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The numerical investigation conducted in this study focuses on the heat and mass transfer in magnetohydrodynamic non‐Newtonian power‐law fluid flow of temperature‐dependent Al2O3–Fe3O4–water hybrid nanofluid within cylindrical annuli across four different eccentricities. This type of problem finds widespread application in various engineering contexts, where hybrid non‐Newtonian fluids offer enhanced efficiency for cooling and insulation purposes. In this configuration, the inner circle of the geometry is hot while the outer circle is cold, with the nanofluid filling the space between the cylinders. The governing equations are simulated using the Galerkin weighted residual finite element method. Various parameters are controlled in the study, including the Rayleigh number ranging from 104 $$ {10}^4 $$to 106 $$ {10}^6 $$ , power‐law index ranging from 0.7 $$ 0.7 $$to 1.4 $$ 1.4 $$ , nanoparticle volume fraction ranging from 0% $$ 0\\% $$to 4% $$ 4\\% $$ , Hartmann number ranging from 0 $$ 0 $$to 30 $$ 30 $$ , Buoyancy ratio ranging from −1 $$ -1 $$to 1 $$ 1 $$ , and Lewis number ranging from 1 $$ 1 $$to 10 $$ 10 $$ , in addition to the fixed Prandtl number (6.8377). The study presents visualizations such as streamlines, isotherms, and iso‐concentration contours, along with the assessment of heat and mass transfer rates expressed in terms of Nusselt and Sherwood numbers. The findings reveal that the heat transfer rate increases with higher nanoparticle volume fraction, Rayleigh number, and Buoyancy ratio. Similarly, the mass transfer rate is enhanced with increased Rayleigh number, Lewis number, and power‐law index. Notably, elevating the power‐law index leads to a decrease of 50.1% in the local Nusselt number and 52.4% in the local Sherwood number, respectively. With n=0.7 $$ n=0.7 $$and ϕ=0 $$ \\phi =0 $$ , increasing Ra $$ Ra $$from 104 $$ {10}^4 $$to 106 $$ {10}^6 $$raises Nu‾ $$ \\overline{Nu} $$and Sh‾ $$ \\overline{Sh} $$ . The numerical investigation conducted in this study focuses on the heat and mass transfer in magnetohydrodynamic (MHD) non‐Newtonian power‐law fluid flow of temperature‐dependent Al2O3–Fe3O4–water hybrid nanofluid within cylindrical annuli across four different eccentricities. The Galerkin weighted residual finite element method (GFEM) is employed to simulate the governing equations.

The aim of this study is to investigate the effects of temperature-dependent viscosity on the natural convection flow from a vertical permeable circular cone with uniform heat flux. As part of numerical computation, the governing boundary layer equations are transformed into a non-dimensional form. The resulting nonlinear system of partial differential equations is then reduced to local non-similarity equations which are solved computationally by three different solution methodologies, namely, (i) perturbation solution for small transpiration parameter (ξ), (ii) asymptotic solution for large ξ, and (iii) the implicit finite difference method together with a Keller box scheme for all ξ. The numerical results of the velocity and viscosity profiles of the fluid are displayed graphically with heat transfer characteristics. The shearing stress in terms of the local skin-friction coefficient and the rate of heat transfer in terms of the local Nusselt number (Nu) are given in tabular form for the viscosity parameter (ε) and the Prandtl number (Pr). The viscosity is a linear function of temperature which is valid for small Prandtl numbers (Pr). The three-fold solutions were compared as part of the validations with various ranges of Pr numbers. Overall, good agreements were established. The major finding of the research provides a better demonstration of how temperature-dependent viscosity affects the natural convective flow. It was found that increasing Pr, ξ, and ε decrease the local skin-friction coefficient, but ξ has more influence on increasing the rate of heat transfer, as the effect of ε was erratic at small and large ξ. Furthermore, at the variable Pr, a large ξ increased the local maxima of viscosity at large extents, particularly at low Pr, but the effect on temperature distribution was found to be less significant under the same condition. However, at variable ε and fixed Pr, the temperature distribution was observed to be more influenced by ε at small ξ, whereas large ξ dominated this scheme significantly regardless of the variation in ε. The validations through three-fold solutions act as evidence of the accuracy and versatility of the current approach.

The present work investigates the magnetohydrodynamic (MHD) convective heat transport of hybrid nanofluids in a chamber with multiple heaters (such as hot microchips). The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) and graphics processing unit (GPU) computing are used here. The present study is important due to its relevance to real-world applications, the use of advanced simulation techniques, the consideration of hybrid nanofluids, the inclusion of magnetohydrodynamics, and the identification of critical parameters influencing heat transfer. Thermally homogeneous blocks are set at the bottom of a rectangular enclosure filled with ethylene glycol Cu-Al2O3 hybrid nanofluids with temperature-dependent viscosity. The cold temperature of the enclosure’s left and right walls and the bottom and top surfaces is kept at adiabatic conditions. The numerical outcomes for the various parameters Rayleigh number (104≤Ra≤106), volume fraction (0.00≤ϕ≤0.04), Hartmann number (0≤Ha≤60), and viscosity variation parameter (0≤ε∗≤5) are presented in terms of streamlines, isotherms, and the peripheral local and average Nusselt numbers for the heated chips. The results demonstrated that inside the chamber, the Rayleigh number (Ra), the Hartmann number (Ha), and the volume fraction of nanoparticles (ϕ) have the highest impact on the heat transfer rate for hybrid nanofluid. For increased Ha from 0 to 20, while ϕ=0.0 and Ra=106, average Nusselt number decreased with 13.65%. For the same case, if the volume fraction was increased to ϕ=0.04, then the average Nusselt number decreased 14%. Finally, a sensitivity analysis was done to analyze the system’s correctness and effectiveness to determine the significance of the specified parameters.

Maintaining an optimal concentration of nutrients in photobioreactors (PBRs) is a key issue for their optimal design and operation. In this study, a numerical investigation was conducted to quantify the dissolution of KNO 3 and Na 2 HPO 4 inside a thin-layer cascade (TLC) reactor and determine its consequential effect on the reactor performance for algal cultivation. A computational fluid dynamics (CFD) model based on Euler–Euler approach was used to investigate nutrient mixing in TLC and evaluate the effect of flow and geometric properties of the reactor. A wide range of pertinent parameters such as channel width, channel depth, mass flow rate and nutrient particle size were considered. Nutrient concentration plots, nutrient mixing in terms of mass transfer coefficient, and solid hold-up in the reactor were established. The nutrient dissolution improved in the reactor with small dimensions operating at high mass flow rates and was inversely related to the nutrient particle size; that is, small particle results in increased nutrient mixing due to the enlarged interfacial area. Graphical Abstract

The present work investigates the magnetohydrodynamic (MHD) convective heat transport of hybrid nanofluids in a chamber with multiple heaters (such as hot microchips). The multiple‐relaxation‐time (MRT) lattice Boltzmann method (LBM) and graphics processing unit (GPU) computing are used here. The present study is important due to its relevance to real‐world applications, the use of advanced simulation techniques, the consideration of hybrid nanofluids, the inclusion of magnetohydrodynamics, and the identification of critical parameters influencing heat transfer. Thermally homogeneous blocks are set at the bottom of a rectangular enclosure filled with ethylene glycol Cu‐Al 2 O 3 hybrid nanofluids with temperature‐dependent viscosity. The cold temperature of the enclosure’s left and right walls and the bottom and top surfaces is kept at adiabatic conditions. The numerical outcomes for the various parameters Rayleigh number (10 4 ≤ Ra ≤ 10 6 ), volume fraction (0.00 ≤ ϕ ≤ 0.04), Hartmann number (0 ≤ Ha ≤ 60), and viscosity variation parameter (0 ≤ ε ∗ ≤ 5) are presented in terms of streamlines, isotherms, and the peripheral local and average Nusselt numbers for the heated chips. The results demonstrated that inside the chamber, the Rayleigh number (Ra), the Hartmann number (Ha), and the volume fraction of nanoparticles ( ϕ ) have the highest impact on the heat transfer rate for hybrid nanofluid. For increased Ha from 0 to 20, while ϕ = 0.0 and Ra = 10 6 , average Nusselt number decreased with 13.65%. For the same case, if the volume fraction was increased to ϕ = 0.04, then the average Nusselt number decreased 14%. Finally, a sensitivity analysis was done to analyze the system’s correctness and effectiveness to determine the significance of the specified parameters.

Turbulent flow mixing plays a critical role in optimising microalgal cultivation in thin-layer cascade (TLC) systems. However, the small size of microalgal cells makes them highly susceptible to hydrodynamic stresses generated by turbulent mixing. The mechanical properties of microalgal cell walls under turbulent conditions and their implications on cell viability and biofuel production in TLC systems remain largely unexplored. In this study, a novel fluid–structure interaction-based numerical model was developed to investigate the effects of turbulent mixing on microalgal cell wall damage in TLC systems. This study focused on assessing cell wall damage at various locations within the TLC system, considering the hydrodynamic and geometric characteristics of the system. It examined parameters such as aspect ratio, flow depth and mass flow rate to analyse cell wall shear stress, deformation and von Misses stress. Results demonstrated that appropriate turbulent mixing conditions are crucial in TLC systems to mitigate the risk of microalgal cell wall damage. Specifically, shallow and narrow TLC systems with high mixing intensities were found to pose a great risk to cell wall integrity. This study provides valuable insights into optimising turbulent mixing in TLC systems, enabling enhanced microalgal cultivation and improved biofuel production. By understanding and managing the impact of turbulent flow on microalgal cell wall integrity, this research contributes to the development of efficient and sustainable TLC systems for microalgae-based applications.

Purpose – The purpose of this paper is to conduct a detailed investigation of the two-dimensional natural convection flow of a dusty fluid. Therefore, the incompressible boundary layer flow of a two-phase particulate suspension is investigated numerically over a semi-infinite vertical flat plate. Comprehensive flow formations of the gas and particle phases are given in the boundary layer region. Primitive variable formulation is employed to convert the nondimensional governing equations into the non-conserved form. Three important two-phase mechanisms are discussed, namely, water-metal mixture, oil-metal mixture and air-metal mixture. Design/methodology/approach – The full coupled nonlinear system of equations is solved using implicit two point finite difference method along the whole length of the plate. Findings – The authors have presented numerical solution of the dusty boundary layer problem. Solutions obtained are depicted through the characteristic quantities, such as, wall shear stress coefficient, wall heat transfer coefficient, velocity distribution and temperature distribution for both phases. Results are interpreted for wide range of Prandtl number Pr (0.005-1,000.0). It is observed that thin boundary layer structures can be formed when mass concentration parameter or Prandtl number (e.g. oil-metal particle mixture) are high. Originality/value – The results of the study may be of some interest to the researchers of the field of chemical engineers.

The present study aims to investigate the impact of air pollutants dispersion from traffic emission under the influence of wind velocity and direction considering the seasonal cycle in two major areas of Dhaka city: namely, Tejgaon and Gazipur. Carbon monoxide (CO) mass fraction has been considered as a representative element of traffic-exhausted pollutants, and the distribution of pollutants has been investigated in five different street geometries: namely, single regular and irregular, double regular and irregular, and finally, multiple irregular streets. After the grid independence test confirmation as well as numerical validation, a series of case studies has been presented to analyze the air pollutants dispersion, which mostly exists due to the traffic emission. The popular Reynolds-averaged Navier–Stokes (RANS) approach has been considered, and the finite volume method (FVM) has been applied by ANSYS FluentTM. The k−ϵ turbulence model has been integrated from the RANS approach. It was found that the wind velocity as well as wind direction and the fluid flow fields can play a potential role on pollution dispersion in the Dhaka city street canyons and suburbs. Inhabitants residing near the single regular streets are exposed to more traffic emission than those of single irregular streets due to fewer obstacles being created by the buildings. Double regular streets have been found to be a better solution to disperse pollutants, but city dwellers in the east region of double irregular streets are exposed to a greater concentration of pollutants due to the change of wind directions and seasonal cycles. Multiple irregular streets limit the mobility of the pollutants due to the increased number of buildings, yet the inhabitants near the multi-irregular streets are likely to experience approximately 11.25% more pollutants than other dwellers living far from the main street. The key findings of this study will provide insights on improving the urbanization plan where different geometries of streets are present and city dwellers could have less exposure to traffic-exhausted pollutants. The case studies will also provide a template layout to map pollutant exposure to identify the alarming zone and stop incessant building construction within those regions by creating real-time air quality monitoring to safeguard public safety.

An analysis is carried out to thoroughly understand the characteristics of heat and mass transfer for the natural convection boundary layer flow along a triangular horizontal wavy surface. Combine buoyancy driven boundary layer equations for the flow are switched into convenient form via co-ordinate transformations. Full non-linear equations are integrated numerically for Pr = 0.051. Interesting results for the uneven surface are found which are expressed in the form of wall shear stress, rate of heat transfer and rate of mass transfer. Solutions are also visualized via streamlines, isotherms, and isolines for concentration. Computational results certify that, shear stress, temperature gradient and concentration gradient enhances as soon as the amplitude of the wavy surface, a, increases, but complex geometry do not allow to carry simulations for a > 1.5. This factor probably ensures that sinusoidal waveform is better than triangular waveform. This article has been corrected. Link to the correction 10.2298/TSCI170525126E nema

This paper studies the unsteady MHD flow of a viscous fluid in which each point of the parallel planes are subject to the non-torsional oscillations in their own planes. The streamlines at any given time are concentric circles. Exact solutions are obtained and the loci Γ of the centres of these concentric circles are discussed. It is shown that the motion so obtained gives three infinite sets of exact solutions in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks. These solutions reduce to a single unique solution when symmetric solutions are looked for. Some interesting special cases are also obtained from these solutions.