THERMOPHORESIS

In this study, the problem of boundary layer flow of magnetohydrodynamic stagnation point flow past a stretching sheet with convective heating is examined. Condition of zero normal flux of nanoparticles at the wall for the stretched flow is the most recent phenomena that have yet to be explored in the literature. The nanoparticle fractions on the boundary are considered to be passively controlled. Similarity transformation is used to reduce the governing non-linear boundary value problems into coupled high-order non-linear ordinary differential equation. These equations were numerically solved using the function bvp4c from the matlab for different values of governing parameters. Numerical results are obtained for velocity, temperature and concentration, as well as the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A increase. The local Nusselt
number theta′(0) decreases as the values of thermophoresis
parameter Nt increase and increases as the values of both
Biot number Bi and Prandtl number Pr increase. A comparison
with previous studies available in the literature has been done and an excellent agreement has been confirmed.

The influence of Thermo-Diffusion and Diffusion-Thermo effects on a viscousincompressible heat and mass transfer flow of a micropolar fluid saturated porous medium along a vertical plate with thermophoresis has been investigated. The governing partial differential equations are converted into ordinary differential equations using similarity transformation and are solved numerically using finite element method.Comparisons with previously published work on special cases of the problem have been performed and results are found to be good agreement.The effect of various parameters entered into the problem on velocity,angular velocity(micro-rotation),temperature and concentration fields as well as shear stress, Nusselt number and Sherwoodnumberare calculated and the results are shown in graphically and in tabular form to know the physical importance of the problem.

The viscous fluid flow past a sheet, stretching exponentially, is investigated under the influence of thermophoresis, Hall currents and viscous dissipation. The coupled nonlinear equations governing the flow are transformed to nonlinear ordinary differential equations. The successive linearization method is implemented to linearize the nonlinear ordinary differential equations. The obtained linearized system is solved using Chebyshev collocation method. The influences of the various flow governing physical parameters on the velocity components, temperature and concentration are presented graphically and analysed. Also, the skin frictions in x-and z-directions are computed and presented in the tabular form.

ABSTRACT In this paper we analyzed the effect of magnetic field on stagnation point flow and heat transfer due to nanofluid towards a stretching sheet. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. The solution for the temperature and nanoparticle concentration depends on six parameters viz. velocity ratio parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations to coupled higher order nonlinear ordinary differential equation. These equations were numerically solved using Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for velocity, temperature and concentration distribution, as well as the skin friction coefficient, local Nusselt number and Sherwood number. The results indicate that the skin friction coefficient Cf and local Nusselt number increases with an increase in velocity ratio parameter A. Likewise, the local Sherwood number increases with an increase in both velocity ratio A and Lewis number Le. Besides, it is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. A > 1, and it decreases when A < 1. A comparison with a previous study available in the literature has been done and we found an excellent agreement with them.

In the present analysis, the Dufour and Soret effects on unsteady heat-mass transfer of a viscous incompressible Powell-Eyring fluids flow past an expanding/shrinking permeable sheet are reported. The fluid boundary layer develops over the variable sheet with suction/injection to the non-uniform free stream velocity. Under the symmetry group of transformations, the governing equations along with three independent variables, are converted into a system of PDEs with two independent variables. Finally, by employing the order-reduction technique the PDEs are transformed into ODEs, which are then solved numerically. The results are presented graphically and analyzed. The main advantage of this technique is that without any prior knowledge, one can easily find the scaling transformations, expanding velocity, suction/injection velocity, and free-stream velocity. From computed numerical results many important findings are obtained. Most importantly, thermal and concentration overshoots are ...

This paper deals with two-dimensional steady boundary layer flow, heat, and mass transfer characteristics of micropolar nanofluid past on exponentially stretching/shrinking surface. The effect of different physical parameters like magnetic field, buoyancy, thermal radiation, and connective heat transfer are examined. Furthermore, similarity solutions are obtained by similarity transformation on the governing system of partial differential equations. The shooting method with help of the Maple software is used to achieve the numerical solutions of the equations. For the different ranges of the applied parameters, triple solutions are obtained for both cases of the surface. In view of the triple solutions, stability analysis is performed by bvp4c in the MATLAB software, where only first solution is found feasible which is discussed. The main findings of the first solution indicate the skin friction, drag force, heat, and mass transfer rates are increasing for the λ > 0 and decreasin...

This article focuses on analyzing the impact of the movement of
gyrotactic microorganisms on the heat and mass transfer characteristics
of Casson nanofluid flowing between divergent. Further, the
analysis is performed through simulation to have a better understanding
of the impact. Since the microorganisms are self-propelled,
they move on their own in the nanofluid due to the concentration
gradient and stabilize the nanoparticle suspension. This movement
of microorganisms constitutes the formation of bioconvection. Further,
the random motion of nanoparticles gives rise to two major
slip mechanisms termed thermophoresis and Brownian motion. The
mathematical model comprising these effects is designed using partial
differential equations that are converted to ordinary differential
equations with the help of suitable similarity transformation. The
resulting system of equations is then solved using the differential
transformation method and the outcomes are interpreted through
graphs. It is indicated that the nanoparticle concentration and the
motile density profiles increase with the increase in Schmidt number
and also, the concentration profile is found to be increasing
for higher Brownian motion parameter and lower thermophoretic
parameter. The simulations performed through the finite element
method portrayed that the heat flow in the diverging channel is
occurring along the isothermal planes.

Local modulation of temperature has emerged as a new mechanism for regulation of molecular transport through nanopores. Predicting the effect of such modulations on nanopore transport requires simulation protocols capable of reproducing non-uniform temperature gradients observed in experiment. Conventional molecular dynamics (MD) method typically employs a single thermostat for maintaining a uniform distribution of temperature in the entire simulation domain, and, therefore, can not model local temperature variations. In this article, we describe a set of simulation protocols that enable modeling of nanopore systems featuring non-uniform distributions of temperature. First, we describe a method to impose a temperature gradient in all-atom MD simulations based on a boundary-driven non-equilibrium MD protocol. Then, we use this method to study the effect of temperature gradient on the distribution of ions in bulk solution (the thermophoretic effect). We show that DNA nucleotides exhib...