number, Schmidt number, and three micropolar parameters. Previous similarity solutions focused on analyzing the effect of changes in each parameter on the four dimensionless quantities. However, this type of analysis is mainly mathematical and does not provide practical results. This study's primary novelty is to redefine the magnetic parameter, Eckert number, stretching Reynolds number, and two micropolar parameters to analyze physical parameters that depend on the stretching rate of the two discs or the distance between them. The semi-analytical hybrid analytical and numerical method (HAN-method) is used to solve the equations. The results demonstrate that structural changes affect all five quantities of radial velocity, axial velocity, microrotation, temperature, and concentration. The study's most significant finding is that an increase in the stretching rate of the two disks causes a sharp increase in temperature and Nusselt number. Conversely, increasing the distance between the two disks causes a sharp decrease in micro-rotation and wall couple stress. They were compared to a previous study in a specific case to validate the results' accuracy.

An investigation into a semi-porous channel's forced convection of nano fluid in the presence of a magnetic field as a result of heat radiation.

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.

A novel technique for solving unsteady three-dimensional brownian motion of a thin film nanofluid flow over a rotating surface.

The motion of the fluid due to the swirling of a disk/sheet has many applications in engineering and industry. Investigating these types of problems is very difficult due to the non-linearity of the governing equations, especially when the governing equations are to be solved analytically. Time is also considered a challenge in problems, and times dependent problems are rare. This study aims to investigate the problem related to a transient rotating angled plate through two analytical techniques for the three-dimensional thin film nanomaterials flow. The geometry of research is a swirling sheet with a three-dimensional unsteady nanomaterial thin-film moment. The problem's governing equations of the conservation of mass, momentum, energy, and concentration are partial differential equations (PDEs). Solving PDEs, especially their analytical solution, is considered a serious challenge, but by using similar variables, they can be converted into ordinary differential equations (ODEs). The derived ODEs are still nonlinear, but it is possible to approximate them analytically with semi-analytical methods. This study transformed the governing PDEs into a set of nonlinear ODEs using appropriate similarity variables. The dimensionless parameters such as Prandtl number, Schmidt number, Brownian motion parameter, thermophoretic parameter, Nusselt, and Sherwood numbers are presented in ODEs, and the impact of these dimensionless parameters was considered in four cases. Every case that is considered in this problem was demonstrated with graphs. This study used modified AGM (Akbari-Ganji Method) and HAN (Hybrid analytical and numerical) methods to solve the ODEs, which are the novelty of the current study. The modified AGM is novel and has made the former AGM more complete. The second semi-analytical technique is the HAN method, and because it has been solved numerically in previous articles, this method has also been used. The new results were obtained using the modified AGM and HAN solutions. The validity of these two analytical solutions was proved when compared with the Runge-Kutta fourth-order (RK4) numerical solutions.

The HAN method for a thermal analysis of forced non-Newtonian MHD Reiner-Rivlin viscoelastic fluid motion between two disks.

In this article, the semi-analytical technique of the Hybrid Analytical and Numerical Method (the HAN Method) is used to study the non-transient forced non-Newtonian MHD Reiner-Rivlin viscoelastic fluid motion that is constrained between two plates. The magnetic field is also present in this model. The governing equations are in the PDE form and by using the Von Kármán similarity variables, they transformed into a set of ODEs. The HAN-method is applied to solve the ODEs and their associated boundary conditions, analytically. In addition, for the validation, the HAN solution results were compared with the HPM and numerical technique of Runge-Kutta results. And finally, new results were extracted from the HAN solutions in a quantitative form.