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In this work, we introduce novel postulates to establish fixed figure theorems with a focus on their extension to the domain of mvb−metric spaces. Consequently, we define conditions ensuring the existence and uniqueness of fixed circles, fixed ellipses, fixed Apollonius circles, fixed Cassini curves, fixed hyperbola, and so on for self mapping. We also partially address an open problem demonstrating that a JS−contraction possesses a fixed elliptic disc. This property extends to smaller discs and ellipses within a complete mvb−metric space. By challenging the conventional assumption of zero self-distance, we pave the way for more accurate mathematical models applicable to real-world scenarios. Consequently, our research contributes not only to a deeper comprehension of mathematical concepts but also to practical utility across various scientific domains. Our findings are supported by illustrative examples. Additionally, we explore the concept of fixed figures in the context of Rectified Linear Unit (ReLU), a widely-used activation function in neural networks and machine learning models. Our exploration of fixed figures in the context of Rectified Linear Units (ReLU) further deepens our understanding of nonlinear systems and their relationship to neural network behavior.

Our study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula: see text] and m ≥ 2. We also demonstrate the impact of the parameters on the formatted fractals with numerical examples and graphical illustrations using the MATHEMATICA software, algorithm, and colormap. Moreover, we observe that the Julia set appears when we widen the Mandelbrot set at its petal edges, suggesting that each Mandelbrot set point contains a sizable quantity of Julia set picture data. It is commonly known that fractal geometry may capture the complexity of many intricate structures that exist in our surroundings.

Worldwide pure drinkable and usable water demand is increasing such as in the regions of Middle East, North Africa, and South Asia majority of the population are facing extreme water scarcity. Among numerous types of solar desalination technologies, interfacial solar steam generation (ISSG) has the potential practical applications on wastewater treatments, power generation, sterilization, and soil remediation beyond the application of only on desalination. In this research, MXene@RuO2 nanocomposite coated on bio-degradable luffa sponge is harnessed where the synthesis of MXene-RuO2@LS is done hydrothermally. As ruthenium oxide (RuO2) is a metal oxide with having the capability of ensuring effective surface area by preventing the restacking of MXene which happens due to their inherently high interfacial van der Waals interactions and surface energy. Bio-degradable luffa sponge is the best example of an evaporator with large pore spaces and rigid structure. As a result, the novel MXene-RuO2@LS absorber exhibited the rate of evaporation about 1.5 Kgm−2h−1 under 1 sun illumination for about 1 h. Furthermore, the prepared sample achieved the total energy consumption of 90.85 % with total heat loss of only 9.15 %. UV–Vis characterization was performed with improved absorptivity of 1.2, enhancement of transmittance by FTIR analysis of about 95 %, XRD analysis, SEM image analysis and water contact angle are evaluated as well. In addition, the collected desalinated water is tested where noticeable reduction of major ion concentrations and salinity achieved. All these enhanced results indicate the practical application of interfacial solar desalination.

This study involves a computational analysis to find the effectiveness of incorporating twisted tape within a twisted square duct for improving heat transfer, focusing on laminar single-phase flow. The primary goal is to study how varying the tape pitch (y) influences the hydrothermal performance of this system. The twisted square duct pitch (S) and twist ratio (H) were kept constant. The numerical analysis is performed under conditions of uniform wall temperature, and varying the pitch ratio (y/S) across values of 0.25, 0.5,0.75, 1, 1.25, 1.5 and 1.75. The obtained findings suggest that the addition of twisted tape within the twisted square duct results in a greater rate of heat exchange and pressure drop relative to the simple twisted square duct. Research reveals that despite a higher rate of heat transfer for a pitch ratio of 0.25 the increased friction factor results in less effective thermal performance compared to the cases with pitch ratios of 0.75 and 0.5. The thermal performance factor reaches its peak at 1.32, corresponding to the Reynolds number 1000 for a pitch ratio of 0.75 case. Conversely, the lowest thermal performance factor value of 0.89 is observed at the Reynolds number 500 for pitch ratio 1.25 case.

Abstract In uniformly convex Banach spaces, we study within this research Fibonacci–Ishikawa iteration for monotone asymptotically nonexpansive mappings. In addition to demonstrating strong convergence, we establish weak convergence result of the Fibonacci–Ishikawa sequence that generalizes many results in the literature. If the norm of the space is monotone, our consequent result demonstrates the convergence type to the weak limit of the sequence of minimizing sequence of a function. One of our results characterizes a family of Banach spaces that meet the weak Opial condition. Finally, using our iterative procedure, we approximate the solution of the Caputo-type nonlinear fractional differential equation.

The global demand for freshwater increased keep interest in water desalination technology. In recent past, solar thermal desalination emerged as a promising technique to water desalination. This review provides an extensive analysis of various solar thermal desalination techniques, including steam generation systems, their mechanisms, structures, and the role of different nanomaterials in enhancing desalination efficiency. We critically analyzed recent studies, focusing on process performance, benefits, limitations, economic viability, and environmental impact. The advantages of solar thermal desalination, such as sustainability, renewability, fossil fuel independence, decentralized water production, and suitability for remote locations, are discussed. We also discussed the materials for desalination based on material's water-transport capability, salt resistance, photothermal conversion efficiency and. Additionally, we provided insights into design principles and thermal management to enhance efficiency, reduce costs, and ensure sustainable freshwater production. This review will provide a guideline facilitate the development of sustainable solar thermal desalination technologies by utilizing existing knowledge and identifying research gaps, promoting the integration of renewable energy and water production for a resilient, water-secure future.

It is the purpose of the present paper to obtain certain fixed point outcomes in the sense of $ C^* $-algebra valued metric spaces. Here, we present the definitions of the gauge function, the Bianchini-Grandolfi gauge function, $ \alpha $-admissibility, and $ (\alpha, \beta) $-admissible Geraghty contractive mapping in the sense of $ C^* $-algebra. Using these definitions, we define $ (\alpha, \beta) $-Bianchini-Grandolfi gauge contraction of type I and type II. Next, we prove our primary results that the function satisfying our contraction condition has to have a unique fixed point. We also explain our results using examples. Additionally, we discuss some consequent results that can be easily obtained from our primary outcomes. Finally, there is a useful application to integral calculus.

This study presents an innovative iterative method designed to approximate common fixed points of generalized contractive mappings. We provide theorems that confirm the convergence and stability of the proposed iteration scheme, further illustrated through examples and visual demonstrations. Moreover, we apply s-convexity to the iteration procedure to construct orbits under convexity conditions, and we present a theorem that determines the condition when a sequence diverges to infinity, known as the escape criterion, for the transcendental sine function sin(um)−αu+β, where u,α,β∈C and m≥2. Additionally, we generate chaotic fractals for this orbit, governed by escape criteria, with numerical examples implemented using MATHEMATICA software. Visual representations are included to demonstrate how various parameters influence the coloration and dynamics of the fractals. Furthermore, we observe that enlarging the Mandelbrot set near its petal edges reveals the Julia set, indicating that every point in the Mandelbrot set contains substantial data corresponding to the Julia set’s structure.

This study examines the impact of varying the porosity density of twisted tape inserts (TTI) on the temperature distribution, fluid velocities, heat transfer coefficients (HTC), Nusselt numbers (Nu), turbulent kinetic energy (TKE), and performance from 5000 to 12500 Reynolds numbers (Re). The entire process involved the design of TTIs and double pipe heat exchangers using SolidWorks. Subsequently, a three-dimensional fluid flow model was employed to solve equations related to energy mass, energy, and momentum within the ANSYS Fluent interfaces. The findings highlight the noteworthy impact of high porosity TTIs, which consistently reduce temperature spans, increase fluid velocities, and greatly HTC and Nu when compared to low porosity TTI, typical TTI, and plain tubes. Furthermore, high porosity TTI significantly increases TKE, indicating increased fluid turbulence and higher heat transfer efficiency, especially at Re = 12500. The assessment of PEC emphasizes the superiority of high porosity TTI, demonstrating their significant performance increase potential of over 6.44 % over low porosity TTI and a staggering 62.5 % above typical TTI. In conclusion, high porosity TTI emerges as a potential solution for improving heat transfer efficiency and overall system performance in a variety of industrial applications, promising enhanced energy efficiency and superior performance.

In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the Sb-metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works on the presence and uniqueness of a fixed point in Sb-metric space. Also, the outcomes are achieved by removing the continuity constraint of self-operators. We also provide examples to elaborate on the obtained results and an application to the integral equation to illustrate the significance in the literature.

MXene-based nanofluids are novel trends with improved dispersion stability and thermophysical characteristics over previously established nanofluids. In the present work, the thermohydraulic characteristics of a double pipe heat exchanger (DPHEX) with a Therminol55(TH55)/MXene + Al2O3 nanofluid and various geometrically shaped (triangular, rectangular) ribbed twisted tape (TT) inserts are numerically investigated using the ANSYS Fluent interface. A counter flow arrangement with three different types of inserts (RRTT, TRTT, TT) and TH55/MXene + Al2O3 nanofluid at 0.20 wt% are studied inside the heat exchanger. Adding ribbed inserts to the conventional TT insert enhances the turbulence intensity by creating extra vortices. The thermal boundary layer grows thinner due to increased axial and radial velocity. Due to the substantial flow obstruction, adding ribs increases the overall pressure drop between the inlet and outlet. The maximum increase in Nu is 11.04 % using nanofluid instead of water, whereas the combination of insert and nanofluid exhibited up to 105 % enhancement for rectangular-ribbed TT compared to the plain tube. Nevertheless, the pressure decrease is found to be maximum in rectangular-ribbed TT because of significant flow disruption. This was likewise true with triangular-ribbed TT and TT insert. According to the PEC assessment, the RRTT insert had a maximum PEC value of 1.67 greater than TRTT and traditional TT for both TH55 and nanofluid flowing inside the tube. To summarize, the combination of TH55/MXene + Al2O3 RRTT insert may be a promising choice for improving heat exchanger performance in a new generation efficient thermal system.

Nano-refrigerant is announced to become an excellent refrigerant, which often improves heat transfer efficiency in the cooling systems. Different materials can be applied to be suspended in traditional coolants in the same way as nanoparticles. In this comprehensive research, mathematical modeling was used to investigate the effect of suspended nanoparticles (Al2O3, CuO, SiO2 and ZnO) on 1,1,1,2-Tetrafluoroethane, R-134a. The thermal conductivity, dynamic viscosity, density and specific heat capacity of the nano-refrigerant in an evaporator pipe were investigated. Compared to conventional refrigerants, the maximum increase in thermal conductivity was achieved by Al2O3/R-134a (96.23%) at a volume concentration of 0.04. At the same time, all nano-refrigerant types presented the same viscosity enhancement of(45.89%) at the same conditions. These types of complex thermophysical properties have enhanced the heat transfer tendencies in the pipe. Finally, the nano-refrigerant could be a likely working fluid generally used in the cooling unit to improve high-temperature transfer characteristics and save energy use.

To meet the growing energy demand, double pipe heat exchangers (DPHEX), which are used in a variety of energy and thermal engineering applications, require improved heat transfer performance. In this study, a new class of surfactant-free Ionanofluid is formulated at three different concentrations of 0.01, 0.05 and 0.10 wt% and thermophysical and rheological properties are assessed. Zeta potential analysis is executed to assess the dispersion stability. An optimum concentration has been selected to investigate the hydrothermal performance of an insert fitted DPHEX at varying Re from 400 to 2000. The conventional twisted tape (TT) insert is modified by introducing different types of geometrical (triangular, rectangular, and circular) cuts on its surface. According to the Ionanofluid characterization, 0.10 wt % Ionanofluid has the highest thermal conductivity enhancement of 64% and heat capacity of 16.1% when compared to the base fluid, with a maximum enhancement in Nu of about 116–136% at varying Re. The rectangular-cut TT imparts highest heat transfer enhancement as the additional vortices is more intensive than other cut-inserts. Nevertheless, the value of PEC for the combination of Ionanofluid and RCTT insert, remaining between 1.61 and 1.68 over the entire range of Re, is greater than other combinations.

Nanofluids are identified as advanced working fluids in the solar energy conversion field with superior heat transfer characteristics. This research work introduces carbon-based diamond nanomaterial and Therminol®55 oil-based nanofluids for implementation in a concentrated photovoltaic/thermal (CPV/T) solar collector. This study focuses on the experimental formulation, characterization of properties, and performance evaluation of the nanofluid-based CPV/T system. Thermo-physical (thermal conductivity, viscosity, and rheology), optical (UV-vis and FT-IR), and stability (Zeta potential) properties of the formulated nanofluids are characterized at 0.001–0.1 wt.% concentrations of dispersed particles using experimental assessment. The maximum photo-thermal energy conversion efficiency of the base fluid is improved by 120.80% at 0.1 wt.%. The thermal conductivity of pure oil is increased by adding the nanomaterial. The highest enhancement of 73.39% is observed for the TH-55/DP nanofluid. Furthermore, dynamic viscosity decreased dramatically across the temperature range studied (20–100 °C), and the nanofluid exhibited dominant Newtonian flow behavior, with viscosity remaining nearly constant up to a shear rate of 100 s−1. Numerical simulations of the nanofluid-operated CPV/T collector have disclosed substantial improvements. At a concentrated solar irradiance of 5000 W/m2 and an optimal flow rate of 3 L/min, the highest thermal and electrical energy conversion efficiency enhancements are found to be 11 and 1.8%, respectively.

The current research focuses on formulating a new class of Therminol55-based nanofluids that incorporates an MXene/Al2O3 nanocomposite as the new class of dispersant at three different concentrations of 0.05, 0.10, and 0.20 wt%. The optical and thermophysical properties of the formulated nanofluid are assessed experimentally. Zeta potential and FTIR analyses are employed to evaluate the composite particles' surface charge and chemical stability, respectively. Thermal conductivity is observed to increase with nanoparticle loading and maximally augmented by 61.8% for 0.20 wt%, whereas dynamic viscosity increased with adding nanoparticles but remarkably dropped with increasing temperature. In addition, the prepared TH55/MXene + Al2O3 samples are thermally stable up to 200 °C according to TGA analyses. Moreover, the proposed correlations for the thermal conductivity and viscosity showed good agreement with the experimental data. The study’s findings suggest that the formulated nanofluid could be a viable contender to be used as a heat transfer fluid in the thermal sector.

Since technology progresses, the need to optimize the thermal system’s heat transfer efficiency is continuously confronted by researchers. A primary constraint in the production of heat transfer fluids needed for ultra-high performance was its intrinsic poor heat transfer properties. MXene, a novel 2D nanoparticle possessing fascinating properties has emerged recently as a potential heat dissipative solute in nanofluids. In this research, 2D MXenes (Ti3C2) are synthesized via chemical etching and blended with a binary solution containing Diethylene Glycol (DEG) and ionic liquid (IL) to formulate stable nanofluids at concentrations of 0.1, 0.2, 0.3 and 0.4 wt%. Furthermore, the effect of different temperatures on the studied liquid’s thermophysical characteristics such as thermal conductivity, density, viscosity, specific heat capacity, thermal stability and the rheological property was experimentally conducted. A computational analysis was performed to evaluate the impact of ionic liquid-based 2D MXene nanofluid (Ti3C2/DEG+IL) in hybrid photovoltaic/thermal (PV/T) systems. A 3D numerical model is developed to evaluate the thermal efficiency, electrical efficiency, heat transfer coefficient, pumping power and temperature distribution. The simulations proved that the studied working fluid in the PV/T system results in an enhancement of thermal efficiency, electrical efficiency and heat transfer coefficient by 78.5%, 18.7% and 6%, respectively.

The addition of ionic liquids with MXene nanofluid has a substantial impact on the solar thermal collectors’ working fluid’s optical properties that effectively absorb and distribute solar radiation. Increased solar radiation absorption potential ensures that heats are transported more rapidly and effectively. This research endeavors to investigate the concept of accumulating solar energy via the usage of ionic liquid-based 2D MXene nanofluid (Ionanofluids) for solar applications. In this study, the optical potential of Diethylene Glycol/MXene nanofluid incorporated with 1-ethyl-3-methyl imidazolium octyl sulfate ([Emim][OSO4]) ionic liquid was extensively investigated with respect to MXene concentration (0.1 to 0.4 wt%) and time (first day and seventh day) through UV-Vis Spectroscopy. A two-step approach was employed to synthesize the proposed ionanofluids with nanoparticle concentrations from 0.1 to 0.4 wt%. In wavelengths between 240 to 790 nm, the effect of ionic liquids, MXene concentration, and dispersion stability played a significant part in enhancing the absorbance capacity of the formulated MXene based Ionanofluid. Furthermore, the increase in the concentration of MXene nanoparticles resulted in more absorbance peaks facilitating high light absorption. Finally, the electrical conductivity of the ionanofluids is also analyzed as MXene renders them promising for solar cell applications. The utmost electrical conductivity of the formulated fluids of 571 μS/cm (micro siemens per centimeter) was achieved at 0.4 wt% concentration.

In recent years, solar energy technologies have developed an emerging edge. The incessant research to develop a power source alternative to fossil fuel because of its scarcity and detrimental effects on the environment is the main driving force. In addition, nanofluids have gained immense interest as superior heat transfer fluid in solar technologies for the last decades. In this research, a binary solution of ionic liquid (IL) + water based ionanofluids is formulated successfully with two dimensional MXene (Ti3C2) nano additives at three distinct concentrations of 0.05, 0.10, and 0.20 wt % and the optimum concentration is used to check the performance of a hybrid solar PV/T system. The layered structure of MXene and high absorbance of prepared nanofluids have been perceived by SEM and UV–vis respectively. Rheometer and DSC are used to assess the viscosity and heat capacity respectively while transient hot wire technique is engaged for thermal conductivity measurement. A maximum improvement of 47% in thermal conductivity is observed for 0.20 wt % loading of MXene. Furthermore, the viscosity is found to rise insignificantly with addition of Ti3C2 by different concentrations. Conversely, viscosity decreases substantially as the temperature increases from 20 °C to 60 °C. However, based on their thermophysical properties, 0.20 wt % is found to be the optimum concentration. A comparative analysis in terms of heat transfer performance with three different nanofluids in PV/T system shows that, IL+ water/MXene ionanofluid exhibits highest thermal, electrical, and overall heat transfer efficiency compared to water/alumina, palm oil/MXene, and water alone. Maximum electrical efficiency and thermal efficiency are recorded as 13.95% and 81.15% respectively using IL + water/MXene, besides that, heat transfer coefficients are also noticed to increase by 12.6% and 2% when compared to water/alumina and palm oil/MXene respectively. In conclusion, it can be demonstrated that MXene dispersed ionanofluid might be great a prospect in the field of heat transfer applications since they can augment the heat transfer rate considerably which improves system efficiency.

In this study, the microclimate of the test room was regulated using thermoelectric air duct cooling system (TE-AD) operated at input powers-240 W, 360 W, 480 W, 600 W, 720 W, and 840 W, on subsequent nights. Fifteen (15) healthy male volunteers were recruited to sleep under these test conditions and their sleep quality was assessed by studying objective measures such as sleep onset latency (SOL), mean skin temperature and heart rate as well as subjective parameters like predicted mean vote (PMV) and predicted percentage of dissatisfied (PPD). There was a consistent improvement on all studied parameters when the power of the system was increased from 240 W to 720 W. The mean sleep onset latency time was reduced from (M = 40.7 +/− 0.98 min) to (M = 18.33 +/− 1.18 min) when the operating power was increased from 240 W to 720 W, denoting an improvement in sleep quality. However, increasing the power further to 840 W resulted in deteriorating cooling performance of the TE-AD system leading to an increase in temperature of the test room and reduction in sleep comfort. Analysis of subjective indices of thermal comfort viz. PMV and PPD revealed that subjects are highly sensitive towards variations in microclimate achieved by changing the operating power of the TE-AD. This device was also found to be environmentally sustainable, with estimated reduction in CO2 emission calculated to be around 38% as compared to the conventional air-conditioning.

Our study presents a novel orbit with s−convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for u,α,β∈C and m ≥ 2. We also demonstrate the impact of the parameters on the formatted fractals with numerical examples and graphical illustrations using the MATHEMATICA software, algorithm, and colormap. Moreover, we observe that the Julia set appears when we widen the Mandelbrot set at its petal edges, suggesting that each Mandelbrot set point contains a sizable quantity of Julia set picture data. It is commonly known that fractal geometry may capture the complexity of many intricate structures that exist in our surroundings. [ABSTRACT FROM AUTHOR]

This study presents an innovative iterative method designed to approximate common fixed points of generalized contractive mappings. We provide theorems that confirm the convergence and stability of the proposed iteration scheme, further illustrated through examples and visual demonstrations. Moreover, we apply s-convexity to the iteration procedure to construct orbits under convexity conditions, and we present a theorem that determines the condition when a sequence diverges to infinity, known as the escape criterion, for the transcendental sine function sin (u m) − α u + β , where u , α , β ∈ C and m ≥ 2 . Additionally, we generate chaotic fractals for this orbit, governed by escape criteria, with numerical examples implemented using MATHEMATICA software. Visual representations are included to demonstrate how various parameters influence the coloration and dynamics of the fractals. Furthermore, we observe that enlarging the Mandelbrot set near its petal edges reveals the Julia set, indicating that every point in the Mandelbrot set contains substantial data corresponding to the Julia set's structure. [ABSTRACT FROM AUTHOR]

It is the purpose of the present paper to obtain certain fixed point outcomes in the sense of C*-algebra valued metric spaces. Here, we present the definitions of the gauge function, the Bianchini-Grandolfi gauge function, a-admissibility, and (α, β)-admissible Geraghty contractive mapping in the sense of C*-algebra. Using these definitions, we define (α, β)-Bianchini-Grandolfi gauge contraction of type I and type II. Next, we prove our primary results that the function satisfying our contraction condition has to have a unique fixed point. We also explain our results using examples. Additionally, we discuss some consequent results that can be easily obtained from our primary outcomes. Finally, there is a useful application to integral calculus. [ABSTRACT FROM AUTHOR]

This work aims to prove new results in an Mbv-metric space for a noncontinuous single-valued self-map. As a result, we extend, generalize, and unify various fixed-point conclusions for a single-valued map and come up with examples to exhibit the theoretical conclusions. Further, we solve a mathematical model of the spread of specific infectious diseases as an application of one of the conclusions. In the sequel, we explain the significance of Mbv-metric space because the underlying map is not necessarily continuous even at a fixed point in Mbv-metric space thereby adding a new answer to the question concerning continuity at a fixed point posed by Rhoades. Consequently, we may conclude that the results via Mbv-metric are very inspiring, and underlying contraction via Mb v-metric does not compel the single-valued self-map to be continuous even at the fixed point. Our research is greatly inspired by the exciting possibilities of using noncontinuous maps to solve real-world nonlinear problems. [ABSTRACT FROM AUTHOR]

This study aims to provide a new class of Ćirić α+(θ, ϕ)-proximal contraction, a non-self generalized proximal contraction mapping on a non-empty closed subset of any metric space. Also, we prove that such contractions satisfying some conditions must have a unique best proximity point if we take the base space as complete. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different types of proximal contractions. We substantiate the deduced findings with examples. An application to show the solution of an integral equation in the context of proximity point results over the space of all real-valued continuous functions is discussed. By presenting these findings, we aim to encourage a new wave of scholars to keep exploring this exciting topic that has so many applications ahead of it. [ABSTRACT FROM AUTHOR]