Çizgisel ısı kaynaklı yüzeyde doğal ısı taşınımı
Natural convection for a line source on an adiabatic surface
- Tez No: 21987
- Danışmanlar: DOÇ. DR. FERİDUN ÖZGÜÇ
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Doğal taşınım, Isı geçişi, Süperpozisyon yöntemi, Natural convection, Heat transfer, Superposition method
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu çalışma termal sınır koşullarının kademeli süreksizliklerde dahil olmak üzere keyfi olarak belirtildiği benzer olmayan doğal ve karışık taşınımlı ısı transferi problemlerinde yeni, basit ve güçlü bir yöntem sunmaktadır. Termal olarak uniform olmayan yüzeyler üzerindeki doğal tasınım için sıcaklık ve hız dağılımı, aynı ısı akılı veya isotermal yüzeyler için benzerlik analizinden elde edilen yüzey ısı akısı ve hızların süper pozisyonu ile tanımlanan eşdeğer Grashof sayısı ile formüle edilmektedir. Mevcut benzerlik çözümlerinin kıyaslanması; deneysel sonuçlar, ve nümerik çözümler, elektronik ve imalat araç ve gereçlerinin soğutma konfigürasyonları gibi bir çok pratik durumlardada bu basit süper pozisyon yönteminin kullanımı geçerlidir. Ayrıca bu çalışmada sabit ısı akılı adyabatik düşey bir yüzey üzerinde doğal tasınım halindeki Nusselt dağılımı ile yine adyabatik düşey bir yüzey üzerinde çizgisel ısı kaynakları olması durumundaki Nusselt dağılımı araştırılmış ve bunların karşılaştırılması yapılmıştır. Çizgisel ısı kaynakları arasındaki mesafeler azaldıkça elde edilen Nusselt dağılımlarının, sabit ısı akılı durum için elde edilen Nusselt dağılımına yaklaştığı gösterilmiştir.
Özet (Çeviri)
SUMMARY NATURAL CONVECTION FOR“A LINE SOURCE ON AN ADIABATIC SURFACE Convective cooling technology is fundemental to the performance and relaibility of electronic circuitry. A simple methodology for the estimation of heat transfer in electronic systems is strongly required for practical thermal design. Any attempt to develop such a simple analytical model, however, has been hindered by the comlicated temperature and velocity fields and by the complex structure of electronic systems. The objective of this study, therefore, is to develop a simple analytical technique for the prediction of convective heat transfer in this complicated systems. While the surfaces are assumed to be flat and flow regime is laminar, thermal boundry conditions are specified arbitrarily even with step discontinuities. Analytical solutions of forced convection heat transfer over a plate with arbitrarily surface temperature or heat flux variations can be easily obtained by the superposition method, Kays and Crawford I 1 3. Because of the linearity of the boundry layer energy equation.. On the other hand, due to the nonlinear coupling of flow and energy fields analytical solutions for natural convection boundry layers are limited to the.solutions with uinoform or simply varying boundry conditions, which yield similarity formulations, Jaluria C 2 ]. Moreover analytical solutions are seldom obtained even for simple thermal boundry conditions in the analysis of mixed convection heat transfer »Churchill and Usagi [3 3, Wilks [4 3, Shai and Barnea [ S3,' Lin and Chen [83. For the description of natural convection heat transfer along thermally nonuniform surfaces, several approximating techniques have been developed. For surfaces with continuous thermal boundry conditions, integral method was used by Sparrow [73 and Scherberg [83. Kelleher and Yang [93 employed Gör tier -type series expansion and Kao et al [ 10 3 developed a general theory with local similarity and universal functions. Natural convection over inclined surfaces with power- law variations of wall temperatures or surface heat fluxes -VIII-was numerically analyzed by Chen et al [ 11 ]. For thermally discrete surfaces, Schetz and Eichhorn [ 12 3 conducted an experiment with a Mach-Zehnder Interferometer. Kelleher C 13 ] analyzed the problem using asymptotic series and Hayday et al [ 14 ] applied difference diferential method. Jaluria C 15 ] numerically investigated multi-step discontinuity cases. Recently Lin and Yu C 16 ] numerically studied natural convection induced by an isoflux surface with a line source at its leading edge over a wide range of Prandtl numbers using a unified buoyancy parameter. For mixed convection heat transfer over a thermally nonuniform surfaces, almost all the analysis are assisted by numerical computations. Mixed convective flow along thermally nonuniform surfaces was analyzed numerically by Ousthuizen and Hart [ 17 3. A similarity formulation for mixed convection heat transfer can be obtained for a special situation such as mixed convection over a circular cylinder, where main stream velocity and temperature difference between the surface and the ambient condition vary linearly along the surface, Mahmood and Merkin [ 18 3. In spite of extensive efforts to analyze natural and mixed convection heat transfer on thermally nonuniform surfaces, there has been no simple analytical approach reported, which is generally applicable for practical engineering calculations. In the present work, a simple analytical technique for the approximation of natural and mixed convection heat transfer for arbitrarily boundry conditions will be developed. The superposition method will be employed for the simulation of nonsimilar convection heat transfer in that the superposition method is one of the simplest techniques accommodating arbitrarily varying boundry conditions. Although the superposition method is not rigorously valid for nonlinear cases, the present study attempts to show that such a method can yield very small errors. The superposition technique has rarely been employed for natural or mixed convection heat transfer due to the coupling effects and the nonlinear i ty of the field equations and,if at all, has been used only for the case where local buoyancy effects are negligibly small, Ortega and Moffat [ 1Q 3. In this study, temperature and velocity fields for natural convection thermally nonuniform surfaces are described in terms of equivalent Grashof numbers defined -IX-by the superposition of surface heat fluxes and velocities formulated from similarity analyses or correlatons for simple boundry conditions. Local heat transfer rates for mixed convection on thermally nonuniform surfaces are expressed by the third root of the sum of the third power of Mussel t numbers for pure forced and pure natural convction on such surfaces. These Nusselt numbers are obtained by the superposition method. This summation method was devised originally for mixed convection over thermally uniform surface for practical engineering applications, Churchill and Usagi [3 ], Shai and Bernea to]. Various cornparisions are made between the results from the proposed technique and those from numerical studies, experiments, and similarity analyses. Despite the coupled and nonlinear nature of the momentum and the temperature fields for natural and mixed convection, the superposition method predicts local heat transfer rates very well on thermally discrete as well as thermally continous vertical surfaces. The underlying concept for superposition is the linearity of energy, and not that of temperature. Since this method utilizes analytic formulations obtained from similarity analyses or experimental correlations for thermally uniform surfaces, a desk-type calculator is sufficient to calculate the local heat transfer rate on thermally complicated surfaces. When the surface temperature is specified, the superposition method is shown to be useful except for the region very close to the surface temperature discontinuities and the region of positive surface temperature gradients. When the surface heat fluxe is specified, this method is generally useful even near the discontinuities. An extreme example, natural convection due to a line source on an vertical adiabatic surface, can be predicted well by the super p>osi t ion method. Local heat transfer rates for mixed convection over thermally nonuniform vertical surfaces are predicted succes fully by the superposition method using the Nusselt numbers for pure forced and natural convection over such surfaces. The linearizing effect of the forced convection results in a more accurate prediction of heat transfer rates for mixed convection by the superposition method than those for natural convection. -X-The presents study shows that this superposition method is a simple and powerful tool for the prediction of the thermal and momentum fields induced by natural convection phenomenon and local heat transfer rates controlled by mixed convection in such systems as electronic circuitry and some manufacturing systems without extensive numerical calculations. Moreover, this superposition technique can be applied for any body force induced flow systems with arbitrarily specified thermal boundry conditions, provided that local heat transfer rates for thermally uniform surfaces are supplied. The other purpose of this- study is to compare the Nusselt number distribution over distributed line source on an vertical adiabatic surface and on an vertical adiabatic surface whose heat flux is constant. As it is shown figure. 1, the length between two, different line source on an vertical adiabatic surface is chosen respectively 20, 5 » 1 Cmm3. As the length between two different line source is decreased, the Nusselt number distribution is approached to the Nusselt Number distribution of an adiabatic surface whose heat flux is constant. -XI-[ Nusselt Sayısı ] 1.8 1.6 0. 8.a-,f W. IT jzr M- a”.0 Ü. D 0. 4 u. 2 i if İZ“.,-*.0”0 ', ? I J L Ö 10 15 20 25 30 35 40' 45 50 55 60 6ö' 7C Tim Series 1 20 [mm] :j<: Series 3 1 [mm] '“”Series 2 S [mm] _".|;:;|._.._ Series 4 q=st. Figure. 1 Comparison of Mux for natural convection over distributed line sources which are placed in a three different position on an vertical adiabatic surface and on an vertical adiabatic surface whose heat flux is constant. -XII-
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