Soret and Dufour Effects on Hydromagnetic Flow of H2O-Based Nanofluids Induced by an Exponentially Expanding Sheet Saturated in a Non-Darcian Porous Medium

Diffusion-thermo effect (Dufour effect) and thermal-diffusion effect (Soret effect) on an MHD flow through porous medium taking nanoparticles may be considered to be useful in many engineering problems when there is a species concentration along with the solid nanoparticles. To study such an attracting problem, it is necessary to consider the flow to be single-phase. In the present investigation, the hydromagnetic flow of H2O-based nanofluids due to an exponentially expanding sheet saturated in non-Darcian porous material is examined with Dufour and Soret effects. In addition, temperature and species concentration along the surface in flow distribution are considered to be variable exponentially. Two sorts of nanofluids are considered, to be specific, Cu–H2O and Ag–H2O. Use of proper similarity transformations transfers the governing PDEs to coupled ODEs. Then the solutions of the coupled equations are computed by very efficient shooting method. Non-dimensionless velocity species concentration and temperature are introduced in graphical mode for several values of involved parameters. Out of several obtained outcomes, it is noticeable that similar to the magnetic parameter and permeability parameter, due to increase in non-Darcy Forchheimer parameter velocity diminishes and while temperature and species concentration increments are witnessed. Due to presence of Dufour effect, temperature enhances and similarly, the concentration increases for Soret effect. While due to Dufour effect, the concentration initially decreases, but away from surface it increases and similar behaviour is found for temperature in the case of Soret effect. Also, it is obtained that skin-friction coefficient for Cu–H2O nanofluid is larger than it value for Ag–H2O nanofluid. Dufour effect turns into the reason for the reduction of Nusselt number and increment of Sherwood number for both nanofluids, but Soret effect affects the two nanofluids reversely. The analysis and its findings provide some tools which may be applied in engineering and industrial problems.

MHD Free Convection from a Semi-infinite Vertical Porous Plate with Diffusion-Thermo Effect

An analytical solution for two-dimensional unsteady MHD free convective mass transfer flows of viscous incompressible optically thin fluid past a semi-infinite vertical porous plate in the presence of thermal radiation and chemical reaction is presented in this paper. A uniform magnetic field is applied normally to the plate with a first-order chemical reaction. The non-dimensional governing equations are solved analytically by using the regular perturbation technique. The effects of various physical parameters like radiation parameter Q, Dufour effect Du, chemical reaction parameter K, thermal Grashof number Gr, Hartmann number M, porosity parameter k, etc., are studied and demonstrated graphically. One of the significant findings of this analysis includes that an intensification of the chemical reaction effect causes a downfall in the fluid concentration. In contrast, another important outcome of the present study is that the rate of heat transfer and shear stress at the wall increases under the diffusion thermo effect or Dufour effect. Still, it tends to fall for high radiation. Further, the rate of mass transfer rises under the chemical reaction effect.

THE DUFOUR EFFECT IN FILM COOLING EXPERIMENTS WITH FOREIGN GASES

In typical film cooling experiments, the adiabatic wall temperature may be determined from surface temperature measurements on a low thermal conductivity model in a low temperature wind tunnel. In such experiments, it is generally accepted that the adiabatic wall temperature must be bounded between the coolant temperature and the freestream recovery temperature as they represent the lowest and highest temperature introduced into the experiment. Many studies have utilized foreign gas coolants to alter the coolant properties such as density and specific heat to more appropriately simulate engine representative flows. In this paper, we show that the often ignored Dufour effect can alter the thermal physics in such an experiment from those relevant to the engine environment that we generally wish to simulate. The Dufour effect is an off-diagonal coupling of heat and mass transfer that can induce temperature gradients even in what would otherwise be isothermal experiments. These temperature gradients can result in significant errors in calibration of various experimental techniques, as well as lead to results that at first glance may appear non-physical such as adiabatic effectiveness values not bounded by zero and one. This work explores Dufour effect induced temperature separation on two common cooling flow schemes, a leading edge with compound injection through a cylindrical cooling hole, and a flat plate with axial injection through a 7-7-7 shaped cooling hole. Air, argon, carbon dioxide, helium, and nitrogen coolant were utilized due to their usage in recent film cooling studies.

Dufour Effect on Transient MHD Double Convection Flow of Fractionalized Second-Grade Fluid with Caputo–Fabrizio Derivative

This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo–Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters α and β on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.

Numerical Computation of Dufour and Soret Effects on Radiated Material on a Porous Stretching Surface with Temperature-Dependent Thermal Conductivity

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.