Abstract This study investigates exact traveling wave solutions for two important nonlinear models: the hyperbolic chemotaxis model and the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Using the G ′ G 2 \frac{{G}^{^{\prime} }}{{G}^{2}} -expansion method, we derive solutions in the form of trigonometric, exponential, and rational functions, showcasing diverse wave behaviors such as periodic solitons, kink-type waves, and singular solitons. By visualizing these solutions with 3D and contour plots, we provide deeper insights into the spatial–temporal evolution of the wave dynamics. The findings highlight the versatility of the G ′ G 2 \frac{{G}^{^{\prime} }}{{G}^{2}} -expansion method for solving complex nonlinear equations and demonstrate its relevance in both biological systems, like chemotaxis, and physical wave dynamics.

Abstract The role of generalized nanoparticles was observed to be significant while increasing the surface area interaction between the base materials and the solid surface. The conductivity of such materials with the occurrence of similar and nonsimilar reactants has been observed to be very effective. Particularly, the processing of many rheological materials in industries is considered one of the significant applications. However, this study explored the unique features of the melting heat approach while considering the spinning motion of nanocomposite shear-thinning materials. The rheological material model was tested in the presence of autocatalytic reactions during its transparent conversion to a liquid state. Furthermore, the flow, temperature distribution, and nanoparticle concentration of the materials were represented by the conservation of momentum, concentration, and energy concepts. The leading problem is then presented using dimensionless local similar equations. The same equations are then numerically approximated by adopting one of the improved building three-stage formulas. The results were presented in terms of physical velocity, concentration, pressure, temperature, resistive forces, mass, and heat flow rates. The material dynamics are significantly reduced by plugging the higher relaxation time, and a reverse conduct is determined in the case of thermal analysis of the same materials. The melting heating factor and Brownian motion variation enhanced the flow speed and material temperature. On the other hand, a remarkable reduction in the material concentration was observed while uplifting similar and non-similar reaction factors. The method’s accuracy is confirmed through a well-matched comparison with the literature.

Abstract This study investigates thermally radiative nanofluid flows on an elongating surface using porous media. The flow dynamics are affected by the combined impacts of exponential and thermally dependent heat sources. Additionally, magnetic effects are introduced to the flow system while it is inclined. Copper (Cu) and copper oxide (CuO) nanoparticles are mixed in water (H 2 O) to fabricate nanofluid flows. Different shapes of Cu and CuO nanoparticles, including column, sphere, hexahedron, tetrahedron, and lamina, were studied in this analysis. The system flow is triggered by the stretching properties of the sheet. The textured surface of the stretching sheet facilitates the exploration of the slip velocity phenomenon. The modeled equations are evaluated using the bvp4c approach in a dimensionless form. The present study is validated by comparing its findings with established datasets available in the literature. The results of this analysis show that the velocity distributions decline with increasing values of the porosity factor, velocity slip factor, and magnetic factor. The reduction in velocity profiles is quite significant in the case of Cu–water nanofluid, in contrast to the CuO–water nanofluid due to more dominance of resistive constraints in the case of the Cu–water nanofluid. The thermal distribution increases with an increase in the magnetic factor, radiation factor, Eckert number, thermal-dependent heat source, and space-based heat source, and declines with an increase in the inclination angle and thermal slip factor. The Nusselt number augments for both types of nanofluids with an increase in various emerging factors in the scenarios of thermal slip and no-slip, where an increase in the Nusselt number is maximum for the scenario where there is no thermal slip. A higher thermal distribution and heat transfer rate are determined for the lamina-shaped Cu–water and CuO–water nanofluid flows for both slip and no-slip thermal conditions. On the basis of the current findings, this study aims to design efficient cooling systems for microelectronics, improve solar thermal collectors, enhance drug delivery via heat-sensitive nanoparticles, optimize industrial heat exchangers, and advance smart textile technologies requiring controlled thermal regulation using shape-engineered Cu and CuO nanofluids.

Abstract Hybrid nanofluids, an advanced class of working fluids, gained significant attention due to their superior thermal performance and heat transfer characteristics. These fluids consist of two types of nanoparticles suspended in a base fluid, offering enhanced thermal performance, making them crucial in engineering applications. In many industrial processes, magnetohydrodynamic (MHD) hybrid nanofluid flow plays a vital role in controlling mass and heat transfer in systems involving precipitation and chemical processing. The interaction between thermal radiation, chemical reactions, Joule heating, and heat sources significantly affects the efficiency of such systems, necessitating an in-depth analysis of their combined effects. This study focuses on the heat and mass transfer in hybrid nanofluid flow over various geometries, which is crucial for thermal management in electronic devices, precipitation, and filtration processes. Practical applications of a hybrid nanofluid flow around cones and wedges include spacecraft design, nuclear reactors, solar power collectors, etc. Therefore, this research examines the MHD hybrid nanofluid flow over a cone and wedge, using a suspension of SWCNTs and MWCNTs as nanomaterials in H 2 O as the base fluid. The study also considers the impact of Joule heating, an exponential space-based heat source in the temperature equation with thermal and mass convective conditions over two geometries (cone and wedge). Additionally, chemical reactions play a significant role in various natural and industrial processes. With this initiation, this research explores the effect of the activation energy and binary chemical reaction on the MHD hybrid nanofluid flow. The hybrid nanofluid model over two different geometries is governed by partial differential equations and converted to ordinary differential equations using similarity variables. The bvp4c method in MATLAB was employed to solve these equations numerically. The effects of the sundry flow parameter on the velocity, temperature, and concentration distributions were determined and discussed briefly. The study’s findings show that the improvement in both the thermal and mass Grashof numbers results in an increase in the velocity profile, supporting the effectiveness of hybrid nanofluids in cooling technologies for electronic devices. The increasing impression of the activation energy and mass Biot number on the concentration profile is progressive for wedges compared to cones. Furthermore, the results reveal that the presence of a nonlinear heat source tends to intensify the thermal profiles for wedges more significantly than the flow over cones, which is also related to the application of solar power collectors. The rate of heat transfer for the flow over a cone case is higher for the growing estimation of radiation, and the Biot number is particularly relevant to high-temperature applications such as nuclear reactors and spacecraft. The increasing impact of the Schmidt number, chemical reaction, and mass Biot number on the mass transfer rate is higher for cones as compared to wedges, while the activation energy has an opposite behavior for both flow cases. The observed trends in the mass transfer rate also support filtration and separation technologies, optimizing their efficiency based on fluid and material properties.

Abstract This work focuses on the impact of a magnetic field and viscous dissipation on the mixed convective flow of a couple stress nanofluid over a sheet that is stretching linearly. The research focuses on how these variables impact the model’s overall heat transfer characteristics and the fluid’s behavior. The sheet’s stretching causes the fluid to move as it extends, which is what causes the flow. When considering a heating procedure at the prescribed surface temperature, the heat transmission problem has been examined. The modified Adomian decomposition method (ADM) is a computational method that simplifies the complex governing equations of the model under study and finds their numerical solutions. This technique uses the Mohand transform in conjunction with the ADM, which ensures a high degree of convergence, producing a series solution that closely resembles the exact solution to the problem. In addition, we evaluate the residual error function to satisfy the effectiveness and accuracy of the introduced technique. When the current findings were compared with other methods for particular flow scenarios, they demonstrated strong agreement, confirming the accuracy of the solution. A complete examination of the effects of the different parameters has been provided, including graphic and tabular illustrations of the effects. Additionally, a comparison chart illustrating the agreement between the two sets of data has been given to show the coherence between the present numerical outcomes and previously published findings.

Abstract In response to the problem that traditional hydraulic fracturing technology is difficult to describe the specific situation of ground fissures, this study proposes to introduce a mechanics model of fracturing disappearance and optimize the model in order to achieve accurate description of the distribution of ground fissures after hydraulic fracturing. The model is validated and analyzed through case studies, and it is found that stress sensitivity, invasion factor, and retention factor all have varying degrees of influence on the tracing process. In addition, the model can accurately infer the fractures of hydraulic fracturing wells, with a variance of 148.9, a coefficient of determination of 0.81, and a root mean square error of 1.87. In terms of production, the oil production reaches 104.2 m3, accounting for 20.4% of the total oil production, and the water production reaches 47.6 m3, accounting for 15.8% of the total water production. In the examination of economic and environmental benefits, it is found that the model proposed by the research reduces labor expenditure costs to 292,000 yuan, equipment costs to 392,000 yuan, chemical supplies costs to 217,000 yuan, and maintenance costs to 98,000 yuan, but the revenue increases to 1.34 million yuan, and environmental satisfaction reaches 81.4%. The comprehensive results indicate that the model can be well applied in the tracing technology of hydraulic fracturing radioactive sources.

Abstract Thermal transport in ternary nanofluid is a topic of interest in different engineering systems. These fluids have higher thermal conductivity than traditional nanofluids. Hence, the present study aims to develop a new ternary nanofluid model for a cylindrical working domain. For this, thermophysical properties of ternary nanoliquids and appropriate transformations are used. The problem is then investigated through a numerical approach and the comparative results are obtained. The ternary nanofluid shows an optimum decrease in the velocity due to the involvement of three types of nanoparticles. Suction of the fluid with strength α = 0.1 , 0.9 , 1.7 , 2.5 \alpha =0.1,\hspace{.5em}0.9,\hspace{.5em}1.7,\hspace{.5em}2.5 and Reynolds effects Re = 1.0 , 1.5 , 2.0 , 2.5 \text{Re}=1.0,\hspace{.5em}1.5,\hspace{.5em}2.0,\hspace{.5em}2.5 significantly control the motion and dominant behaviour is examined for a simple nanofluid. The thermal capability of the nanofluids is enhanced against the concentration factor ϕ 1 = 0.01 , 0.0.3 , 0.05 , 0.07 {\phi }_{1}=0.01,\mathrm{0.0.3},0.05,0.07 while suction phenomena resist the temperature. Inclusion of radiations ( Rd = 0.1 , 0.5 , 0.9 , 1.3 ) (\text{Rd}\hspace{.25em}=\hspace{.25em}0.1,0.5,0.9,1.3) and convective transport ( B i = 0.01 , 0.02 , 0.03 , 0.04 {B}_{i}=0.01,0.02,0.03,0.04 ) contribute dominantly for thermal applications in nanofluids. The shear drag magnitude changes from 107.4995 to 162.287% (TNF), 113.427 to 170.666% (HNF), and 120.886 to 180.704% (SNF) for varying ϕ 1 {\phi }_{1} from 1.0 to 7.0%. Further, the efficiency of TNF, HNF, and SNF showed a prominent increase from 42.0126 to 68.8055% (TNF), 40.6019 to 66.6076% (HNF), and 39.8879 to 65.5324% (SNF), for stronger Biot effects from 0.5 to 2.0. Hence, the study’s outcomes would help to address the heat transfer issues from multiple aspects.

Abstract In this study, we investigate the fractional regularized long-wave (FRLW) equation using the Aboodh transform iteration method (ATIM), a semi-analytical technique that effectively combines the Aboodh integral transform with iterative schemes to handle fractional differential equations. The FRLW equation, a nonlinear model arising in ion-acoustic wave propagation in plasma, is extended to the fractional domain to better capture the temporal nonlocal behavior. The proposed method provides approximate analytical solutions in a straightforward and computationally efficient manner. Graphical results are presented to demonstrate the impact of the fractional-order parameter on wave dynamics, including dispersion and stability. The results confirm that ATIM is a powerful and accurate approach for solving nonlinear fractional partial differential equations and enriches the analytical understanding of fractional plasma wave models.

Abstract The present study investigates different types of wave symmetries in the ( 3 + 1 ) \left(3+1) -dimensional Chafee–Infante equation via the Hirota bilinear transformation technique. In this work, we derived exact solutions that include bright and dark solitons, periodic cross kink, multiple waves, mixed waves, homoclinic breathers, M-shaped related waves and periodic lump waves. These solutions exhibit stability, energy confinement, and dynamic interactions. It is observed that the Hirota method captures the highly nonlinear complex phenomena that result from the balance between the nonlinearity and the dispersion. These factors lead to a stability and coherent formation of wave forms. We employed Mathematica 11.1 software to obtain 3D, contour, and 2D graphs of our solution. The graphs present the spatial and temporal evolution of these solutions. The periodic structures, oscillatory solitons, and cross-kink configurations have dynamic interaction while maintaining fundamental properties of waves. Breather and homoclinic breather solutions present the basis of oscillatory local dynamics, which stress on energy transfer and phase modulation. The novelty of this article is in the use of the Hirota bilinear technique to the Chafee–Infante equation in ( 3 + 1 ) \left(3+1) -dimensional dimension, which allows the derivation of a wide variety of exact multidimensional wave solutions, including intricate hybrid solutions previously unreported for the equation. This provides great value by extending the analytical theory and improving the understanding of nonlinear wave behaviors in high-dimensional environments. It is worth noting that all the solutions have been verified and found to satisfy the governing equation.

Abstract Practical fields, including materials processing, space technology, ocean technology, and many mechanical machineries, play a major part in advancing the modern world. Lack of energy production and energy reduction have been noticed as one of the main challenges in recent decades. To properly address this, one should need to modify the thermal characteristics of traditional materials with different surface dynamics involvement. The present investigation examines the heat transfer performance and pumping power of destructive flow patterns of rheological materials caused by viscous stress is significant due to physical aspects. One key objective is to demonstrate the conversion of kinetic energy into internal energy, highlighting its applications across various fields of engineering, science, and technology. The current study is about to address the impacts of viscous stress, stagnation point, gravity, slip flow, and thermal slip in the typical swirling motion of Cross liquid. The main problem that arises from these physical aspects is presented in the form of dimensionless mathematical equations. The flow problem configured in this study is based on the higher viscous forces and lower inertial forces. The leading dimensionless equations are formulated by using the Lie symmetry analysis. A well-known modified collocation formula is used to examine the higher radial flow speed of the material with the parallel variation in the Richardson number, and the other components decline with the same variation. The temperature of the dissipated materials is enhanced by considering the higher values of the Eckert number. Time relaxation caused a reduction in the resistance forces in the r-direction and is noticed with the opposite trend in the case of θ-direction which is more prominent. An excellent agreement is observed by introducing a comparison with the existing works.