Large eddy simulation was conducted for flow development in a chamber with wall injection which simulates the cold flow in an idealized hybrid rocket motor. It was found that a peculiar timescale, roughly corresponding to St~0.5, resides in the flowfield resulting from the interaction between the main oxidizer and wall injected flows. However, the fact that this time characteristics is absent in the temperature field in the vicinity of the wall indicates that even a small regression rate renders the passive scalar, such as temperature, dissimilar to the velocity field. This implies that a classical approach, which assumes that constant turbulent Prandtl number, should be replaced by a more sophisticated turbulence models to accurately predict the temperature field in the hybrid motor.