This chapter first presents and discusses a dynamic mathematical model which is developed to simulate a tubular photobioreactor (PBR) and microalgae growth within at any desired location. The model has options to evaluate the effects of location, time of the year, orientation, shading and night curtains, heating and cooling systems, and indoor and outdoor operating conditions. Then the chapter focuses on the algal growth kinetics of microalgae cultivated with coal-fired flue gas, and presents two algal strains, Chlorella vulgaris and Tetraselmis sp. cultivated in lab-scale PBRs to assess the feasibility of using flue gas as a carbon source. And then, the chapter presents an economic feasibility analysis for manufacturing biodiesel from algae using a PBR. The chapter then introduces a mathematical model to investigate the thermal effects on algae population in growth in both fluid and porous media. The study reveals the potential feedback between hydrodynamic and local demographic processes in microorganism populations in the context of the influence of climate change on natural ecological systems. Finally, the chapter discusses the relationship dynamics between algae and nutrient or herbivore and algae using the predator-prey approach based on classical Lotka-Volterra system.