The present article investigates laminar mixed convection with upward and downward flow over a vertical flat plate in supercritical fluid, numerically. At first four different equations for thermal expansion coefficient estimation in supercritical fluids are derived as a function of pressure, temperature and the compressibility factor. Calculated values of thermal expansion coefficient and Nusselt number have been compared with the experimental results and show better accuracy of Redlich-Kwong EOS in comparison with others. After that governing equations for mixed convection are solved numerically by using finite difference method. A parametric study is performed to illustrate the interactive influence of the governing parameters, specifically the Richardson number and the effect of its variation on the rate of heat transfer and Nusselt number in supercritical condition. Finally, heat transfer curves as a function of Richardson number are plotted and observed that general trend of supercritical fluids curves are similar for water and carbon dioxide. The achieved results can also be validated with shown velocity and temperature counters and vectors. (C) 2015 Elsevier B.V. All rights reserved.