In this paper, we present an analytical solution to carry out performance analysis of various frequency reuse schemes in an OFDMA based cellular network. We study the performance in downlink in terms of signal to interference (SIR) ratio and total cell data rate. The latter is analyzed while keeping in view three different scheduling schemes: equal data rate, equal bandwidth and opportunist. Analytical models are proposed for integer frequency reuse (IFR), fractional frequency reuse (FFR) and two level power control (TLPC) schemes. These models are based on a fluid model that was originally being proposed for CDMA networks. The modeling key of this approach is to consider the discrete base station entities as a continuum. To validate our approach, Monte Carlo simulations are carried out. Validation study shows that results obtained through our analytical method are in conformity with those obtained through simulations. A comparison between the above-mentioned frequency reuse schemes and scheduling policies is also presented. We also propose an optimal tuning of involved parameters (inner cell radius and power ratios).