Heat transfer and magneto-hydrodynamic nanofluids flow behaviors past a nonlinear stretching surface considering viscous dissipation and joule heating

33-46Mathematical investigation has been presented to examine the magnetohydrodynamic boundary layer flow of viscous nanofluids bygone a nonlinear stretched plate among cumulative impact of viscous dissipation and joule heating. Physical formulation produced a system of partial differential equations which has been converted into a set of ordinary differential equations through employing suitable similarity variables. For numerical solutions of resulting governing equations of flow, a Keller-box method has been addressed. Results of dimensionless velocity and dimensionless temperature for impacts of various types of nanoparticle along with water base fluid and effects of physical parameters, namely solid volume fraction, nonlinear stretching parameter, magnetic parameter and Brinkmann number have been deliberated via graphs. Additionally, surface shear stress and surface heat flux for selected suitable values of pertinent parameters have been computed and explicated via table

Numerical investigation of unsteady MHD flow and radiation heat transfer past a stretching surface in porous media with viscous dissipation and heat generation/absorption

71-78Viscous dissipation and radiation effects on unsteady flow of laminar incompressible viscous electrically conducting fluid through stretching surface in a porous media with magnetic field and heat generation/absorption have been investigated. Taking suitable similarity variables, the governing boundary layer equations are converted into a set of ordinary differential equations and solved numerically by Runge-Kutta fourth order method along with shooting technique. The effects of the various physical dimensionless parameters such as unsteadiness parameter, permeability parameter, magnetic parameter, radiation parameter, Prandtl number, heat generation/absorption parameters and Eckert number for velocity and temperature distributions have been analyzed in detail through graphical representations. Further skin friction coefficient and Nusselt number at the surface are numerated and compared with previous researchers

Numerical investigation of unsteady MHD flow and radiation heat transfer past a stretching surface in porous media with viscous dissipation and heat generation/absorption

Viscous dissipation and radiation effects on unsteady flow of laminar incompressible viscous electrically conducting fluid through stretching surface in a porous media with magnetic field and heat generation/absorption have been investigated. Taking suitable similarity variables, the governing boundary layer equations are converted into a set of ordinary differential equations and solved numerically by Runge-Kutta fourth order method along with shooting technique. The effects of the various physical dimensionless parameters such as unsteadiness parameter, permeability parameter, magnetic parameter, radiation parameter, Prandtl number, heat generation/absorption parameters and Eckert number for velocity and temperature distributions have been analyzed in detail through graphical representations. Further skin friction coefficient and Nusselt number at the surface are numerated and compared with previous researchers

Navier's slip condition and magnetic field effects on unsteady stagnation point flow subject to a stretched plate along to viscous dissipation and Joule heating utilizing nanofluids

This article mainly addresses Navier's slip boundary condition impact on two-dimensional, unsteady magneto hydrodynamic flow of electrically conducting viscous nanofluids adjacent to stagnation region due to a stretchable wall along to viscous dissipation and Joule heating. Nanofluids are taken namely silver-water, copper-water, titanium dioxide-water and alumina-water. Transformation procedure applied reduces the set of nonlinear partial differential equations into a system of nonlinear ordinary differential equations. Resulting governing boundary layer equations are numerically solved by establishing a Keller-box method. Effects of different nanofluids, stretching parameter, slip parameter; solid volume fraction, unsteadiness parameter, magnetic parameter and Eckert number on velocity and temperature distributions are illustrated via graphs and explained in details. Computational values of local skin friction and local Nusselt number for influences of specified parameters are found out and indicated in tabular mode. Moreover, dual solutions exist by cause of negative values of unsteadiness parameter in fluid flow, fluid temperature, wall shear stress and wall heat flux

Navier's slip condition and magnetic field effects on unsteady stagnation point flow subject to a stretched plate along to viscous dissipation and Joule heating utilizing nanofluids

861-876This article mainly addresses Navier's slip boundary condition impact on two-dimensional, unsteady magneto hydrodynamic flow of electrically conducting viscous nanofluids adjacent to stagnation region due to a stretchable wall along to viscous dissipation and Joule heating. Nanofluids are taken namely silver-water, copper-water, titanium dioxide-water and alumina-water. Transformation procedure applied reduces the set of nonlinear partial differential equations into a system of nonlinear ordinary differential equations. Resulting governing boundary layer equations are numerically solved by establishing a Keller-box method. Effects of different nanofluids, stretching parameter, slip parameter; solid volume fraction, unsteadiness parameter, magnetic parameter and Eckert number on velocity and temperature distributions are illustrated via graphs and explained in details. Computational values of local skin friction and local Nusselt number for influences of specified parameters are found out and indicated in tabular mode. Moreover, dual solutions exist by cause of negative values of unsteadiness parameter in fluid flow, fluid temperature, wall shear stress and wall heat flux

Viscous dissipation and Joule heating effects on an unsteady magnetohydrodynamic flow over a linearly stretching permeable surface with uniform wall temperature

An analysis has been presented to describe the effects of viscous dissipation and Joule heating on an unsteady laminar two-dimensional flow of a viscous incompressible electrically conducting fluid over a stretching permeable surface in the presence of a uniform transverse magnetic field. Similarity solutions for the problem have been formulated and reduced nonlinear ordinary differential equations have been solved numerically using fourth order Runge-Kutta method with shooting technique. Influences of various parameters, namely, mass transfer parameter, unsteadiness parameter, magnetic parameter, Prandtl numberand Eckert number on velocity and temperature distributions have been plotted graphically while skin-friction coefficient and Nusselt number have been shown numerically. A comparison of the obtained numerical results has been made with previously published results for non-magnetic case

General weighted extropy of minimum and maximum ranked set sampling with unequal samples

In industrial, environmental, and ecological investigations, ranked set sampling is a sample method that enables the experimenter to use the whole range of population values. The ranked set sampling process can be modified in two extremely helpful ways: maximum ranked set sampling with unequal samples and minimum ranked set sampling with unequal samples. They permit an increase in set size without too many ranking errors being introduced. In this paper, we are defining general weighted extropy (GWJ) of minimum and maximum ranked set samples when samples are of unequal size (minRSSU and maxRSSU, respectively). Stochastic comparison and monotone properties have been studied under different situations. Additionally, we compare the extropy of these two sampling data with that of ranked set sampling data and simple random sampling data. Finally, Bounds of GWJ of minRSSU and maxRSSU have been obtained.Comment: 16 page

Unsteady flow of CNT-water nanofluid past a stretching sheet with slip effect

396-403In this analysis, an unsteady flow over a stretching plate with slip effect in CNT-water nanofluid has been examined. A set of ordinary differential equations have been obtained by applying the convenient similarity variables. Perturbation technique has been used to find numerical solutions of the study by applying Runge-Kutta fourth order scheme. Plots of velocity and temperature distributions for physical parameters such as velocity slip parameter, solid volume fraction, unsteadiness parameter and thermal slip parameter have been given via graphs, whereas numerical values of local skin friction coefficient and local Nusselt number have been presented in tabular form. Comparison with earlier published results specified that Runge-Kutta method of order four is applicable to solve this problem

Analysis of Cu - water nanofluid flow with different particle shapes over an isothermal moving plate

Contribution of Cu (copper) nanoparticle shapes in base fluid – water on nanofluid flow over a moving plate has been scrutinized. Five classic models of nanoparticle shapes (sphere, cube, triangular pyramid, cylinder, lamina) have been taken into account. Employing similarity transformation, basic boundary layer controlling equations have been reduced to a set of nonlinear ordinary differential equations. Solutions have been attained numerically for them by executing the MATLAB’s boundary layer problem solver (bvp4c). Outcomes have, then, been applied to compare the influence of pertinent parameters on velocity and temperature graphically, while, the impact on shear stress and heat flux have been compared in tables. Moving parameter, sphericity and shape of Cu nanoparticles have been the significant controlling parameters

Unsteady flow of CNT-water nanofluid past a stretching sheet with slip effect

In this analysis, an unsteady flow over a stretching plate with slip effect in CNT-water nanofluid is examined. A set of ordinary differential equations is obtained by applying the convenient similarity variables. Perturbation technique is used to find numerical solutions of the study by applying Runge-Kutta fourth order scheme. Plots of velocity and temperature distributions for physical parameters such as velocity slip parameter, solid volume fraction, unsteadiness parameter and thermal slip parameter are given via graphs, whereas numerical values of local skin friction coefficient and local Nusselt number are presented in tabular form. Comparison with earlier published results specified that Runge-Kutta method of order four is applicable to solve this problem