Abstract—The present paper considers the steady free convection boundary layer flow of a viscoelastics fluid with constant temperature in the presence of heat generation. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing boundary layer equations are first transformed into non-dimensional form by using special dimensionless group. Computations are performed numerically by using Keller-box method by augmenting an extra boundary condition at infinity and the results are displayed graphically to illustrate the influence of viscoelastic K, heat generation γ , and Prandtl Number, Pr parameters on the velocity and temperature profiles. The results of the surface shear stress in terms of the local skin friction and the surface rate of heat transfer in terms of the local Nusselt number for a selection of the heat generation parameter γ (=0.0, 0.2, 0.5, 0.8, 1.0) are obtained and presented in both tabular and graphical formats. Without effect of the internal heat generation inside the fluid domain for which we take γ = 0.0, the present numerical results show an excellent agreement with previous publication. Keywords—Free Convection, Boundary Layer, Circular Cylinder, Viscoelastic Fluid, Heat Generation I. INTRODUCTION ATURAL convection has been the subject of research for many years due to its importance in the understanding of phenomena appearing in nature and their extensive engineering applications. Studies on the natural convection boundary layer flow past a horizontal cylinder have been conducted by several researchers. For example, Saville and Churchill [1] investigated the laminar natural convection boundary layer flow near horizontal cylinders and vertical axisymmetric bodies. Merkin [2] studied the natural convection boundary layer flow over a cylinder of elliptic cross section. Besides that, a study related to this topic was also carried out by Lien et al. [3] by examining the free convection heat transfer of micropolar fluid near a horizontal permeable cylinder at a non-uniform thermal condition while Bhattacharyya and Pop [4] studied the free convection heat transfer from an elliptical cylinder in micropolar fluids. Mansour et al. [5] studied the coupled heat and mass transfer in the magnetohydrodynamic flow of micropolar fluid on circular cylinders with uniform heat and mass flux, while Abdul Rahman Mohd Kasim, Mohd Ariff Admon, and Sharidan Shafie are with the Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, MALAYSIA (e-mail: abdulrahmanmohdkasim@yahoo.com, ariffadmon@yahoo.com, ridafie@yahoo.com). Cheng [6] studied the natural convection heat and mass transfer from a horizontal cylinder of elliptic cross section in micropolar fluid. In addition, Hossain et al. [7] examined the effect of thermal radiation on natural convection over cylinders of elliptic cross section. In recent years, the natural convection in viscoelastic fluids was investigated due to the applications these materials have in industry and geophysics. In the linear stability problem of viscoelastic fluids, only overstable convection was investigated as their stationary motion is identical to that of Newtonian fluids. Jitchote and Robertson [8] used a perturbation method to analyze the viscoelastic second order fluid flow in curved pipes of circular cross section for the case where the second normal stress difference is non-zero, as a model of polymeric liquid. Ariel and Teipel [9] investigated the laminar two-dimensional viscoelastic flow near a stagnation point using the orthogonal collocation point method with Laguerre polynomials. Meanwhile, the natural convection of a viscoelastic fluid with deformable free surface was studied by L.A. DaÂvalos-Orozco and E. V. Luis [10]. It was found that for different values of the Galileo number and relaxation times that are large enough, the curves of the critical Rayleigh numbers are lower than those of stationary convection and those of overstability of the Newtonian fluid with deformable free surface. When the lower surface is rigid, maxima in the curves of criticality against the relaxation time are found. Rasmussen and Hassager [11] used the Lagrangian Integral Method to model the classical problem of unsteady viscoelastic flow from a sphere in a cylinder. Conversely, Wood [12] investigated the unsteady start-up helical flows for Oldroyd-B and upper-convected Maxwell fluids in straight pipes of circular and annular cross-section.In chemical engineering systems, viscoelastic flows arise in numerous processes in chemical engineering systems. Such flows possess both viscous and elastic properties and can exhibit normal stresses and relaxation effects. Recently, the numerical study of transient free convective mass transfer in a Walters-B viscoelastic flow with wall suction was investigated by T. B Chang et al. [13]. Velocity was found to increase with a rise in viscoelasticity parameter with both time and distances close to the plate surface. An increase in Schmidt number and a separation from the plate was also observed to significantly decrease both velocity and concentration in time. Increasing species of Grashof number boosted the flow velocity at all times and caused a significant rise primarily near the plate surface.A large number of physical phenomena also involve Free Convection Boundary Layer Flow of a Viscoelastic Fluid in the Presence of Heat Generation Abdul Rahman Mohd Kasim, Mohd Ariff Admon, and Sharidan Shafie N World Academy of Science, Engineering and Technology 75 2011 492