Viscous Dissipation Effects and Developing Heat Transfer for Fully Developed Power-Law Fluid Flow in the Entrance Region of a Tube

Background/Motivation: Viscous dissipation enhances temperature. Determination of its impact is needed to avoid degradation of products in industrial processes. Methodology: The inlet-filled thermal entrance region model addresses the Graetz–Brinkman problem of viscous dissipation in developing heat transfer in a tube subject to a constant heat flux at the wall, considering Newtonian, pseudoplastic, and dilatant fluids. The inlet-filled region concept is used to solve for developing heat transfer, with the thermal entrance region divided into a thermal boundary layer zone, called the thermal inlet region, ending at the point where the thermal boundary layer fills the whole tube cross section, followed by a thermally filled region where fully developed conditions are asymptotically reached. Key Results: The model is essentially analytical. The results include profiles of the dimensionless thermal boundary layer thickness, Nusselt number, dimensionless bulk, wall and centerline temperatures, and entrance region length for different values of the Brinkman number and power-law index, with validation against the derived fully developed solution and published results. Implications: New results are obtained for the case of nonzero viscous dissipation. Results can be obtained with minor computational tasks needed.