Natural convection to horizontal wires — The conduction limit

Laminar Natural Convection from a Horizontal Cylinder in Power-Law Fluids

“…By using dimensional considerations, Ng and Hartnett showed these data to be consistent with the scaling suggested by the boundary layer analysis of Acrivos . Subsequently, they argued that owing to extremely high values of viscosity of their polymer solutions (∼0.001 ≤ Ra ≤ ∼100) there was virtually no fluid motion at all in the fluid adjacent to the immersed heated cylinder, and indeed, their experimental values of the average Nusselt number were close to those based on the assumption of heat transfer by pure conduction only . Their subsequent experimental studies , elucidated the role of curvature effects (by using very thin wires such that the boundary layer thickness would be comparable to the radius of the wire) and the viscoelasticity of fluids.…”

“…Note that the three definitions of the Rayleigh number, namely, Ra, Ra D , and Ra N , used here and in the literature only differ through a function of power-law index, n. Ng and Hartnett 42,44 further argued that eq 17 correctly predicts the limiting case of Nu µ Ra (1/4) for Newtonian fluids. Since the present results are in fair agreement with the boundary layer analysis of Acrivos 32 at high values of Grashof and/or Prandtl numbers, it suggests these to be consistent with eq 17 also.…”

“…Finally, Ng and Hartnett , rearranged the results of Acrivos in the following form N u = C R a normalN 1 / 3 n + 1 where the modified Rayleigh number, Ra N , is defined as follows R a normalN = false( normalρ g normalβ normalΔ T false) D 2 n + 1 m normalα n Note that the three definitions of the Rayleigh number, namely, Ra , Ra D , and Ra N , used here and in the literature only differ through a function of power-law index, n . Ng and Hartnett , further argued that eq correctly predicts the limiting case of Nu ∝ Ra (1/4) for Newtonian fluids. Since the present results are in fair agreement with the boundary layer analysis of Acrivos at high values of Grashof and/or Prandtl numbers, it suggests these to be consistent with eq also.…”

“…However, suffice to say here that their results are within (10% of the predictions of eq 16 which is regarded to be satisfactory. Finally, Ng and Hartnett 42,44 rearranged the results of Acrivos 32 in the following form…”

“…32 Subsequently, they argued that owing to extremely high values of viscosity of their polymer solutions (∼0.001 e Ra e ∼100) there was virtually no fluid motion at all in the fluid adjacent to the immersed heated cylinder, and indeed, their experimental values of the average Nusselt number were close to those based on the assumption of heat transfer by pure conduction only. 42 Their subsequent experimental studies 43,44 elucidated the role of curvature effects (by using very thin wires such that the boundary layer thickness would be comparable to the radius of the wire) and the viscoelasticity of fluids. The resulting values of the Rayleigh number were too small (<1) for the boundary layer approach to be applicable to these results, and therefore, Ng et al 43 correlated their data empirically.…”