Due to stringent constraints on resources, it may be infeasible to acquire the current channel state information at the transmitter in energy harvesting communication systems. In this paper, we optimize an energy harvesting transmitter, communicating over a slow fading channel, using layered coding. The transmitter has access to the channel statistics, but does not know the exact channel state. In layered coding, the codewords are first designed for each of the channel states at different rates, and then the codewords are either time-multiplexed or superimposed before the transmission, leading to two transmission strategies. The receiver then decodes the information adaptively based on the realized channel state. The transmitter is equipped with a finite-capacity battery having non-zero internal resistance. In each of the transmission strategies, we first formulate and study an average rate maximization problem with non-causal knowledge of the harvested power variations. Further, assuming statistical knowledge and causal information of the harvested power variations, we propose a sub-optimal algorithm, and compare with the stochastic dynamic programming based solution and a greedy policy.