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In this research communication, the (3 + 1)-dimensional Wazwaz Kaur Boussinesq equation is studied and solved by the direct algebraic method, namely the F expansion method. The F expansion method converts the nonlinear partial differential equation into an ordinary differential equation and finally into an algebraic equation. The Jacobi elliptic solutions of the Wazwaz Kaur Boussinesq equation are reported under six sets of classifications, followed by the existence condition and elliptic modulus limiting cases. The three-dimensional graphs for the few Jacobi solutions are drawn. [ABSTRACT FROM AUTHOR]

Understanding the intricate Korteweg–de Vries ( c K d V ) equation is paramount for comprehending various nonlinear wave phenomena, owing to its capacity to depict the propagation of nonlinear waves in media characterized by complex-valued dispersive and nonlinear coefficients. The practical ramifications of the c K d V equation are extensive, spanning disciplines such as optics, plasma physics, and other realms dealing with intricate media. This investigation employs the Khater II method and a generalized rational approach as analytical methodologies to generate novel exact solutions for the c K d V equation. The Khater II method is employed to transform the nonlinear partial differential equation into a nonlinear ordinary differential equation, thus facilitating a systematic resolution. Moreover, the generalized rational technique utilizes a rational ansatz function to derive diverse forms of solutions. Application of these methodologies leads to the discovery of fresh exact solutions, encompassing solitary and periodic wave solutions for the c K d V equation. These solutions are expressed in rational forms featuring arbitrary functions, thereby expanding the repertoire of known solutions for the model. The efficacy of the analytical methodologies employed becomes evident through the discovery of these novel exact solutions, thereby enriching our understanding of the physical interpretations and wave characteristics associated with the c K d V equation. The derived solutions augment the existing body of knowledge pertaining to the model. This research enhances our comprehension of the c K d V equation, thereby advancing nonlinear wave analysis with potential applications in physics, optics, plasma science, and allied engineering domains. Future investigations may explore the extension of these methodologies to address other nonlinear wave equations. [ABSTRACT FROM AUTHOR]

The current flow model is dedicated to capture the role of Dufour and Soret on heat and mass transmission of rotating flow of γ Al 2 O 3 - C 2 H 6 O 2 and γ Al 2 O 3 - water nanoparticles due to exponential stretching under the action of thermal radiation, magnetic, and Eckert numbers. The problem is modelled in terms if partial differential equations (PDEs) with associated physical conditions. The ordinary differential equations (ODEs) are obtained via suitable transformations. The reduced nonlinear ODEs set is tackled via a new scheme. We suggested significant improvements in the traditional technique and further formulated an extended version of wavelets scheme-based Chebyshev polynomials thoughts. The detailed procedure of the wavelet scheme and flow chart are provided. To validate the numerical outcomes; a comparative study with numerical technique RK (order-4) is also provided. Furthermore; numerical consequences of velocity, concentration and temperature profiles are further examined using several plots. The graphical plots, compared and convergence analyses are endorsing that our proposed modifications are worthy. Velocities profiles in view of γ Al 2 O 3 - C 2 H 6 O 2 nanofluid are lower than the γ Al 2 O 3 - H 2 O nanofluid. Temperature and concentration profiles are dominant when γ Al 2 O 3 - H 2 O nanofluid is considered. [ABSTRACT FROM AUTHOR]

The nanofluid flows play a vital role in many engineering processes owing to their notable industrial usage and excessive heat transfer abilities. Lately, an advanced form of nanofluids namely "hybrid nanofluids" has swapped the usual nanofluid flows to further augment the heat transfer capabilities. The objective of this envisaged model is to compare the performance of two renowned hybrid nanofluid models namely Hamilton–Crosser and Yamada–Ota. The hybrid nanoliquid (TiO2-SiC/DO) flow model is comprised of Titanium oxide (TiO2) and Silicon carbide (SiC) nanoparticles submerged into Diathermic oil (DO). The subject flow is considered over a stretched surface and is influenced by the magnetic dipole. The uniqueness of the fluid model is augmented by considering the modified Fourier law instead of the traditional Fourier law and slip conditions at the boundary. By applying the suitable similarity transformations, the system of ordinary differential equations obtained from the leading partial differential equations is handled by the MATLAB solver bvp4c package to determine the numerical solution. It is divulged that the Yamada–Ota model performs considerably better than the Hamilton–Crosser flow model as far as heat transfer capabilities are concerned. Further, the velocity reduces on increasing hydrodynamic interaction and slip parameters. It is also noted that both temperature profiles increase for higher hydrodynamic interaction and viscous dissipation parameters. The envisioned model is authenticated when compared with an already published result in a limiting case. [ABSTRACT FROM AUTHOR]

Prandtl–Eyring hybrid nanofluid (P-EHNF) heat transfer and entropy generation were studied in this article. A slippery heated surface is used to test the flow and thermal transport properties of P-EHNF nanofluid. This investigation will also examine the effects of nano solid tubes morphologies, porosity materials, Cattaneo–Christov heat flow, and radiative flux. Predominant flow equations are written as partial differential equations (PDE). To find the solution, the PDEs were transformed into ordinary differential equations (ODEs), then the Keller box numerical approach was used to solve the ODEs. Single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) using Engine Oil (EO) as a base fluid are studied in this work. The flow, temperature, drag force, Nusselt amount, and entropy measurement visually show significant findings for various variables. Notably, the comparison of P-EHNF's (MWCNT-SWCNT/EO) heat transfer rate with conventional nanofluid (SWCNT-EO) results in ever more significant upsurges. Spherical-shaped nano solid particles have the highest heat transport, whereas lamina-shaped nano solid particles exhibit the lowest heat transport. The model's entropy increases as the size of the nanoparticles get larger. A similar effect is seen when the radiative flow and the Prandtl–Eyring variable-II are improved. [ABSTRACT FROM AUTHOR]

The present study analyzes the comparison of the Xue and Yamada-Ota models for a hybrid nanoliquid flow in porous media occurring amidst a rotating channel with surface catalyzed reaction. Here, the hybrid nanofluid flow is studied under the effect of Cattaneo Christov (C–C) heat flux and homogenous heterogeneous (Homo-Hetero) chemical reaction with entropy generation minimization analysis. The assumptions of the viscosity of hybrid nanomaterial fluid and variable thermal conductivity are added characteristics to the inimitability of the flow model. Two kinds of nanoparticles, namely single-wall carbon nanotubes and multi-wall carbon nanotubes with ethylene glycol (EG) as the base fluid are considered. Carbon nanotubes possess diverse applications in daily life including energy storage, drug delivery, cancer treatment, tissue generation, platelet activation, magnetic force microscopy, and microwave absorption, etc. Similarity transformations are utilized to translate the modeled problem into the coupled ordinary differential equations. This system of ordinary differential equations is addressed numerically. The graphical outcomes are scrutinized by utilizing the MATLAB software bvp4c function. The results revealed that the velocity profile decreases for the higher rotation parameter while increases for the escalated slip parameter. Furthermore, the fluid concentration and temperature are on the decline for higher surface catalyzed reaction and thermal relaxation parameters respectively. [ABSTRACT FROM AUTHOR]

A numerical approach for solving second order singularly perturbed boundary value problems (SPBVPs) is introduced in this paper. This approach is based on the basis function of a 6-point interpolatory subdivision scheme. The numerical results along with the convergence, comparison and error estimation of the proposed approach are also presented. [ABSTRACT FROM AUTHOR]