[Ahamad, 3(10): October, 2014] ISSN: 2277-9655 Scientific Journal Impact Factor: 3.449 (ISRA), Impact Factor: 2.114 http: // www.ijesrt.com (C)International Journal of Engineering Sciences & Research Technology [112] IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Visualization of Natural Convection in a Vertical Annular Cylinder with a Partially Heat Source and Viscous Dissipation N.Ameer Ahamad, Hasan Ahmed Mohamed Hassan EL Arabawy, Syed Iqbal Ahmed Mathematics Department, Faculty of Science, P.O.BOX. 741, University of Tabuk, Zip.71491, Kingdom of Saudi Arabia Abstracts In this work, we visualize the effect of viscous dissipation parameterሺሻ on the heat transfer by supplying the heat at three different positions to the vertical annular cylinder embedded with porous medium. Finite element method has been used to solve the governing equations. Influence of Aspect Ratioሺ ܣ  ሻ, Radius Ratioሺ  ሻ on Nusselt number ሺ     ሻ is presented. The effect of viscous dissipation parameter ሺሻ, for different values of Rayleigh number is discussed. The fluid flow and heat transfer is presented in terms of streamlines and isotherms. Keywords: Natural Convection, Porous medium, viscous dissipation parameterሺሻ, Aspect Ratioሺ ܣ  ሻ, Radius Ratioሺ  ሻ and Rayleigh number(Ra) Introduction The viscous dissipation effect, which is a local production of thermal energy through the mechanism of viscous stresses, is a ubiquitous phenomenon and it is encountered in both the viscous flow of clear fluids and the fluid flow within porous media. When compared with other thermal influences on fluid motion (i.e., by means of buoyancy forces induced by heated or cooled walls and by localized heat sources or sinks) the effect of the heat released by viscous dissipation covers a wide range of magnitudes from being negligible to being significant. Gebhart [1] discussed this range at length and stated that “a significant viscous dissipation may occur in natural convection in various devices which are subject to large decelerations or which operate at high rotational speeds. In addition, important viscous dissipation effects may also be present in stronger gravitational fields and in processes wherein the scale of the process is very large, e.g., on Larger planets, in Large masses of gas in space, and in Geological processes in fluids internal to various bodies.” In contrast to such situations, many free convective processes are not sufficiently vigorous to result in a significant quantitative effect, although viscous dissipation sometimes serves to alter the qualitative nature of the flow. Although viscous dissipation is generally regarded as a weak effect, a property it shares with relativistic and quantum mechanical effects in everyday life, it too has played a seminal role in history of physics. It was precisely this “weak” physical effect that allowed James Prescott Joule in 1843 to determine the mechanical equivalent of heat using his celebrated paddle-wheel experiments, and thereby to set in place one of the most important milestones towards the formulation of the first principle of thermodynamics. There is an increasing interest in the study of natural convection in fluid saturated porous media as proved by the explosive growth in the literature on the subject and also an increasing interest in the consideration of the viscous dissipation effects on the flow and temperature fields as well as on the heat transfer performance of the involved devices. From an order of magnitude analysis it can be concluded that the viscous dissipation can be neglected in many situations of practical interest both for domains filled with a clear fluid or for domains filled with fluid-saturated porous media. This is, however, a subject that attracts many researchers and in particular special attention is being devoted to the natural convection in enclosures filled with a fluid-saturated porous medium including the viscous dissipation effects. Going on to the literature, one can find many recent works concerning the natural convection in fluid- saturated porous media including viscous dissipation effects. Examples of work considering the Darcy Law to describe the fluid flow are these of Nakayama and Pop [2] Magyari and Keller [3], Rees et al. [4], Saied and Pop [5] and Rees [6]. In the work of Al-Hadhrami et al. [7] it is considered the Brinkman extension of the Darcy Law and a quadratic drag term on the momentum equation is considered in the works of Murthy and Singh [8], Murthy [9], Tashtoush [10] and Magyari et al. [11].