Boundary conditions for constant wall heat flux in the absence of local thermal equilibrium conditions are analyzed in this work. Effects of variable porosity and thermal dispersion are also analyzed. Different forms of constant heat flux boundary conditions found in the literature were investigated in this work. The effects of pertinent parameters such as porosity, Darcy number, Reynolds number, inertia parameter, particle diameter and solid-to-fluid conductivity ratio were analyzed. Quantitative and qualitative interpretations of the results are utilized to investigate the prominent characteristics of the models under consideration. Limiting cases resulting convergence or divergence of the models are also considered. Results are presented in terms of the fluid, solid and total Nusselt numbers.