INCOM18: Proceedings of the 1 st International Conference on Mechanical Engineering Jadavpur University Kolkata India January 4 – 6, 2018 Paper No.96, INCOM18 1 Numerical Analysis of Laminar Natural Convection in a Quadrantal Cavity with Non-uniform heating of Bottom Wall Shantanu Dutta 1 ,Arup Kumar Biswas 3 ,Sukumar Pati 2 1 Department of Mechanical Engineering, National Institute of TechnologyDurgapur, Durgapur- 713212, India, E mail: shantanudut@gmail.com 2 Department of Mechanical Engineering, National Institute of TechnologyDurgapur, Durgapur- 713212, India, E mail: arup.biswas10@gmail.com 3 Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar-788010, India Email: sukumarpati@gmail.com ABSTRACT In this paper, we analyze the fluid flow and heat transfer characteristics inside a two dimensional quadrantal cavity filled with air. The cavity is heated non-uniformly from the bottom wall and the vertical wall is cooled to a constant temperature while the curved wall is thermally insulated. Finite element method is used to solve the transport equations. The results are illustrated in the form of streamlines, isotherms, local Nusselt number and average Nusselt number. It reveals that the local Nusselt number at the bottom wall follows a sinusoidal variation and moreover at some location, the Nusselt number is negative because of the imposed temperature distribution on the wall. It further reveals that the mechanism of heat transfer is conduction at lower values of Rayleigh number, while heat transfer is due to convection at higher values of Rayleigh number. Keywords: Natural convection; Quadrantal cavity; Non-uniform heating; Nusselt Number NOMENCLATURE c p Specific heat (Jkg -1 K -1 ) g Acceleration due to gravity (ms -2 ) H Enclosure height (m) h Heat transfer coefficient (Wm 2 K -1 ) k Thermal conductivity (W m -1 ,K -1 ) L Enclosure length (m)  Nu Average Nusselt Number Nu Nusselt number (dimensionless) P Non-dimensional pressure p Pressure (Nm 2 ) Pr Prandtl number (dimensionless) Ra Rayleigh number (dimensionless) T Temperature (K) U ,V Non-dimensional velocity component in the X and Y direction u, v Velocity component in the x and y direction (ms -1 ) X, Y Non-dimensional coordinates x, y Cartesian coordinate system Greek symbols α Thermal diffusivity (m 2 s -1 ) β Co-efficient of thermal expansion (K -1 ) θ Dimensionless temperature  Kinematic viscosity (m 2 s -1 ) ρ Density(kgm -3 ) ψ Stream function (m 2 s) Ψ Non-dimensional stream function (=ψ /α) Subscripts c Cold wall h Hot, bottom wall max Maximum min Minimum 1.INTRODUCTION Natural convection in an enclosure is a hot topic of research for last few decades because of its importance in various engineering applications. A host of articles both numerical and experimental are available in the literature pertaining to heat transfer and entropy generation characteristics in regular geometries, such as rectangular, square and triangular enclosures. A benchmark solution for free convection of air (Pr = 0.71) in a square cavity with vertical boundaries kept at different temperatures is presented by Davis and De[1] for a range of Rayleigh number (10 3 < Ra < 10 6 ). Hamadi et al.[2] performed an experimental and numerical analysis of free convection of air in a square inclined cavity. It is important to mention here that the geometry of the