Flow around an isolated generic sharp-edged object with varying height ratio (beta= 0-1) i.e. height from the rear end of the object to the front end (beta = H-2/H-1) has been investigated in cross-flow configuration covering steady and periodic regimes at Reynolds number (Re) from 1 to 150 using air as a working fluid. Flow separation is delayed with a decrease in beta. Wake formed is the highest for beta = 1 (square object) and progressively decreases with the decrease in beta. The vortex shedding effect has been demonstrated on the heat transfer phenomena around the objects. For all the cases of height ratios, as Re increases the flow undergoes supercritical Hopf bifurcation to periodic state as steady-state condition loses its stability. Stuart-Landau theory has been used to determine the value of critical Re or the onset of vortex shedding for all the cases of height ratios. As beta increases from 0 to 0.7, the value of critical Re increases. Influence of surface vorticity and surface pressure on the overall drag coefficient (C-D) has been explored. Effect of beta on the Strouhal number (St) has been investigated and the findings are in agreement with previous results. Finally, correlations relating Lr, C-D, (Nu) over bar and St with Re and beta have been developed. (C) 2018 Elsevier Ltd. All rights reserved.