The rheology of different materials at the micro and macro levels is an area of great interest to many researchers, due to its important physical significance. Past experimental studies have proved the efficiency of the utilization of nanoparticles in different mechanisms for the purpose of boosting the heat transportation rate. The purpose of this study is to investigate heat and mass transport in a pseudo-plastic model past over a stretched porous surface in the presence of the Soret and Dufour effects. The involvement of tri-hybrid nanoparticles was incorporated into the pseudo-plastic model to enhance the heat transfer rate, and the transport problem of thermal energy and solute mechanisms was modelled considering the heat generation/absorption and the chemical reaction. Furthermore, traditional Fourier and Fick’s laws were engaged in the thermal and solute transportation. The physical model was developed upon Cartesian coordinates, and boundary layer theory was utilized in the simplification of the modelled problem, which appears in the form of coupled partial differential equations systems (PDEs). The modelled PDEs were transformed into corresponding ordinary differential equations systems (ODEs) by engaging the appropriate similarity transformation, and the converted ODEs were solved numerically via a Finite Element Procedure (FEP). The obtained solution was plotted against numerous emerging parameters. In addition, a grid independent survey is presented. We recorded that the temperature of the tri-hybrid nanoparticles was significantly higher than the fluid temperature. Augmenting the values of the Dufour number had a similar comportment on the fluid temperature and concentration. The fluid temperature increased against a higher estimation of the heat generation parameter and the Eckert numbers. The impacts of the buoyancy force parameter and the porosity parameter were quite opposite on the fluid velocity.

Engineers, scientists and mathematicians are greatly concerned about the thermal stability/instability of any physical system. Current contemplation discusses the role of the Soret and Dufour effects in hydro-magnetized Carreau–Yasuda liquid passed over a permeable stretched surface. Several important effects were considered while modelling the thermal transport, including Joule heating, viscous dissipation, and heat generation/absorption. Mass transportation is presented in the presence of a chemical reaction. Different nanoparticle types were mixed in the Carreau–Yasuda liquid in order to study thermal performance. Initially, governing laws were modelled in the form of PDEs. Suitable transformation was engaged for conversion into ODEs and then the resulting ODEs were handled via FEM (Finite Element Method). Grid independent analysis was performed to determine the effectiveness of the chosen methodology. Several important physical effects were explored by augmenting the values of the influential parameters. Heat and mass transfer rates were computed against different parameters and discussed in detail.

Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions. The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations. This is fulfilled by considering time variable as normal space variable. Under this scheme, there is no need to remove time-dependent variable during the whole solution process. Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method. We propose a simple shifted domain method, which can avoid the full-coefficient interpolation matrix easily. Numerical experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.

Carbon nanotubes (CNTs) are favored materials in the manufacture of electrochemical devices because of their mechanical and chemical stability, good thermal and electrical conductivities, physiochemical consistency, and featherweight. With such intriguing carbon nanotubes properties in mind, the current research aims to investigate the flow of hybridized nano liquid containing MWCNTs (multi-wall carbon nanotubes) and SWCNTs (single-wall carbon nanotubes) across a slendering surface in the presence of a gyrotactic-microorganism. The temperature and solutal energy equation are modified with the impact of the modified Fourier and Fick’s law, binary chemical reaction, viscous dissipation, and joule heating. The slip conditions are imposed on the surface boundaries. The flow equations are converted into ODEs by applying similarity variables. The bvp4c approach is applied to tackle the coupled and extremely nonlinear boundary value problem. The outputs are compared with the PCM (Parametric continuation method) to ensure that the results are accurate. The influence of involved characteristics on energy distribution, velocity profiles, concentration, and microorganism field are presented graphically. It is noted that the stronger values of the wall thickness parameter and the Hartmann number produce a retardation effect; as a result, the fluid velocity declines for MWCNT and SWCNT hybrid nano liquid. Furthermore, the transport of the mass and heat rate improves with a higher amount of both the hybrid and simple nanofluids. The amount of local skin friction and the motile density of microorganisms are discussed and tabulated. Furthermore, the findings are validated by comparing them to the published literature, which is a notable feature of the present results. In this aspect, venerable stability has been accomplished.

In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an “isotropic” space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the hyperbolic telegraph equations can be solved in a direct way. Numerical experiments performed with the proposed numerical scheme for several two-dimensional second-order hyperbolic telegraph equations are presented with some discussions, which show that the DMM solutions are converging very fast in comparison with the various existing numerical methods.

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.