Laminar heat transfer in a round tube with variable circumferential or arbitrary wall heat flux

Analysis of heat transfer for laminar power law pseudoplastic fluids in a tube with an arbitrary circumferential wall heat flux

“…The problem of Newtonian fluids with an arbitrary circumferential wall heat flux is another limiting case of the present work. The related constants for this problem are the same as those obtained by Battacharya and Roy (1970). Finally, a simple result has been obtained for a cosine heat flux around the tube periphery which illustrates all of the limiting cases and shows the simultaneous influences of circumferential wall heat flux variation and non-Newtonian fluid behavior on heat transfer.…”

“…With x+ finite and s = 2 (Newtonian fluids), the Niisselt number expression reduces to the form given by Battacharya and Roy (1970).…”

Flow and convective cooling in lava tubes

“…If additional information is available for a particular tube on burial depth variations or other factors that might introduce a significant axial variation in the temperature or heat flux boundary condition, there are a few analytic solutions available that factor in axial variations in wall heat flux or temperature [Shah and London, 1978]. For example, for a linear variation in wall temperature for the circular tube, see Sellars et al [1956], or for wall heat flux variations, see Bhattacharyya and Roy [1970]. Predictably, wall temperatures are higher where heat flux rates are higher.…”

Laminar flow with an axially varying heat transfer coefficient

“…Boundary conditions of the first or second kind that vary with position either axially and/or radially have received considerable attention in the literature. When thermal energy sources, axial conduction and viscous dissipation are neglected, the resulting homogeneous energy equation can be solved by superposition [26,[32][33][34][35].…”