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This study aims to explore the precise resolution of the nonlinear Benjamin Bona Mahony Burgers (BBMB) equation, which finds application in a variety of nonlinear scientific disciplines including fluid dynamics, shock generation, wave transmission, and soliton theory. Within this paper, we employ two versatile methodologies, specifically the extended exp ( - Ψ ( χ ) ) expansion technique and the novel Kudryashov method, to identify the exact soliton solutions of the nonlinear BBMB equation. The solutions we discovered involve trigonometric functions, hyperbolic functions, and rational functions. The uniqueness of this research lies in uncovering the bright soliton, kink wave solution, and periodic wave solution, and conducting stability analysis. Furthermore, the solutions' graphical characteristics were explored through the utilization of the mathematical software Maple 2022 ( https://maplesoft.com/downloads/selectplatform.aspx?hash=61ab59890f2313b2241fde3423fd975e ). The system's physical interpretation is defined through various types of graphs, including contour graphs, 3D-surface graphs, and line graphs, which use appropriate parameter values. These recommended techniques hold significant importance and are applicable in diverse nonlinear evolutionary equations found in the field of nonlinear sciences for illustrating nonlinear physical models., (© 2024. The Author(s).)

Energy loss during the transportation of energy is the main concern of researchers and industrialists. The primary cause of heat exchange gadget inefficiency during transportation was applied to traditional fluids with weak heat transfer characteristics. Instead, thermal devices worked much better when the fluids were changed to nanofluids that had good thermal transfer properties. A diverse range of nanoparticles were implemented on account of their elevated thermal conductivity. This research addresses the significance of MHD Maxwell nanofluid for heat transfer flow. The flow model comprised continuity, momentum, energy transport, and concentration equations in the form of PDEs. The developed model was converted into ODEs by using workable similarities. Numerical simulations in the MATLAB environment were employed to find the outcomes of velocity, thermal transportation, and concentration profiles. The effects of many parameters, such as Hartman, Deborah, buoyancy, the intensity of an external heat source, chemical reactions, and many others, were also evaluated. The presence of nanoparticles enhances temperature conduction. Also, the findings are compared with previously published research. In addition, the Nusselt number and skin friction increase as the variables associated with the Hartman number and buoyancy parameter grow. The respective transfer rates of heat are 28.26 % and 38.19 % respectively. As a result, the rate of heat transmission increased by 14.23 % . The velocity profiles enhanced while temperature profiles declined for higher values of the Maxwell fluid parameter. As the external heat source increases, the temperature profile rises. Conversely, buoyancy parameters increase as it descends. This type of problem is applicable in many fields such as heat exchangers, cooling of electronic devices, and automotive cooling systems., (© 2024. The Author(s).)

The use of renewable energy sources is leading the charge to solve the world's energy problems, and non-Newtonian nanofluid dynamics play a significant role in applications such as expanding solar sheets, which are examined in this paper, along with the impacts of activation energy and solar radiation. We solve physical flow issues using partial differential equations and models like Casson, Williamson, and Prandtl. To get numerical solutions, we first apply a transformation to make these equations ordinary differential equations, and then we use the MATLAB-integrated bvp4c methodology. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. In addition to numerical and tabular studies of the skin friction coefficient, Sherwood number, and local Nusselt number, important components of the flow field are graphically shown and analyzed. Consistent with previous research, this work adds important new information to the continuing conversation in this area. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. Comparing the Casson nanofluid to the Williamson and Prandtl nanofluids, it is found that the former has a lower velocity. Compared to Casson and Williamson nanofluid, Prandtl nanofluid advanced in heat flux more quickly. The transfer of heat rates are 25.87 % , 33.61 % and 40.52 % at R d = 0.5 , R d = 1.0 , and R d = 1.5 , respectively. The heat transfer rate is increased by 6.91 % as the value of Rd rises from 1.0 to 1.5. This study is further strengthened by a comparative analysis with previous research, which is complemented by an extensive table of comparisons for a full evaluation., (© 2024. The Author(s).)

In this paper, we study linear and nonlinear mixed convection, activation energy, and heat radiation effects caused by nanoparticles. This study aims to improve the understanding of how nanofluids behave in the presence of rotating disks and develop more efficient and effective cooling technologies. The flow problem consisted of partial differential equations (PDE). It is challenging to calculate these equations as a result of these nonlinear PDEs. Consequently, we use appropriate similarities to transform them into ordinary differential equations (ODEs). The bvp4c Matlab built-in technique is then used to resolve these ODEs. The velocities, temperature, and concentration outcomes with the various factors are examined graphically. Additionally, tables are employed to analyze the skin friction and Nusselt number values. It is analyzed that increasing the linear and linear mixed convection parameters enhances the velocity profiles of nanofluid. Enhancements in heat are analyzed by increasing nonlinear thermal radiation and enhancement in concentration is examined by increasing activation energy. Furthermore, as the variables for thermophoresis and Brownian motion are increased, the Nusselt number falls. The heat transfer rate is 27.16% for [Formula: see text] and 39.28% for [Formula: see text]. Thus, the heat transfer rate is enhanced 12.12%. This study's practical applications include improving the behavior of fluids and the transfer of heat in rotating frameworks, which may affect energy systems, heat exchangers, and cooling advances in technology., (© 2023. The Author(s).)