Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder.

*(English)*Zbl 1194.80060Summary: Forced convection heat transfer characteristics of a cylinder (maintained at a constant temperature) immersed in a streaming power-law fluids have been studied numerically in the two-dimensional (2-D), unsteady flow regime. The governing equations, namely, continuity, momentum and thermal energy, have been solved using a finite volume method based solver (FLUENT 6.3) over wide ranges of conditions (power law index, \(0.4 \leqslant n \leqslant 1.8\); Reynolds number, \(40 \leqslant Re \leqslant 140\); Prandtl number, \(1 \leqslant Pr \leqslant 100\)). In particular, extensive numerical results elucidating the influence of Reynolds number, Prandtl number and power-law index on the isotherm patterns, local and average Nusselt numbers and their evolution with time are discussed in detail. Over the ranges of conditions considered herein, the nature of flow is fully periodic in time. The heat transfer characteristics are seen to be influenced in an intricate manner by the value of the Reynolds number \((Re)\), Prandtl number \((Pr)\) and the power-law index \((n)\). Depending upon the value of the power-law index \((n)\), though the flow transits from being steady to unsteady somewhere in the range \(\sim 33 < Re < 50\), the fully periodic behavior is seen only beyond the critical value of the Reynolds number \((Re)\). As expected, the average Nusselt number increases with an increase in the values of Reynolds and/or Prandtl numbers, irrespective of the value of the flow behavior index. A strong influence of the power-law index on both local and time-averaged Nusselt numbers was observed. Broadly, all else being equal, shear-thinning behavior \((n < 1)\) promotes heat transfer whereas shear-thickening behavior \((n > 1)\) impedes it. Furthermore, this effect is much more pronounced in shear-thinning fluids than that in shear-thickening fluids.

##### MSC:

80A20 | Heat and mass transfer, heat flow (MSC2010) |

76R05 | Forced convection |

76A05 | Non-Newtonian fluids |

76M12 | Finite volume methods applied to problems in fluid mechanics |

80M12 | Finite volume methods applied to problems in thermodynamics and heat transfer |

##### Keywords:

power-law fluids; Reynolds number; Prandtl number; Nusselt number; circular cylinder; unsteady forced convection heat transfer
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\textit{V. K. Patnana} et al., Int. J. Heat Mass Transfer 53, No. 19--20, 4152--4167 (2010; Zbl 1194.80060)

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