Journal of the Korean Physical Society, Vol. 67, No. 7, October 2015, pp. 1167∼1174 Investigation of the Effects of Different Models of Nanofluids on their Flow and Heat Transfer Characteristics Kalidas Das * Department of Mathematics, A. B. N. Seal College, Coochbeahr, Pin-736101, India Nilangshu Acharya † Department of Mathematics, Government General Degree college, Rajarhat, India Prabir Kumar Kundu ‡ Department of Mathematics, Jadavpur University, Kolkata-700032, W.B., India (Received 27 April 2015, in final form 7 July 2015) This paper is devoted to an investigation of the influences of thermal radiation on an unsteady, mixed, convection boundary layer flow and the heat transfer over a vertical heated permeable stretching sheet embedded in a porous medium. Different models of the nanofluid based on different formulae for the thermal conductivity and the dynamic viscosity and their effects on the fluid flow and the heat transfer characteristics are discussed. Using the similarity transformation, we transform the governing equations into similarity, non-linear, ordinary differential equations which are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. The obtained results are presented graphically, and the physical aspects of the problem are discussed. PACS numbers: 44.20.+b, 44.05.+e, 44.40.+a, 44.30.+v Keywords: Nanofluid, Heat transfer, Stretching sheet, Thermal radiation, Porous medium DOI: 10.3938/jkps.67.1167 I. INTRODUCTION The study of convective heat transfer in nanoflu- ids is gaining much attention. Because the convective heat transfer in various industrial processes must be im- proved, many efforts have been devoted to heat transfer enhancement from the energy efficiency point of view. The use of nanofluids is a potential solution to improve heat transfer. The term “ nanof luid ” refers to a liquid suspension containing tiny particles having diameter less than 50 nm. An innovative technique, which uses a mix- ture of nanoparticles and base fluids such as water, ethy- lene glycol, toluene and engine oil, was first introduced by Choi et al. [1]. The common nanoparticles that have been used are aluminum, copper, iron and titanium or their oxides. Despite almost a negligible concentration of solid nanoparticles, nanofluids register an extraordinar- ily high thermal conductivity, which largely depends on blend, amount (volume percent), size and shape of the nanoparticles and on the viscosity, density and related * E-mail: kd kgec@rediffmail.com † E-mail: nilangshu.math@gmail.com ‡ E-mail: kunduprabir@yahoo.co.in thermo-physical parameters of the base fluid. Since the newly identified nanofluid proposed by Choi et al. [1]; many researchers [2–6] have investigated the character- istics of nanofluids. Sohn and Chen [7] reported that the heat transfer coefficient could be increased consid- erably by adding small solid particles in a liquid. An Al 2 O 3 -water nanofluid’s heat transfer in laminar flow un- der a wall heat flux was considered by Wen and Ding [8] and an increase in heat transfer cofficient with increas- ing Reynolds number and nanoparticles concentration was observed . The reason for heat transfer enhanced in nanofluids is the decrease in the thermal boundary layer’s thickness due to random movement of particles which plays a major role in increasing the heat trans- fer rate between the fluid and the wall. Li and Xuan [9] investigated the transport properties of nanofluids. A re- view of convective heat transfer of nanofluids was given by Wang and Mujumdar [10]. Nazar et al. [11] dis- cussed the stagnation-point flow past a shrinking sheet in a nanofluid. Recently, the unsteady boundary layer flow of a nanofluid over a stretching/shrinking sheet was examined by Bachok et al. [12]. Considerable research efforts have been made on un- derstanding convective flow in a porous medium in view of its numerous and wide-ranging applications in various -1167-