Understanding mixing in micro-capillary channels is an important aspect for a variety of technological micro-reactor devices applied to biological processes, biomedical diagnostics, drug delivery and decontamination in soils just o name a few examples. In many of these applications, the presence of an electrical field leads to heat generation that may cause micromixing within the device; this phenomenon may affect drastically the efficiency of the process and apriori conditions to avoid such dispersive mixing will be helpful. The authors have used the spatial averaging method in combination with the solute species continuity equation in a micro-channel of rectangular geometry to determine the effect of buoyancy driven type flows on effective parameters, i.e., effective dispersion coefficient and effective convective velocity. This contribution presents explicit analytical expressions derived for the effective parameters as a function of the ambient temperature, non-symmetrical wall-based conditions, ambient temperature, heat-generation parameters, and net mass flow. These mathematical expressions may be useful on the study of process performances and identify operating conditions. Several illustrations are presented to demonstrate the micromixing within the channel with a variety of conditions.