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In this study, the removal of a series of acid dyes by hybrid polymer adsorbent was investigated. Textile industry wastewater is mainly consisted of suspended solid particles and organic compounds with complex and nondecomposable structures. Treatment of such wastewaters has received much attention by researchers because of high water consumption and the presence of various chemical compounds, especially dyes. The use of polymers has recently attracted much attention for the treatment of textile wastewaters. According to the literature, hybrid polymers are highly capable of adsorbing dyes. In this research work, polyacrylamide/iron sulfate (PAM-FeSO₄) hybrid polymer was successfully synthesized through solution polymerization of acrylamide with ammonium persulfate and sodium thiosulfate and gradual addition of iron sulfate. The hybrid polymeric adsorbent was then used for removing acidic dyes with different chemical structures.

The effects of various experimental conditions and parameters, such as initial concentrations of dye and adsorbent, on the adsorption capacity of the adsorbent were investigated. The dye concentration was measured by an UV–vis spectrophotometer. The adsorption equilibrium was studied by plotting adsorption isotherms. The experimental data was fitted to Langmuir and Freundlich isotherms.

The adsorption experiments indicated that the PAM-FeSO₄ hybrid polymer has a high adsorption capacity (117.64 mg g⁻¹ for the Orange ІІ and 80.64 mg g⁻¹ for the Sunset Yellow [SY]) when 80 mg of adsorbent was immersed in the dye solution (1 g L⁻¹) with a pH of 11 at 25°C. The analysis of the equilibrium isotherms using the Langmuir and Freundlich isotherms indicated that the Langmuir model fit well to the experimental data.

To the best of the authors’ knowledge, this study is original. The removal of acid dyes such as Sunset Yellow and Methyl Orange using PAM-FeSO₄ hybrid polymer as flocculant was done for the first time.

Methylene blue (MB) is classified as a cationic dye which is widely used as chemical indicator, coloring agent and biological stain. The discharge of this dye to the water streams is harmful to the human beings. For this reason, this study investigated the removal of MB from aqueous solution by hydrogel nanocomposite.

In experimental part, at first, ultraviolet (UV)-curable hydrogel/chitosan nanocomposite, which improves its elasticity by urethane acrylate, was synthesized and characterized by FTIR and SEM analysis. Afterward, the synthesized hydrogel nanocomposite was applied for the removal of MB and the influence of operational condition including nanocomposite loading, dye concentration, contact time and pH of solution was specified. Moreover, isotherm studies as well as kinetics survey were performed.

Langmuir, Freundlich, Brunauer, Emmett and Teller and Tempkin adsorption isotherms were assessed for the analysis of experimental data indicating the Freundlich isotherm was the best fitted one. The adsorption kinetics data was examined indicating the adsorption kinetics appropriate to pseudo-second-order kinetics model.

The predominant water absorption property of the UV-curable hydrogel/chitosan nanocomposite to 8.5 steps and outstanding adsorption capacity for the elimination of MB on hydrogel nanocomposite subscribed that the synthesized hydrogel could be a favorable adsorbent for simultaneous absorption of water and removal of cationic dyes.

This paper aims to examine the thermal transmission and entropy generation of hybrid nanofluid filled containers with solid body inside. The solid body is seen as being both isothermal and capable of producing heat. A time-dependent non-linear partial differential equation is used to represent the transfer of heat through a solid body. The current study’s objective is to investigate the key properties of nanoparticles, external forces and particular attention paid to the impact of hybrid nanoparticles on entropy formation. This investigation is useful for researchers studying in the area of cavity flows to know features of the flow structures and nature of hybrid nanofluid characteristics. In addition, a detailed entropy generation analysis has been performed to highlight possible regimes with minimal entropy generation rates. Hybrid nanofluid has been proven to have useful qualities, making it an attractive coolant for an electrical device. The findings would help scientists and engineers better understand how to analyse convective heat transmission and how to forecast better heat transfer rates in cutting-edge technological systems used in industries such as heat transportation, power generation, chemical production and passive cooling systems for electronic devices.

Thermal transmission and entropy generation of hybrid nanofluid are analysed within the enclosure. The domain of interest is a square chamber of size L, including a square solid block. The solid body is considered to be isothermal and generating heat. The flow driven by temperature gradient in the cavity is two-dimensional. The governing equations, formulated in dimensionless primitive variables with corresponding initial and boundary conditions, are worked out by using the finite volume technique with the SIMPLE algorithm on a uniformly staggered mesh. QUICK and central difference schemes were used to handle convective and diffusive elements. In-house code is developed using FORTRAN programming to visualize the isotherms, streamlines, heatlines and entropy contours, which are handled by Tecplot software. The influence of nanoparticles volume fraction, heat generation factor, external magnetic forces and an irreversibility ratio on energy transport and flow patterns is examined.

The results show that the hybrid nanoparticles concentration augments the thermal transmission and the entropy production increases also while the augmentation of temperature difference results in a diminution of entropy production. Finally, magnetic force has the significant impact on heat transfer, isotherms, streamlines and entropy. It has been observed that the external magnetic force plays a good role in thermal regulations.

Hybrid nanofluid is a desirable coolant for an electrical device. Various nanoparticles and their combinations can be analysed. Ferro-copper hybrid nanofluid considered with the help of prevailing literature review. The research would benefit scientists and engineers by improving their comprehension of how to analyses convective heat transmission and forecast more accurate heat transfer rates in various fields.

Due to its helpful characteristics, ferrous-copper hybrid nanofluid is a desirable coolant for an electrical device. The research would benefit scientists and engineers by improving their comprehension of how to analyse convective heat transmission and forecast more accurate heat transfer rates in cutting-edge technological systems used in sectors like thermal transportation, cooling systems for electronic devices, etc.

Entropy generation is used for an evaluation of the system’s performance, which is an indicator of optimal design. Hence, in recent times, it does a good engineering sense to draw attention to irreversibility under magnetic force, and it has an indispensable impact on investigation of electronic devices.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyse convective energy transport and entropy generation in a chamber with internal block, which is capable of maintaining heat and producing heat. Effects of irreversibility ratio are scrutinized for the first time. Analysis of convective heat transfer and entropy production in an enclosure with internal isothermal/heat generating blocks gives the way to predict enhanced heat transfer rate and avoid the failure of advanced technical systems in industrial sectors.

This study aims to undertake a comprehensive examination of heat transfer by convection in porous systems with top and bottom walls insulated and differently heated vertical walls under a magnetic field. For a specific nanofluid, the study aims to bring out the effects of different segmental heating arrangements.

An existing in-house code based on the finite volume method has provided the numerical solution of the coupled nondimensional transport equations. Following a validation study, different explorations include the variations of Darcy–Rayleigh number (Ra_m = 10–10⁴), Darcy number (Da = 10^–5–10^–1) segmented arrangements of heaters of identical total length, porosity index (ε = 0.1–1) and aspect ratio of the cavity (AR = 0.25–2) under Hartmann number (Ha = 10–70) and volume fraction of φ = 0.1% for the nanoparticles. In the analysis, there are major roles of the streamlines, isotherms and heatlines on the vertical mid-plane of the cavity and the profiles of the flow velocity and temperature on the central line of the section.

The finding of a monotonic rise in the heat transfer rate with an increase in Ra_m from 10 to 10⁴ has prompted a further comparison of the rate at Ra_m equal to 10⁴ with the total length of the heaters kept constant in all the cases. With respect to uniform heating of one entire wall, the study reveals a significant advantage of 246% rate enhancement from two equal heater segments placed centrally on opposite walls. This rate has emerged higher by 82% and 249%, respectively, with both the segments placed at the top and one at the bottom and one at the top. An increase in the number of centrally arranged heaters on each wall from one to five has yielded 286% rate enhancement. Changes in the ratio of the cavity height-to-length from 1.0 to 0.2 and 2 cause the rate to decrease by 50% and increase by 21%, respectively.

Further research with additional parameters, geometries and configurations will consolidate the understanding. Experimental validation can complement the numerical simulations presented in this study.

This research contributes to the field by integrating segmented heating, magnetic fields and hybrid nanofluid in a porous flow domain, addressing existing research gaps. The findings provide valuable insights for enhancing thermal performance, and controlling heat transfer locally, and have implications for medical treatments, thermal management systems and related fields. The research opens up new possibilities for precise thermal management and offers directions for future investigations.

A few earlier studies presented infeasible heatline trajectories for natural convection within annular domains involving an inner circular cylinder and outer square/circular enclosure. The purpose of this paper is to revisit and illustrate the correct heatline trajectories for various test cases.

Galerkin finite element based methodology and space adaptive grid have been used to simulate natural convective flows within the annular domains. The prediction of heatlines involves derivatives at the nodes, which are evaluated based on finite element basis functions and contributions from neighboring elements.

The heatlines in the earlier work indicate infeasible heat flow paths such as heat flow from one portion to the other of isothermal hot walls and heat flow across the adiabatic walls. Current results illustrate physically consistent heat flow paths involving perpendicularly emerging heatlines from hot to cold walls for conductive transport, long heat flow paths around the closed-loop heatline cells for convective transport and parallel layout of heatlines to the adiabatic walls. Results also demonstrate complex heatlines involving multiple flow vortices and complex flow structures.

Current work translates heatfunctions from energy flux vectors, which are determined by using basis sets. This work demonstrates the expected heatline trajectories for various scenarios involving conductive and convective heat transport within enclosures with an inner hot object as a first attempt, and the results are precursors for the understanding of energy flow estimates.

This study’s aim is to introduce a high-performance sorbent for the removal of both anionic (Congo red; CR) and cationic (methylene blue; MB) dyes from aqueous solutions.

Sodium silicate is adopted as a substrate for GO and AgNPs with positive charge are used as modifiers. The synthesized nanocomposite is characterized by FTIR, FESEM, EDS, BET and XRD techniques. Then, some of the most effective parameters on the removal of CR and MB dyes such as solution pH, sorbent dose, adsorption equilibrium time, primary dye concentration and salt effect are optimized using the spectrophotometry technique.

The authors successfully achieved notable maximum adsorption capacities (Qmax) of CR and MB, which were 41.15 and 37.04 mg g⁻¹, respectively. The required equilibrium times for maximum efficiency of the developed sorbent were 10 and 15 min for CR and MB dyes, respectively. Adsorption equilibrium data present a good correlation with Langmuir isotherm, with a correlation coefficient of R2 = 0.9924 for CR and R2 = 0.9904 for MB, and kinetic studies prove that the dye adsorption process follows pseudo second-order models (CR R2 = 0.9986 and MB R2 = 0.9967).

The results showed that the proposed mechanism for the function of the developed sorbent in dye adsorption was based on physical and multilayer adsorption for both dyes onto the active sites of non-homogeneous sorbent.

The as-prepared nano-adsorbent has a high ability to remove both cationic and anionic dyes; moreover, to the high efficiency of the adsorbent, it has been tried to make its synthesis steps as simple as possible using inexpensive and available materials.

This study aims to delve into the coupled mixed convective heat transport process within a grooved channel cavity using CuO-water nanofluid and an inclined magnetic field. The cavity undergoes isothermal heating from the bottom, with variations in the positions of heated walls across the grooved channel. The aim is to assess the impact of heater positions on thermal performance and identify the most effective configuration.

Numerical solutions to the evolved transport equations are obtained using a finite volume method-based indigenous solver. The dimensionless parameters of Reynolds number (1 ≤ Re ≤ 500), Richardson number (0.1 ≤ Ri ≤ 100), Hartmann number (0 ≤ Ha ≤ 70) and magnetic field inclination angle (0° ≤ γ ≤ 180°) are considered. The solved variables generate both local and global variables after discretization using the semi-implicit method for pressure linked equations algorithm on nonuniform grids.

The study reveals that optimal heat transfer occurs when the heater is positioned at the right corner of the grooved cavity. Heat transfer augmentation ranges from 0.5% to 168.53% for Re = 50 to 300 compared to the bottom-heated case. The magnetic field’s orientation significantly influences the average heat transfer, initially rising and then declining with increasing inclination angle. Overall, this analysis underscores the effectiveness of heater positions in achieving superior thermal performance in a grooved channel cavity.

This concept can be extended to explore enhanced thermal performance under various thermal boundary conditions, considering wall curvature effects, different geometry orientations and the presence of porous structures, either numerically or experimentally.

The findings are applicable across diverse fields, including biomedical systems, heat exchanging devices, electronic cooling systems, food processing, drying processes, crystallization, mixing processes and beyond.

This work provides a novel exploration of CuO-water nanofluid flow in mixed convection within a grooved channel cavity under the influence of an inclined magnetic field. The influence of different heater positions on thermomagnetic convection in such a cavity has not been extensively investigated before, contributing to the originality and value of this research.

This study aims to investigate the impact of different heater geometries (flat, rectangular, semi-elliptical and triangular) on hybrid nanofluidic (Cu–Al₂O₃–H₂O) convection in novel umbrella-shaped porous thermal systems. The system is top-cooled, and the identical heater surfaces are provided centrally at the bottom to identify the most enhanced configuration.

The thermal-fluid flow analysis is performed using a finite volume-based indigenous code, solving the nonlinear coupled transport equations with the Darcy number (10^–5 ≤ Da ≤ 10^–1), modified Rayleigh number (10 ≤ Ra_m ≤ 10⁴) and Hartmann number (0 ≤ Ha ≤ 70) as the dimensionless operating parameters. The semi-implicit method for pressure linked equations algorithm is used to solve the discretized transport equations over staggered nonuniform meshes.

The study demonstrates that altering the heater surface geometry improves heat transfer by up to 224% compared with a flat surface configuration. The triangular-shaped heating surface is the most effective in enhancing both heat transfer and flow strength. In general, flow strength and heat transfer increase with rising Ra_m and decrease with increasing Da and Ha. The study also proposes a mathematical correlation to predict thermal characteristics by integrating all geometric and flow control variables.

The present concept can be extended to further explore thermal performance with different curvature effects, orientations, boundary conditions, etc., numerically or experimentally.

The present geometry configurations can be applied in various engineering applications such as heat exchangers, crystallization, micro-electronic devices, energy storage systems, mixing processes, food processing and different biomedical systems (blood flow control, cancer treatment, medical equipment, targeted drug delivery, etc.).

This investigation contributes by exploring the effect of various geometric shapes of the heated bottom on the hydromagnetic convection of Cu–Al₂O₃–H₂O hybrid nanofluid flow in a complex umbrella-shaped porous thermal system involving curved surfaces and multiphysical conditions.

This study aims to observe the coloring efficacy of graphite (G) and nano bentonite clay (BCNPs) on the adsorption of Basic Blue 5 dye from residual dye bath solution.

Some factors that affected the adsorption processes were examined and found to have significant impacts on the adsorption capacity such as the initial concentration of G and/or BCNPs (Co: 40–2,320 mg/L), adsorbent bath pH (4–9), shaking time (30–150 min.) and initial dye concentration (40–200 mg/L). The adsorption mechanism of dye by using G and/or BCNPs was studied using two different models (first-pseudo order and second-pseudo order diffusion models). The equilibrium adsorption data for the dye understudy was analyzed by using four different models (Langmuir, Freundlich, Temkin modle and Dubinin–Radushkevich) models.

It has been found that the adsorption kinetics follow rather a pseudo-first-order kinetic model with a determination coefficient (R²) of 0.99117 for G and 0.98665 for BCNPs. The results indicate that the Freundlich model provides the best correlation for G with capacities q_max = 2.33116535 mg/g and R² = 0.99588, while the Langmuir model provides the best correlation for BCNPs with R² = 0.99074. The adsorbent elaborated from BCNPs was found to be efficient and suitable for removing basic dyes rather than G from aqueous solutions due to its availability, good adsorption capability, as well as low-cost preparation.

There is no research limitation for this work. Basic Blue 5 dye graphite (G) and nano bentonite clay (BCNPs) were used.

This work has practical applications for the textile industry. It is concluded that using graphite and nano bentonite clay can be a possible alternative to adsorb residual dye from dye bath solution and can make the process greener.

Socially, it has a good impact on the ecosystem and global community because the residual dye does not contain any carcinogenic materials.

The work is original and contains value-added products for the textile industry and other confederate fields.

In this study, polyvinyl alcohol (PVA)/poly[acrylic acid (AAc)-co-acrylamide (AM)] composite hydrogel was prepared by radical copolymerization in the presence of Fe³⁺ freezing-thawing method. The swelling behavior of the hydrogel was investigated. The novel synthesized hydrogel was used as an adsorbent for the removal of dyes from aqueous solutions. In this paper, methylene blue and maxilon blue 5G were selected as representative cationic dyes. In addition, adsorption isotherm models were used to describe the dye adsorption process.

The prepared composite hydrogel was characterized by Fourier transform infrared spectroscopy, thermogravimetric analysis, field emission scanning electron microscopy and UV–visible.

The prepared hydrogel exhibited excellent adsorption ability for both dyes. Various experimental conditions affecting the dye adsorption were explored to achieve maximum removal of both dyes. In addition, adsorption isotherm models were used to describe the dye adsorption process.

To the best of the author’s knowledge, synthesis of PVA/poly(AAc-co-AM) composite hydrogel in the presence of Fe³⁺ and investigation of the removal of methylene blue and maxilon blue 5G dyes is done for the first time successfully.