Hydromagnetic flow of Dusty Viscoelastic (Walter’s liquid model-B) fluid past a plate with chemical reaction and Soret effect

Khem Chand, Nidhi Thakur

Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

*Corresponding Author Email: khemthakur99@gmail.com, nidhithakurmaths55@gmail.com

ABSTRACT:

An unsteady flow of dusty viscoelastic (Walter’s liquid model-B) fluid past an impulsively started vertical plate through porous medium with heat source/sink in the presence of chemical reaction and thermo diffusion (Soret effect) is investigated. The constitutive equations, which are partial differential equations, are converted into ordinary differential equations and then the expressions for velocity, temperature and concentration profile are obtained. The numerical calculations are performed to point up the influence of pertinent flow parameters on velocity, temperature and concentration profile. Some important characteristics of flow field such as non-dimensional skin friction coefficient, Nusselt number and Sherwood number are also studied.

KEYWORDS: Viscoelastic fluid, Walter’s liquid model-B, Porous medium, Dusty fluid

INTRODUCTION:

The study of unsteady boundary layer flow of viscoelastic fluid is a field of active research as it has wide range of applications in engineering processes especially in chemical engineering and petroleum engineering, bio-physics, hydrology, industrial processes such as in fabrication of adhesive tapes, coating and layering onto rigid substrates. The unsteady free convective flow of a viscoelastic fluid past an infinite vertical porous plate has been studied by Chaudhary and Jain [1], Kumar and Chand [2], Uwanta et al. [3], Ghosh and Shit [4] , Choudhury and Das [5], Sahoo [6], Umamaheswar et al. [7] and Choudhury and Das [8].

Walters [9] examined non-Newtonian effects in some elastic-viscous liquids whose behaviour at small rates of shear is characterized by general linear equations of state and presented an elegant model called the Walters’ liquid model-B. Kumar et al. [10] examined MHD flow of viscoelastic (Walters’ liquid model-B) fluids through porous medium. Swarup et al. [11] analyzed MHD flow of viscoelastic (Walters’ liquid model-B) fluids through porous medium with heat source. The unsteady free convection flow in a Walters’-B fluid with heat transfer analysis has been done by Khan et al. [12]. The influence of dust particles on the flow field is encountered in problems concerned with nuclear reactor cooling, paint spraying, sedimentation, atmospheric fallout, purification of crude oil and paper industry. Initially, Saffman [13] studied dusty fluids and examined the stability of the laminar flow of a dusty gas. Helmy [14] investigated free convection of a dusty conducting fluid. The radiation effects on a steady free convective boundary layer flow of a dusty fluid past a vertical permeable surface have been presented by Ramesh et al. [15]. Sharma and Varshney [16] discussed the effect of dusty viscoelastic (Walters’ liquid model-b) fluid on MHD flow through porous medium. Unsteady hydromagnetic natural convection flow of a dusty fluid past an impulsively moving vertical plate with ramped temperature in the presence of thermal radiation has been by examined by Nandkeolyar et al. [17]. Das et al. [18] analyzed unsteady hydromagnetic flow of a heat absorbing dusty fluid past a permeable vertical plate with ramped temperature.

The objective of the present investigation is to extend the work of Sharma and Varshney [16] to account for the effects of chemical reaction and thermo diffusion (Soret effect) on an unsteady flow of dusty viscoelastic (Walter’s liquid model-B) fluid past an impulsively started vertical plate through porous medium with heat source/sink.

CONCLUSIONS:

From the study the following conclusions are drawn:

· The permeability parameter, dusty fluid parameter, Grashof number, modified Grashof number, mass concentration of dust particles and Soret number tend to accelerate velocities of dusty fluid and dust particles throughout the boundary layer region whereas a reverse effect is observed in case of Prandtl number, heat source parameter, Schmidt number, viscoelastic parameter, Hartmann number and chemical reaction parameter.

· There is reduction in fluid temperature for Prandtl number and heat source parameter.

· In the boundary layer region, species concentration enhanced with Soret number and gets reduced with Schmidt number and chemical reaction parameter.

· The skin friction coefficient for dusty fluid () and dust particles () get reduced with Prandtl number, Hartmann number, Schmidt number, chemical reaction parameter, visco-elastic parameter, heat source parameter and time.

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Received on 20.08.2016 Accepted on 05.09.2016

Int. J. Tech. 2016; 6(2): 107-112.

DOI: 10.5958/2231-3915.2016.00017.1