Asian Journal of Engineering and Applied Technology ISSN 2249-068X Vol.8 No.3, 2019, pp. 14-20 © The Research Publication, www.trp.org.in Perturbation Analysis of Rivlin-Ericksen Fluid on Heat Transfer in the Presence of Heat Absorption Y. Sudarshan Reddy 1 , K. S. Balamurugan 2 and G. Dharmaiah 3* 1 Department of Mathematics, Sri Rajeswari College of Education, Chinnachowk, Kadapa, Andhra Pradesh, India 2 Department of Mathematics, RVR & JC College of Engineering, Chowdavaram, Guntur, Andhra Pradesh, India 3 Department of Mathematics, Narasaraopeta Engineering College, Yellamanda, Narasaraopet, Andhra Pradesh, India *Corresponding Author E- Mail: dharma.g2007@gmail.com Abstract - The problem of visco-elastic Rivlin-Ericksen fluid flow past a semi- infinite vertical plate embedded in a porous medium with variable temperature and suction in the presence of a uniform transverse magnetic field and thermal buoyancy effect is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non- harmonic functions. Numerical evaluation of the analytical results is performed and some graphical results such as visco- elastic parameter Rm, heat absorption parameter Q, Grashof number Gr, Prandtl number Pr, time t, suction velocity parameter A, moving velocity parameter Up and an exponential parameter ε, for the velocity and temperature profiles within the boundary layer are presented. Skin-friction coefficient, Nusselt numbers are also discussed with the help of the tables. Keywords: Variable Temperature, Vertical Plate, Suction, Heat Absorption, Rivlin-Ericksen Flow I. INTRODUCTION A few modern applications include the progression of non- Newtonian liquids, and in this manner the stream conduct of such liquids finds an incredible pertinence. Moltenmetal's, plastic, pulps, emulsions; slurries and crude materials in liquid state are a few guides to make reference to. Non- Newtonian stream likewise finds functional applications in bio-designing, wherein blood flows brutal/creature vein is clarified by a fitting Visco-versatile liquid model of little flexibility. The investigation of a visco-versatile pulsatile stream helps in understanding the component of dialysis of blood through a counterfeit kidney. A significant class of two dimensional time ward stream issue managing the reaction of limit layer to outside precarious changes of the free stream speed about a mean worth pulled in the consideration of numerous specialists. Other than that convective course through permeable medium has an application in geothermal vitality recuperation, warm vitality stockpiling, oil extraction, and move through separating gadgets. Presently, magnetohydrodynamics is particularly pulling in the consideration of the numerous creators because of its applications in geophysics and building. MHD stream with warmth and mass exchange has been a subject of enthusiasm of numerous specialists in light of its different applications in science and innovation. Such wonders are seen in lightness initiated movements in the climate, in water bodies, semi strong bodies, for example, earth, and so on. The progression of viscous incompressible fluid past an indiscreetly started infinite horizontal plate in its own plane was first examined by Stokes [1]. Convective heat transfer Non-Newtonian MHD flow permeable plate inspected by the authors [2-5]. Magnificent assessments have the made on visco-elastic impact by the author [6]. An examination of viscous dissipation impacts on free convection heat and mass transfer of MHD non-Newtonian fluid flow through a permeable medium given by Nabil et al.,[7].Unsteady flow of a non-Newtonian fluid over a rotating disk with heat transfer examined by Attia [8]. MHD Rivlin-Ericksen flow through porous medium in slip stream system examined by Ramana Murthy et al., [9]. Unsteady MHD free convective heat and mass transfer flow vertical permeable plate discussed by Rao et al., [10]. Unsteady MHD free convection flow of a Kuvshinski fluid past a vertical permeable plate assumed by Reddy et al., [11]. Unsteady MHD free convection boundary layer flow of radiation on Kuvshinski fluid through porous medium was reported by Vidyasagar et al., [12]. Propelled by these examinations referenced over, the motivation behind the present work is extended the investigation of Kim [13], by considering a notable non-Newtonian fluid namely Rivlin– Ericksen fluid for the instance of a semi-infinite moving porous plate in a permeable medium. We likewise consider the free stream to comprise of a mean velocity and temperature over which are superimposed an exponentially shifting with time. The obtained outcomes here are in great concurrence with the results of Kim without non-Newtonian fluid. The problem of visco-elastic Rivlin-Ericksen fluid past a semi- infinite vertical plate embedded in a permeable medium with variable temperature and suction in the presence of a uniform transverse magnetic field and thermal buoyancy effect is assumed. The plate is considered to move with a steady velocity in the direction of fluid flow while the free stream velocity is expected to follow the exponentially expanding small perturbation law. Time- dependent wall suction is accepted to happen at the 14 AJEAT Vol.8 No.3 July-December 2019