Temperature prescription and control is important within biological media and in bioheat transport applications such as in hyperthermia cancer treatment in which the unhealthy tissue/organ is subject to an imposed heat flux. Thermal transport investigation and optimization is also important in designing heat management devices and small-scale porous-filled-channels utilized in electronic and biomedical applications. In this work, biological media or the stated heat management devices with a nonuniform geometry are modeled analytically as a combination of convergent, uniform and/or divergent configurations. The biological media is represented as blood saturated porous tissue matrix while incorporating cells and interstices. Two primary models, namely, adiabatic and constant temperature boundary conditions, are employed and the local thermal nonequilibrium and an imposed heat flux are fully accounted for in the presented analytical expressions. Fluid and solid temperature distributions and Nusselt number correlations are derived analytically for variable cross-sectional domain represented by convergent, divergent, and uniform or any combination thereof of these geometries while also incorporating internal heat generation in fluid and/or solid. Our results indicate that the geometrical variations have a substantial impact on the temperature field within the domain and on the surface with an imposed heat flux. It is illustrated that, the temperature distribution within a region of interest can be controlled by a proper design of the multisectional domain as well as proper selection of the porous matrix. These comprehensive analytical solutions are presented for the first time, to the best of the authors' knowledge in literature.