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Ayrık doğal taşınım sistemlerinin analizi

Analysis of thermally discrete, natural convection systems

  1. Tez No: 19286
  2. Yazar: İ.YALÇIN URALCAN
  3. Danışmanlar: PROF.DR. OSMAN F. GENCELİ
  4. Tez Türü: Doktora
  5. Konular: Makine Mühendisliği, Mechanical Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1991
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 65

Özet

ÖZET Düşey bir yüzeydeki, ayrık ısıl sistemlerden ortama doğal taşınım ile ısı geçişi probleminin, yaklaşık bir analitik yöntem ile teorik; termoeleman çiftleri İle sıcaklık ölçerek ve holografik interferometri ile de sınır tabakayı görünür hale getirerek deneysel analizleri yapılmıştır. Analitik yöntemde, sürekli sistemler için sınır tabakadaki korunum denklemlerinin, benzerlik dönüşümü ile çeşitli araştırmacılar tarafından elde edilmiş tam analitik cözümü esas alınmış; nonsimilar C benzerlik dönüşümüne müsaade etmeyen} sınır şartları haiz ayrık doğal taşınım sistemleri, Stieltjes integrali kullanılarak süperpoze edilmiştir. Böylece, nonsimilar problemin, yüzeydeki ısıl sınır şartta mevcut süreksizliklere rağmen, yaklaşık analitik çözümü elde edilmiştir. Düşey bir levhada, yükseklikleri eşit, ayrık olarak birbirinden farklı sabit yüzey ısı akıları ile ısıtılan yüzey elemanları hali, deneysel olarak incelenerek, süper pozisyon yönteminin geçerlilik sınırları tespit edilmiştir. Deneylerde, öncelikle tek düşey levha hali incelenerek, deney sisteminin kontrolü yapılmış, yapılan ölçmelerin mevcut çözümler ile uyumlu olduğu görülmüştür. Daha sonra iki ve üc ayrık yüzey halleri için yapılan deneylerde, yüzey sıcaklıkları termoeleman çiftleri ile ölçülürken, sınır tabakadaki sıcaklık alanı, holografik interferometri ile görünür- hale getirilmiştir. Süperpozisyon yöntemi ile elde edilen sonuçlarla deney verilerinin karşılaştırılmasından, yöntemin özellikle, yüzey sıcaklığının çalışma şartlarını belirlediği ve azami yüzey sıcaklığının da, performansı ve ömrü sınırladığı, elektronik devre plakaları ve elemanlarının soğutulması ve tasarımı probleminde, büyük bir yaklaşıklıkla, kullanılabileceği görülmüştür. viii

Özet (Çeviri)

ANALYSIS OF THERMALLY DISCRETE NATURAL CONVECTION SYSTEMS SUMMARY Natural, forced or mixed convective heat transfer from vertical surfaces has received a fair amount of attention in the heat transfer literature, due to its importance in cooling of heat dissipating elements on electronic circuit boards and machinery elements exposed to thermal enforcement. In forced convection, because the energy equation is linear, analytical solutions for arbitrarily specified thermal boundary conditions can easily be obtained. In natural convection heat transfer, however, boundary layer equations are nonlinear, because the free convection motion is due completely to temperature differences. This coupling of thermal and momentum fields in natural convection, disables analytical solutions for disconti nuous or arbitrarily varying thermal boundary conditions. On thermally nonuniform surfaces, exact analytical solutions were obtained by Sparrow and Gregg [31, only for the situations where wall temperature variations give rise to similar solutions of the laminar boundary layer equations. The vertical plate in laminar free convection with a step discontinuity in surface temperature was first investigated experimentally by Schetz and Eichorn 171 using a Mach-Zehnder Interferometer. In their numerical analysis, Hayday et al. [81 employed difference differential method and Kelleher [91 used asymptotic series and compared their results with the above mentioned experimental data. Zinnes [101 studied the coupling of conduction in a vertical plate of finite thickness with arbitrary heating distribution in its surface, with a finite difference method and conducted experiments using a holographic interferometer. In addition to all above summarized classical boundary layer solutions, Yang and Jerger [111 conducted a second-order perturbation analysis for the vertical plate in free convection and computed corrections to account for finite plate length. Messiter et al. [121 attempted to describe the asymptotic flow structure near a discontinuity in one of the plate boundary conditions, as at a leading or trailing edge or at a jump in plate temperature and pointed out the various effects which must be considered for the calculation of the second order heat transfer from an isothermal plate of finite length. ixIn this PhD thesis, a superposition technique for nonsimilar natural convection heat transfer problems, presented by Park and Tien [13] and Ural can et al. [14], is described. Selecting surface heat, flux as the superposition variable, Stieltjes Integral is employed in the method. Even with step discontinuities in boundary conditions, thermal field for natural convection over a thermally nonuniform vertical surface is formulated in terms of an equivalent Grashof number defined by the superposition of surface heat fluxes obtained from similarity solutions. In order to validate the super-position method, an experimental analysis of natural convection over a vertical plate with step discontinuities in surface heat flux has been carried out, utilizing a holographic interferometer. The limits of the superposition method, to which its validity extends, are observed. The superposition technique utilizes the similarity solution of Sparrow and Gregg [31, conducted for T-T-Nxn Cl> W 00 They obtained solutions for temperature and velocity distributions in terms of the independent similarity variable r/, defined by 1/4 n m Cy/x) CGr ^4) C2'.> and dependent variables, dimensionless velocity and di mensi onless temperature, respectively given as uCx, yf> F'Cyp » r-- C35 CA:X>SvC> CGr X43 x 4 = (T - T ) /CT -T3 C4) ^ ' 00 W 00 where the prime represents differentiation with respect to r; and Gr ? g ft CT - T i x3. ı>2 C5J Xs*' W 00 The exponent n»0 corresponds to an isothermal surface, n=l«^S to an isoflux surface and n=-3/5 to a horizontal line thermal source mounted just at the leading edge of an adiabatic surface. The local heat transfer from the surface to the fluid for an isothermal or isoflux surface is,q - - k CT ^w w T 3 CD r d +“J 1 r Grx -i1'4 I d r? J^q x [ 4 j C6I> where the surface t emper- at ur e gradient ip' COD is a function of both the Prandtl number and the exponent n. Introducing the local Nusselt number Nu q x/k CT -T:> W W CO C73 the dimensionless representation of the local heat flux becomes.1'4 Nu #'co:> RH C8> On the other hand, in nonsimilar natural convection heat transfer problem, thermal boundary condition discontinuities result in accumulating effects on the downstream thermal and momentum fields. The superposition method utilizes the Stieltjes integral t*o predict this accumulation, selecting surface heat flux as the super position variable [13,141. Using Eq. C6>, a continuous variation of discrete thermal boundary conditions, with a finite number CpD of step discontinuities, can be specified using Stieltjes integral as qw - C r Cx - ÇJ a.a d CT - T > -İSA w eo_ SS4 D- i=l -İ/4 ACT _ T 5 s i W 00 i 5-”4 C9*J or CT - T 5 W 00 5V4 q u Cx - Ç31 - d % oJ d ? J y~cx - ç15ı.4 Aq wi i=»i CI CO xiEqs. C93 and Cİ03, respectively, stand for the cases where surface temperature and surface heat flux is specified. C_ and C are constants defined by 1 q [4^ 1/4 CT - - k 0T'CO) | 5-| CUD 1^-1 1^4 Cq“ ”k VC°* ' *~l C12J for isothermal and isoflux cases respectively. A heat flux based equivalent Grashof number is defined as, ?,4 CI 3) from Eqs. C7) and C8D and is used instead of Gr. ^ x A holographic interferometer is used to visualize the temperature field and observe boundary layer charac teristics. The real time technique is employed and both finite and infinite fringe patterns of the boundary layer are recorded. Heat transfer experiments are conducted using 0.04 mm thick Manganin plates supported within the test section of the interferometer. Each plate is heated electrically through a seperate DC circuit supplied by DC converters. In addition to interf erometric visualisations, plate temperatures are measured with Chr omel -Al umel thermocouples located with 10 mm spacing. Experiments are carried out for i. a single vertical plate 0.06 or 0.08 m high, ii. two discrete plates each 0.04 m high, iii. three discrete plates each 0.02 m high with equal or unequal heat fluxes at each discrete plate. Thermal boundary condition configurations, employed in the experiments, are summarized in the table below, where m is the number of discrete surfaces, *i“ Vl ' qwi C14j> and q, and q. are the surface heat fluxes at the most ^wl ^wi upstream and at the i discrete plates, respectively. xiiExperiments for single vertical plate or discrete plates with equal uniform heat fluxes are conducted, in order to validate the experimental apparatus and method, by comparing present data with relevant previous works existing in the literature. Thermal boundary conditions employed in experiments, In the present study, a complicated relation of* Churchill and Chu 1161, applicable over a wide range of Grashof number is used for comparison. Their correlation ch^İX4Ch^_ 0>683 m 0.67 Cq* Pr)1'4, II + C0.492.PrD9'16 l4^9 C153 is recommended here and is also in perfect agreement with an earlier experimental study of Uralcan and Genceli 1171. The fluid, in present experiments, is air at atmospheric pressure and room temperature. Surface heat flux Cq ”> is varied from 7 WVm w boundary condition configuration. to 380 wVm for each Interpretation of results is made in means of nondimensional variables, the vertical coordinate X «? x/L surface heat flux q " 9 ft qw L S k v Cİ60 CI 73 xiiisurface temperature e - g ft L3 CT Cx) - T 3 X t>2 CIS) 31 W 00 average heat transfer coefficient h* ? q L/k CT CL/2} - T 3 CI 9) ^W W CO local Nusselt number Nu and local Grashof number ^r, respectively defined in C7) and CI 35. In particular, Ca.» Churchill and Chu *s overall heat transfer correlation CIS) is recommended with a maximum error of -4 H in average Nusselt number, which arises from the leading and trailing edge effects; (W in laminar convective heat transfer, the superposition method for discrete vertical plates is useful for y> ^ 1S&, except for the very close vicinity of the discontinuity, where conduction in fluid due to the sudden jump in the thermal boundary condition disturbs the fully convective character of the boundary layer; CcD a negative jump in the thermal boundary condition, e. g. y> < 1/4, results in errors which cannot be neglected, in tPie predictions of the superposition method and this error increases with decreasing y> to a maximum for yt = O Cadiabatic downstream discrete plate); Cd) for either single or discrete plates cases, heat transfer coefficients, especially at the close viscinity of leading and trailing edges, are larger than those predicted by classical boundary layer solutions. Corrections with second order perturbation analysis discussed by Yang and Jerger [111 and Messiter et al. E12J are in good agreement with present experimental work. xiv

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