絕熱橢圓管之準確一維近似熱傳解和臨界特性分析

Accurate one-dimensional approximate solutions and critical heat transfer characteristics analysis of an insulated oval duct

黃景德(Ching-Te Hwang)

指導教授 ： 陳文立 ； 黄景良

崑山科技大學/工程學院/機械工程研究所/碩士(2006年)

摘要

傳統使用橢圓近似周長公式分析所得絕熱橢圓管之熱傳特性結果不夠正確，且隨著橢圓長短軸比值越大時其誤差越大。本文以積分法求出準確之橢圓周長來獲得之二維數值結果與一維PWTR模型和CPWTR模型解作比較。本文發現，絕熱橢圓管的熱傳特性，在以實際管尺寸在真實應用狀態下，當橢圓管長短軸比≦3.5:1時，可應用一維PWTR模型分析，或當橢圓管長短軸比≧3.5:1時，可採用一維9-1 CPWTR模型分析，兩者均能獲得可靠的一維近似解；若在實用絕熱厚度(t/R2＜0.5)的情況下，其熱傳率誤差率則大多在0.5%以內; 即使在包覆相當大絕熱厚度(t/R2=2.0)的情況，其熱傳率誤差率大多在2%以內。此外，本文對於小尺寸絕橢圓管的臨界厚度和中性厚度的熱傳特性，亦進行了深入探討。 本文發現小尺寸絕熱橢圓管之臨界特性，隨著長短軸比值增大而逐漸不同於等效的絕熱圓管，而且隨著無因次尺寸和/或長短軸比的改變而有不同臨界結果。

關鍵字

橢圓管 ； PWTR 模型 ； 9-1CPWTR 模型 ； 臨界厚度 ； 中性厚度 ； 絕熱

並列摘要

Conventional unreliable heat transfer results of an insulated oval duct are generated by an inaccurate approximation of an oval perimeter equation. The greater the long-short-axes ratio, the bigger the error becomes. On the other hand, the present results are based on very accurate oval perimeters obtained by an integral method. The one-dimensional results of PWTR and 91-CPWTR models are compared with those of numerical results. It is found that in practical situations, that is, long-short-axes ratio is less or equal to 3.5, satisfactory and reliable solutions can be obtained by the one-dimensional PWTR model. However, when the long-short-axes ratio is greater than 3.5, accurate and reliable solutions can only be achieved by the one-dimensional 9-1CPWTR model, which returns most errors within ±0.5 % for situations of practical duct sizes and insulated thickness (t/R2＜0.5). Even in situations of a extraordinary large insulated thickness (t/R2=2.0), most errors are within ±2 %. Apart from this, the heat transfer characteristics of critical and neutral thickness of a very small insulated oval duct are also investigated in this study. It is found that the critical heat transfer characteristics of a very small insulated oval duct are different from those of an equivalent insulated circular duct. The bigger the long-short-axes ratio is, the greater difference becomes. In here, results are presented along with the change of dimensionless duct size or/and long-short-axes ratio.

並列關鍵字

insulation ； critical thickness ； oval duct ； neutral thickness ； 9-1CPWTR model ； PWTR model

參考文獻

[1]W.L. Chen, L.C. Fang, A numerical study on the flow over a staggered oval pipe for heat-transfer enhancement, J.CSME, Vol.25, 2004, pp.209-216.

[2]W.L. Chen, K.L. Wong and C.T. Huang, A parameter study on the laminar flow in an alternating horizontal or vertical oval cross-section pipe with computational fluid dynamics, International Journal of Heat and Mass Transfer, Vol. 49, 2006, SCI, pp.287-296.

[3]Y. Chen, M. Fiebig, N.K. Mitra, Conjugate heat transfer of a finned oval tube with a punched longitudinal vortex generator in form of a delta winglet-parametric investigations of the winglet, International Journal of Heat and Mass Transfer, Vol.41, 1998, pp.3961-3978.

[4]Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of a finned oval tube with punched longitudinal vortex generators in-line, International Journal of Heat and Mass Transfer, Vol.41, 1998, pp.4151-4166.

[5]Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of finned oval tubes with staggered punched longitudinal vortex generators, International Journal of Heat and Mass Transfer, Vol.43, 2000, pp.417-435.