Open Journal of Fluid Dynamics, 2017, 7, 231-262 http://www.scirp.org/journal/ojfd ISSN Online: 2165-3860 ISSN Print: 2165-3852 Mixed Convection and Heat Transfer Studies in Non-Uniformly Heated Buoyancy Driven Cavity Flow A. D. Abin Rejeesh 1 , Selvarasu Udhayakumar 1 , T. V. S. Sekhar 2 , Rajagopalan Sivakumar 1* 1 Department of Physics, Pondicherry University, Puducherry, India 2 School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India Abstract We analyse the mixed convection flow in a cavity flow which is driven by buoyancy generated due to a non-uniformly heated top wall which is moving uniformly. A fourth order accurate finite difference scheme is used in this study and our code is first validated against available data in the literature. The results are obtained for different sets of Reynolds number Re , Prandtl number Pr and Grashof number Gr which are in the ranges 100 - 3000, 0.0152 - 10 and 10 2 - 10 6 respectively. Here Gr is related to the Richardson number according to 2 Ri Gr Re = . While increasing the Richardson num- ber, the growth of upstream secondary eddy (USE) is observed together with a degradation of downstream secondary eddy (DSE). When mixed convection is dominant, the upstream secondary eddy and the downstream secondary eddy merge to form a large recirculation region. When the effect of Pr is studied in the forced convection regime, 1 Ri  , the temperature in the central re- gion of the cavity remains nearly a constant. However, in the mixed convec- tion regime, the temperature in cavity undergoes non-monotonic changes. Finally, using the method of divided differences, it is shown that numerical accuracy of the derived numerical scheme used in this work is four. Keywords Navier-Stokes Equation, High Order Compact Scheme, Mixed Convection, Divided Difference Principle 1. Introduction In order to fill the gap between the results of numerical simulations and experi- ments, several factors have to be considered and one among them is the accuracy and reliability of numerical scheme employed in the simulations. If we use the How to cite this paper: Rejeesh, A.D.A., Udhayakumar, S., Sekhar, T.V.S. and Siva- kumar, R. (2017) Mixed Convection and Heat Transfer Studies in Non-Uniformly Heated Buoyancy Driven Cavity Flow. Open Journal of Fluid Dynamics, 7, 231-262. https://doi.org/10.4236/ojfd.2017.72016 Received: May 3, 2017 Accepted: June 20, 2017 Published: June 23, 2017 Copyright © 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution-NonCommercial International License (CC BY-NC 4.0). http://creativecommons.org/licenses/by-nc/4.0/ Open Access DOI: 10.4236/ojfd.2017.72016 June 23, 2017