M. Ijaz Khan

Squeezing flow of second grade liquid subject to non-Fourier heat flux and heat generation/absorption

Two-dimensional squeezing flow of second grade fluid between two parallel plates is addressed. The lower plate is stretched while the upper plate is either moving away or towards the lower one. Temperature-dependent thermal conductivity is considered. Further, heat source/sink is present. Unlike the classical situation, the heat flux by Cattaneo-Christov theory is adopted instead of Fourier’s heat conduction law. Homotopic convergent solutions of velocity and temperature are developed and analyzed. Reduction in the thermal layer thickness is observed for Cattaneo-Christov heat flux model when compared with that of Fourier’s law of heat conduction. It is observed that velocity profile is enhanced by increasing the squeezing parameter. Also, a positive squeezing parameter enhances the thermal field due to a higher squeezing force applied on the fluid.

MHD stagnation point flow accounting variable thickness and slip conditions

This communication addresses the second-order velocity and thermal slip features in magnetohydrodynamic (MHD) stagnation point flow past a stretching sheet with variable thickness. Energy expression in presence of dissipation and thermal radiation are examined. A comparative study with first-order velocity and thermal slip condition is analyzed. Analytical solutions of the resulting systems are obtained by homotopy analysis method. Plots for important variables in the flow quantities are made and discussed. It is observed that velocity of fluid increases for higher estimation of velocity power index while it decreases for wall thickness parameter. Surface drag force and heat transfer rate are decreased for larger wall thickness and Prandtl number. Present computations are consistent with those of existing studies in limiting sense.

Numerical investigation for entropy generation in hydromagnetic flow of fluid with variable properties and slip

This modeling and computations present the study of viscous fluid flow with variable properties by a rotating stretchable disk. Rotating flow is generated through nonlinear rotating stretching surface. Nonlinear thermal radiation and heat generation/absorption are studied. Flow is conducting for a constant applied magnetic field. No polarization is taken. Induced magnetic field is not taken into account. Attention is focused on the entropy generation rate and Bejan number. The entropy generation rate and Bejan number clearly depend on velocity and thermal fields. The von Karman approach is utilized to convert the partial differential expressions into ordinary ones. These expressions are non-dimensionalized, and numerical results are obtained for flow variables. The effects of the magnetic parameter, Prandtl number, radiative parameter, heat generation/absorption parameter, and slip parameter on velocity and temperature fields as well as the entropy generation rate and Bejan number are discussed. Drag forc...

Magneto-hydrodynamical numerical simulation of heat transfer in MHD stagnation point flow of Cross fluid model towards a stretched surface

ABSTRACT Here formulation and computations are presented to introduce the novel concept of activation energy in chemically reacting stagnation point flow towards a stretching sheet. Constitutive expression for Cross liquid is taken into account. Magnetic field is utilised in the transverse direction. Application of suitable variables generates the non-linear differential systems. Numerical solution by Runge–Kutta–Fehlberg approach is presented. Characteristics for the significant variables like Weissenberg number, Hartmann number, Schmidt number, activation energy chemical reaction parameter, velocity ratio parameter and Prandtl number on the physical quantities are addressed through graphs and tables. Our computations reveal that species concentration rises via larger activation energy parameter whereas it decays when Schmidt number is incremented. The Weissenberg number has opposite characteristics for local Nusselt and Sherwood numbers when compared with surface drag force.

Modeling Chemically Reactive Flow of Sutterby Nanofluid by a Rotating Disk in Presence of Heat Generation/Absorption

In this article we investigate the flow of Sutterby liquid due to rotating stretchable disk. Mass and heat transport are analyzed through Brownian diffusion and thermophoresis. Further the effects of magnetic field, chemical reaction and heat source are also accounted. We employ transformation procedure to obtain a system of nonlinear ODEs. This system is numerically solved by Built-in-Shooting method. Impacts of different involved parameter on velocity, temperature and concentration are described. Velocity, concentration and temperature gradients are numerically computed. Obtained results show that velocity is reduced through material parameter. Temperature and concentration are enhanced with thermophoresis parameter.

Thermally radiated squeezed flow of magneto-nanofluid between two parallel disks with chemical reaction

This research is exhibited to visualize the squeezed flow of magneto-nanoliquid between two parallel disks. Transportations of heat and mass are characterized through thermal radiation and chemical reaction. Suitable similarity variables lead to dimensionless problem. The homotopic technique is adopted to find out the solutions. Behavior of sundry variables is declared graphically. Physical quantities of curiosity such as skin friction and Nusselt number at both disks are estimated and elaborated. Our investigation depicts that thermal field is augmented via radiation and Brownian diffusion variables. Besides, comparative table is also designed to validate our present outcomes with previous limiting study.

Corrigendum to “Squeezing flow of second grade liquid subject to non-Fourier heat flux and heat generation/absorption” [Colloid Polym. Sci. 295 (2017) 967–975]

In this recently published paper, we noted few typing errors. In this recently published paper, we noted a few typing errors. These may be read as follows: Q denotes the heat generation/absorption parameter when Q > 0/Q < 0. Here, Th and Tw are the temperatures of the upper and the lower walls. In Eq. (10), it should read no τ0 in the first term and no (T − Th) in the second term on RHS. The values of heat generation/absorption (δ) and modified heat generation/absorption (δ1) parameters in Eq. (14) are δ 1⁄4 Q 1−ct ð Þ ρcpa ;

Entropy Generation and Activation Energy Impact on Radiative Flow of Viscous Fluid in Presence of Binary Chemical Reaction

Abstract The main theme of this paper is to investigate entropy generation analysis for unsteady three-dimensional flow of viscous (Newtonian) fluid between two horizontal parallel plates. Lower plate is porous and stretching while upper plate squeezed downward. Further effects of nonlinear thermal radiation, viscous dissipation, heat source/sink and activation energy are accounted. Entropy generation rate calculated in terms of thermal radiation, fluid diffusion and fluid friction. Transformations procedure used lead to reduction of PDE’s into ordinary ones. Built-in-Shooting technique is used for the computational analysis. Impacts of different flow variables on temperature, velocity, concentration, volumetric entropy generation and Bejan number are discussed and presented through graphs. Temperature and concentration gradient are discussed numerically. It is examined from obtained results that velocity of liquid particle decays through larger estimation of squeezing parameter. It is also examined that temperature distribution enhances for higher estimation of radiative heat flux. Moreover temperature and concentration gradient increase for larger squeezing parameter.