  Development of a new framework for derivation of order-by-order hydrodynamics
from Boltzmann equation is necessary as the widely used Anderson-Witting
formalism leads to violation of fundamental conservation laws when the
relaxation-time depends on particle energy, or in a hydrodynamic frame other
than the Landau frame. We generalize an existing framework for consistent
derivation of relativistic dissipative hydrodynamics from the Boltzmann
equation with a energy-dependent relaxation-time by extending the
Anderson-Witting relaxation-time approximation. We argue that the present
framework is compatible with conservation laws and derive first-order
hydrodynamic equations in landau frame. Further, we show that the transport
coefficients, such as shear and bulk viscosity as well as charge and heat
diffusion currents, have corrections due to the energy dependence of relaxation
time compared to what one obtains from the Anderson-Witting approximation of
the collision term. The ratio of these transport coefficients are studied using
a parametrized relaxation-time, and several interesting scaling features are
reported.
