Second Law Analysis of Unsteady MHD Viscous Flow over a Horizontal Stretching Sheet Heated Non-Uniformly in the Presence of Ohmic Heating: Utilization of Gear-Generalized Differential Quadrature Method.

In this article, the entropy generation characteristics of a laminar unsteady MHD boundary layer flow are analysed numerically for an incompressible, electrically conducting and dissipative fluid. The Ohmic heating and energy dissipation effects are added to the energy equation. The modelled dimensional transport equations are altered into dimensionless self-similar partial differential equations (PDEs) through suitable transformations. The reduced momentum and energy equations are then worked out numerically by employing a new hybrid method called the Gear-Generalized Differential Quadrature Method (GGDQM). The obtained numerical results are incorporated in the calculation of the Bejan number and dimensionless entropy generation. Quantities of physical interest, like velocity, temperature, shear stress and heat transfer rate, are illustrated graphically as well as in tabular form. Impacts of involved parameters are examined and discussed thoroughly in this investigation. Exact and GGDQM solutions are compared for special cases of initial unsteady flow and final steady state flow. Furthermore, a good harmony is observed between the results of GGDQM and those given previously by the Spectral Relaxation Method (SRM), Spectral Quasilinearization Method (SQLM) and Spectral Perturbation Method (SPM).

Irreversibility Analysis of Dissipative Fluid Flow Over A Curved Surface Stimulated by Variable Thermal Conductivity and Uniform Magnetic Field: Utilization of Generalized Differential Quadrature Method.

The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the energy equation. Appropriate transformations are used to develop the self-similar equations from the governing equations of momentum and energy. The resulting self-similar equations are then solved by the Generalized Differential Quadrature Method (GDQM). For the validation and precision of the developed numerical solution, the resulting equations are also solved numerically using the Runge-Kutta-Fehlberg method (RKFM). An excellent agreement is found between the numerical results of the two methods. To examine the impacts of emerging physical parameters on velocity, temperature distribution and entropy generation, the numerical results are plotted against the various values of physical flow parameters and discussed physically in detail.

Dual solutions of unsteady flow of copper-alumina/water based hybrid nanofluid with acute magnetic force and slip condition.

Suspending particles of tiny solid in a fluid used to transport energy can enhance its thermal conductivity and heat transport properties. Our main goal of this examination is to study the radiative unsteady two-dimensional (2D) flow on a continuously diminishing, horizontal sheet. with suction for the hybrid water-based nanofluid and an aligned field of magnetic, including the combined suction, magnetic, and velocity slip conditions effect. The Tiwari & Das model of nanofluid equations is used, which takes into consideration the solid volume percentage. Equations of similarity are derived by employing the transformations of similarity, and the associated equations have been simplified numerically by employing the bvp4c method in MATLAB software for a variety of values of the nanoparticle volume fraction, the unsteadiness, and the wall mass suction in water. It is discovered that, within the given the unsteadiness parameter range, two solutions exist. Moreover, it is found that the fluid velocity slows down in 1st solution as volume fraction of copper nanoparticles rises but speeds up in the second solution at first before slowing down again. Using a temporal stability analysis, it is found that only one of the dual branches is stable over the long run, while the other is unstable.

Significance of Rosseland's Radiative Process on Reactive Maxwell Nanofluid Flows over an Isothermally Heated Stretching Sheet in the Presence of Darcy-Forchheimer and Lorentz Forces: Towards a New Perspective on Buongiorno's Model.

This study aimed to investigate the consequences of the Darcy-Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno's model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier-Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others.

Numerical Scrutinization of Darcy-Forchheimer Relation in Convective Magnetohydrodynamic Nanofluid Flow Bounded by Nonlinear Stretching Surface in the Perspective of Heat and Mass Transfer.

The aim of this research is mainly concerned with the numerical examination of Darcy-Forchheimer relation in convective magnetohydrodynamic nanofluid flow bounded by non-linear stretching sheet. A visco-elastic and strictly incompressible liquid saturates the designated porous medium under the direct influence of the Darcy-Forchheimer model and convective boundary. The magnetic effect is taken uniformly normal to the flow direction. However, the model is bounded to a tiny magnetic Reynolds number for practical applications. Boundary layer formulations are taken into consideration. The so-formulated leading problems are converted into highly nonlinear ordinary problems using effectively modified transformations. The numerical scheme is applied to solve the governing problems. The outcomes stipulate that thermal layer receives significant modification in the incremental direction for augmented values of thermal radiation parameter Rd. Elevation in thermal Biot number γ1 apparently results a significant rise in thermal layer and associated boundary layer thickness. The solute Biot number is found to be an enhancing factor the concentration profile. Besides the three main profiles, the contour and density graphs are sketched for both the linear and non-linear cases. Furthermore, skin friction jumps for larger porosity and larger Forchheimer number. Both the heat and mass flux numbers receive a reduction for augmented values of the Forchheimer number. Heat flux enhances, while mass flux reduces, the strong effect of thermal Biot number. The considered problem could be helpful in any several industrial and engineering procedures, such as rolling, polymeric extrusion, continuously stretching done in plastic thin films, crystal growth, fiber production, and metallic extrusion, etc.

Thermally Enhanced Darcy-Forchheimer Casson-Water/Glycerine Rotating Nanofluid Flow with Uniform Magnetic Field.

This numerical study aims to interpret the impact of non-linear thermal radiation on magnetohydrodynamic (MHD) Darcy-Forchheimer Casson-Water/Glycerine nanofluid flow due to a rotating disk. Both the single walled, as well as multi walled, Carbon nanotubes (CNT) are invoked. The nanomaterial, thus formulated, is assumed to be more conductive as compared to the simple fluid. The properties of effective carbon nanotubes are specified to tackle the onward governing equations. The boundary layer formulations are considered. The base fluid is assumed to be non-Newtonian. The numerical analysis is carried out by invoking the numerical Runge Kutta 45 (RK45) method based on the shooting technique. The outcomes have been plotted graphically for the three major profiles, namely, the radial velocity profile, the tangential velocity profile, and temperature profile. For skin friction and Nusselt number, the numerical data are plotted graphically. Major outcomes indicate that the enhanced Forchheimer number results in a decline in radial velocity. Higher the porosity parameter, the stronger the resistance offered by the medium to the fluid flow and consequent result is seen as a decline in velocity. The Forchheimer number, permeability parameter, and porosity parameter decrease the tangential velocity field. The convective boundary results in enhancement of temperature facing the disk surface as compared to the ambient part. Skin-friction for larger values of Forchheimer number is found to be increasing. Sufficient literature is provided in the introduction part of the manuscript to justify the novelty of the present work. The research greatly impacts in industrial applications of the nanofluids, especially in geophysical and geothermal systems, storage devices, aerospace engineering, and many others.

Significance of nanoparticle's radius, heat flux due to concentration gradient, and mass flux due to temperature gradient: The case of Water conveying copper nanoparticles.

The performance of copper selenide and effectiveness of chemical catalytic reactors are dependent on an inclined magnetic field, the nature of the chemical reaction, introduction of space heat source, changes in both distributions of temperature and concentration of nanofluids. This report presents the significance of increasing radius of nanoparticles, energy flux due to the concentration gradient, and mass flux due to the temperature gradient in the dynamics of the fluid subject to inclined magnetic strength is presented. The non-dimensionalization and parameterization of the dimensional governing equation were obtained by introducing suitable similarity variables. Thereafter, the numerical solutions were obtained through shooting techniques together with 4th order Runge-Kutta Scheme and MATLAB in-built bvp4c package. It was concluded that at all the levels of energy flux due to concentration gradient, reduction in the viscosity of water-based nanofluid due to a higher radius of copper nanoparticles causes an enhancement of the velocity. The emergence of both energy flux and mass flux due to gradients in concentration and temperature affect the distribution of temperature and concentration at the free stream.

Exploration of dual solutions for an enhanced cross liquid flow past a moving wedge under the significant impacts of activation energy and chemical reaction.

The mathematical modeling and numerical simulation are conferred to offer the novel perception of binary chemical reaction with an activation energy aspect on magneto flow comprising Cross liquid inspired by a moving wedge. The influences of Soret and Dufour are also presented. The similarity procedure is utilized to modify the leading PDEs into a non-linear system of ODEs and then analyzed through a significant technique namely bvp4c based on the collocation method. The impacts of varying distinct parameters under the temperature and the velocity distribution are explored and discussed with the support of the graphs. The outcomes indicate that the multiple results are attained for a specific amount of shrinking/stretching constraint. Furthermore, the Weissenberg number reduces the skin factor and speed up the heat and mass transport rate in the lower and upper branch solutions. Also, an assessment of current results with earlier published literature is made in the limiting case.

Second Law Analysis of Dissipative Nanofluid Flow over a Curved Surface in the Presence of Lorentz Force: Utilization of the Chebyshev⁻Gauss⁻Lobatto Spectral Method.

The primary objective of the present work is to study the effects of heat transfer and entropy production in a nanofluid flow over a curved surface. The influences of Lorentz force and magnetic heating caused by the applied uniform magnetic field and energy dissipation by virtue of frictional heating are considered in the problem formulation. The effects of variable thermal conductivity are also encountered in the present model. The dimensional governing equations are reduced to dimensionless form by introducing the similarity transformations. The dimensionless equations are solved numerically by using the Chebyshev⁻Gauss⁻Lobatto spectral method (CGLSM). The rate of increase/increase in the local Nusselt number and skin friction coefficient are estimated by using a linear regression model. The expression for dimensionless entropy production is computed by employing the solutions obtained from dimensionless momentum and energy equations. Various graphs are plotted in order to examine the effects of physical flow parameters on velocity, temperature, and entropy production. The increase in skin friction coefficient with magnetic parameter is high for nanofluid containing copper nanoparticles as compared to silver nanoparticles. The analysis reveals that velocity, temperature, and entropy generation decrease with the rising value of dimensionless radius of curvature. Comparative analysis also reveals that the entropy generation during the flow of nanofluid containing copper nanoparticles is greater than that of containing silver nanoparticles.