The current research is prepared to address the transport phenomenon in a hydro-magnetized flow model on a porous stretching sheet. Mass and heat transport are modeled via temperature dependent models of thermal conductivity and diffusion coefficients. Accordingly, the involvement of radiation, chemical reaction, the Dufour effect, and the Soret effect are involved. The flow presenting expression has been modeled via boundary layer approximation and the flow is produced due to the experimental stretching sheet. The governing equations have been approximated numerically via shooting method. The efficiency of the scheme is established by including the comparative study. Moreover, a decline in the velocity field is recorded against the escalating values of the porosity parameter and the magnetic parameter.

In this investigation, the motion of ${\mathrm{TiO}}_2/{\mathrm{H}}_2\mathrm{O}$ nano-structures towards heated and porous sheets by considering the MHD effect and partial slip at the boundary is inspected. The non-linear PDEs that correspond to the basic conservation laws are converted into ODEs with the help of suitable similarity transformation. Furthermore, the shooting method is used to solve these transformed ODEs and boundary conditions. The impact of thermophoresis properties has been shown graphically and the effect of these properties on the skin friction coefficient $\left(\mathrm{Cf}\right)$ and Nussetl number $\left(\mathrm{Nu}\right)$ are given in table form. The comparison between the present exploration and published work is carried out and validation among results is prepared. The enhancement in thermophysical parameters showed contrary results to the velocity profile of the ${\mathrm{TiO}}_2/{\mathrm{H}}_2\mathrm{O}$ nanofluid as compared with temperature profile. Moreover, it is observed that the higher estimation in the velocity slip parameter retards the flow and an enhancement in volume fraction increases the fluid’s temperature. Furthermore, it has been discovered that the geometry of nanoparticles has a major impact on the flow behaviour. The temperature distribution diminishes when the shape of the nanoparticles changes from platelet to spherical.

Heat transfer in an Eyring-Powell fluid that conducts electricity and flows past an exponentially growing sheet is considered. As the sheet is stretched in the x direction, the flow develops in the region with y > 0. The problem is tackled through a set of partial differential equations accounting for Magnetohydrodynamics (MHD), radiation and Joule heating effects, which are converted into a set of equivalent ordinary differential equations through a similarity transformation. The converted problem is solved in MATLAB in the framework a fourth order accurate integration scheme. It is found that the thermal relaxation period is inversely proportional to the thickness of the thermal boundary layer, whereas the Eckert-number displays the opposite trend. As this characteristic number grows, the temperature within the channel increases.

This communication deals with the analytical solutions of Cauchy problem for Cauchy-Riemann system of equations which is basically unstable according to Hadamard but its solution exists if its initial data is analytic. Here we used the Vectorial Adomian Decomposition (VAD) method, Vectorial Variational Iteration (VVI) method, and Vectorial Modified Picard’s Method (VMP) method to get the convergent series solution. These suggested schemes give analytical approximation in an infinite series form without using discretization. These methods are effectual and reliable which is demonstrated through six model problems having variety of source terms and analytic initial data.

In my opinion, the paper seems to be scientifically correct and interesting, and I recommend it be accepted for publication after taking the following important points during the preparation of the revised paper: 1.The Introduction should make a com...

The present work discusses heat transfer in thin liquid films past a stretching surface in the presence of Joule heating, radiation, viscous dissipation, and magnetic effects. Using a suitable similarity transformation, the nonlinear coupled partial differential equations are reduced to nonlinear ordinary differential equations. The coupled nonlinear ordinary differential equations are then solved by using the shooting method. The physical quantities, such as the unsteadiness parameter, the Prandtl number, the magnetic field parameter, the radiation parameter, and the viscous dissipation parameter on temperature distributions, are depicted graphically. It is observed that the effects of Prandtl and Eckert numbers are same over the temperature distribution. Furthermore, it is also evident that the increasing values of the unsteadiness parameter enhance the thermal conductivity of the fluid.