The scale invariance technique has been employed to discuss theηi-driven turbulent transport under a new fluid model developed by Kimet al . Our analysis reveals that the finite Larmour radius effect plays a decisive role to determine the scaling behaviour of the energy transport under the new fluid model. However, the overall scaling of the transport coefficient remains unchanged as compared to that derived by Connor  under the traditional fluid model. The approximations considered by Connor  are qualified with additional requirements within the new fluid approach. In the dissipative case, which has not been discussed earlier, additional constraints on the power scaling laws of the transport properties are imposed due to the dissipative mechanisms in the basic governing equations.