An infinite horizontally extended sparcely packed chemically inert porous channel flow of a Newtonian liquid is considered. The walls of the channels are assumed to be at different temperatures so that the viscosity of the fluid varies across the channel. A dimensionless variable viscosity coefficient is introduced in the Darcy–Forchheimer- Brinkman model, along with the Darcy number, Forchheimer number and the Brinkman number. A series solution is obtained for the Darcy-Forchheimer-Brinkman equation using the differential transform method (DTM). Using this solution for the fully developed flow velocity and the convective diffusion equation, the influence of the variable viscosity coefficient and the Darcy, Brinkman and Forchheimer numbers on the all-time valid dispersion coefficient is analyzed. An increase the variable viscosity parameter is to increase the dispersion coefficient while an increase in all the other parameters will decrease the dispersion coefficient. The Light hill, Taylor-Aris and Taylor dispersion coefficients are obtained as the limiting cases of the generalized dispersion coefficient.