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Düşey levhalarda ısı iletkenliği düşük yatay kanatların doğal ısı taşınımına etkisi

Düşey levhalarda ısı iletkenliği düşük yatay kanatların doğal ısı taşınımına etkisi

##### Dosyalar

##### Tarih

1997

##### Yazarlar

Türkmen, Nedim

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

Institute of Science and Technology

Institute of Science and Technology

##### Özet

Düşey levhalarda ısıl iletkenliği düşük yatay kanatların doğal ısı taşınımına etkisi deneysel ve sayısal olarak incelenmiştir. Deneyler; 20x20x1.2 cm boyutlarındaki bakır plaka üzerine yatay olarak yerleştirilmiş pleksiglas kanatlardan oluşan deney parçası üzerinde holografik interferometri yöntemi kullanılarak yapılmıştır. Bakır plaka elektrik direnci ile ısıtılmış ve sabit yüzey sıcaklığı elde edilmiştir. Kanat yüksekliği ve kanat aralığı parametre alınarak dokuz farklı geometride deneyler yapılmıştır. Holografik interferomtri ile elde edilen görüntüler video kamera ile kaydedilmiş ve bir görüntü kartı ile bilgisayara aktarılmıştır. Bu görüntüler; hazırlanan bir pragram ile değerlendirilerek yüzeydeki ısı taşınım katsayıları hesaplanmıştır. Sayısal çözüm için PHEONICS CFD paket programı kullanılmıştır. Buradan elde edilen sonuçlar ile deney sonuçlarının karşılaştırılması yapılmıştır. Deneysel olarak belirlenen boyutsuz ısı geçişi parametreleri arasında, en küçük kareler yöntemi kullanılarak bir bağıntısı elde edilmiştir.

Natural convective heat transfer from extended surfaces has received a fair amount of attention and has remained as one of the most challenging topics in the expanding realm of thermo-fluid sciences and engineering. Besides its fundamental importance in understanding many aspects of buoyancy-driven flows, this geometry also has various applications, from flow around structural elements in heated buildings to solar thermal receiver systems or to cooling of electronic packages. Topics of related studies in the open literature include some basic problems, for instance, natural convection in rectangular enclosures or in open cavities, and some more complicated problems, such as, repeated horizontal ribs, dispersed pins or dense protrusions on a vertical surface. Numerical methods have been employed to solve these problems for various boundary conditions, as well as experimental studies. In almost all of these studies, height and width of the roughness elements were small compared to spacings between these elements. Namely, the spacing-to- protuberance height ratio (the aspect ratio) was considered much larger than unity. In the present study, natural convective heat transfer from a vertical plate with uniform base temperature and having transverse rectangular fins of low thermal conductivity has been investigated for a wide range of the spacing-to-fin height ratio. Values of the aspect ratio employed were, 4, 2, 1, Vz and V\. Both experimental and numerical techniques were used in the analysis. XI In the experimental study, a 24 mm thick and 200 mm high copper plate was used as the vertical base plate. It was heated electrically through a plane electric heater placed at the vertical midplane of the copper plate. Plexiglas with a thermal conductivity of «0.134 W/mK was used for the horizontal fins with rectangular cross- section. These fins were attached to both sides of the vertical base plate, thus ensuring symmetry at both sides. Fin height and spacing were varied to yield different aspect ratios. The base temperature was also varied as a second parameter. Air at atmospheric conditions was used as the ambient fluid. Temperature of the base plate was measured at six points, using Chromel- Alumel (K-type) thermocouples embedded at locations, 40 mm from edges and 2 mm from the vertical base surface. A holographic interferometer was employed as well, to visualize the temperature distribution in the boundary layer. Holographic images of the thermal field were recorded using a video camera. These records were loaded on a PC using a video frame grabber. A software for digital processing of these images has been developed and used for the analysis, instead of the conventional manual methods of image processing. Use of this software not only sped up the process but also made "real time analysis" available. Although the most reliable information about a physical process is obtained through experiments, the predictive tools such as CFD can play more valuable role if the process under consideration can be realistically modelled into soluble mathematical relations. The mass, momentum, and energy conservation equations are exact representation of mass and energy transfer. But, there is no analytical solution for as they stand because of the non-linearity of equations, and in the case of natural convection the coupling of equations. Several numerical methods have been developed to numerically solve the conservation equations. The method followed in CFD is to discretise the governing partial differential equations into set of linear algebraic equations that can be solved by iterative numerical techniques. The most common discretisation method used in CFD is the finite-volume method. The finite- difference and finite-element methods are also frequently used. The commercial CFD code PHOENICS used in this study employs finite-volume discretisation. xn PHOENICS is an acronym standing for Parabolic, Hyperbolic Or Elliptic Numerical-Integration Code Series. PHOENICS is a finite-volume based general purpose CFD program for the solution of one or two phase, steady or unsteady fluid flow and heat transfer problems either reacting or non-reacting flows in one, two or three dimensional geometries of cartesian, polar or body-fitted coordinates. PHOENICS has three main components. These are the preprocessor called SATELLITE, the main processor called EARTH, and the post processor called PHOTON. PHOENICS has three stand-alone components called GUIDE, AUTOPLOT, and PINTO. Figure l.The layout of PHOENICS code. SATELLITE receives instructions from the user either via the input file called Ql or during an interactive session through the input device, and creates a data file called EARDAT that EARTH can understand and executes. The main processor EARTH contains the main flow simulation code. It processes the instruction supplied by the satellite via EARDAT and produces two files, namely RESULT and either Xlll PHIDA or PHI. The RESULT is a text file with crude graphics for the inspection of user. PHIDA or PHI are binary and ASCII files respectively, and are the input files containing the results and geometry information of the calculation domain for the post processing. The post-processor PHOTON visualizes the solution data provided by either of the PHI or PHIDA. The stand-alone component GUIDE provides information about PHOENICS, how to run it and CFD in general. AUTOPLOT facilitates the plotting of graphs either from PHOENICS data or of other origin. PINTO is the code that lets the transfer of PHOENICS data from one grid to another of different fineness. A schematic diagram of the components of PHOENICS and their relationship is given in the above figure. Both EARTH and SATELLITE provide an option for additional FORTRAN coding of the user. That allows the user to build in the extra modelling and property equations that are not provided as standard by the PHOENICS. These coding frameworks are called GROUND and SATLIT for earth and satellite respectively. The general transport equation solved by PHOENICS, in cartesian tensor notation has the following form. |:(p*) + ir-(poj*) = ^-(rt ?£-) + s, (i) öt dxj dXj * dXj This equation represents transport of mass when $ is replaced by 1, and conservation of the variable replacing variable § is replaced with. The terms of this differential equations are known as transient, convective, diffusive, and source terms from left to right respectively. T$ is the diffusion coefficient of variable . Any analytic solution of the general transport equation would contain continuous information on the variable <|> in space and time within the calculation domain. Since analytical solution is impossible, numerical solutions are sought for. The practice in the numerical solution of differential equations is to replace the XIV continuous information that would be contained in the exact solution with discrete values. That is achieved by transforming the differential equations into algebraic equations involving the unknown values of the variable 4> at discrete points in the calculation domain. Thus the distribution of variable <|> within the calculation domain is discretised. If the number of discrete points in space and time within the calculation domain are infinitely large the numerical solution will be the same as the exact solution. There are different ways of discretisation. The method used in PHOENICS is the finite volume discretisation. Holographic pictures have proved the existence of air cells with low velocities near the corners below and above the fins. These cells result in the reduction of the convective heat transfer coefficient. Results of the experiments have proved that as the aspect ratio (A) decreases, i.e. the interfin cavity gets deeper, these air cells grow up, forming insulating layers of air in these cavities. As a consequence, the convective heat transfer coefficient also decreases. Thus, fins with low thermal conductivity are not suitable for use at surfaces which need to be cooled effectively, as in the case of the cooling of electronic equipment. However, in case of surfaces on which reduction of natural convective heat transfer is desired, as for a solar receiver, high fins with low thermal conductivity can be effectively used. The convective heat transfer coefficients calculated by PHOENICS are approximately 10-40 % smaller than those obtained experimentally. The reason for this fact may be that in the numerical calculations, the influence of thermal radiation from the fins on natural convection from the base plate has not been considered. A best-fit regression of experimental data in the ranges, 103 < RaH < 105 and 0.25

Natural convective heat transfer from extended surfaces has received a fair amount of attention and has remained as one of the most challenging topics in the expanding realm of thermo-fluid sciences and engineering. Besides its fundamental importance in understanding many aspects of buoyancy-driven flows, this geometry also has various applications, from flow around structural elements in heated buildings to solar thermal receiver systems or to cooling of electronic packages. Topics of related studies in the open literature include some basic problems, for instance, natural convection in rectangular enclosures or in open cavities, and some more complicated problems, such as, repeated horizontal ribs, dispersed pins or dense protrusions on a vertical surface. Numerical methods have been employed to solve these problems for various boundary conditions, as well as experimental studies. In almost all of these studies, height and width of the roughness elements were small compared to spacings between these elements. Namely, the spacing-to- protuberance height ratio (the aspect ratio) was considered much larger than unity. In the present study, natural convective heat transfer from a vertical plate with uniform base temperature and having transverse rectangular fins of low thermal conductivity has been investigated for a wide range of the spacing-to-fin height ratio. Values of the aspect ratio employed were, 4, 2, 1, Vz and V\. Both experimental and numerical techniques were used in the analysis. XI In the experimental study, a 24 mm thick and 200 mm high copper plate was used as the vertical base plate. It was heated electrically through a plane electric heater placed at the vertical midplane of the copper plate. Plexiglas with a thermal conductivity of «0.134 W/mK was used for the horizontal fins with rectangular cross- section. These fins were attached to both sides of the vertical base plate, thus ensuring symmetry at both sides. Fin height and spacing were varied to yield different aspect ratios. The base temperature was also varied as a second parameter. Air at atmospheric conditions was used as the ambient fluid. Temperature of the base plate was measured at six points, using Chromel- Alumel (K-type) thermocouples embedded at locations, 40 mm from edges and 2 mm from the vertical base surface. A holographic interferometer was employed as well, to visualize the temperature distribution in the boundary layer. Holographic images of the thermal field were recorded using a video camera. These records were loaded on a PC using a video frame grabber. A software for digital processing of these images has been developed and used for the analysis, instead of the conventional manual methods of image processing. Use of this software not only sped up the process but also made "real time analysis" available. Although the most reliable information about a physical process is obtained through experiments, the predictive tools such as CFD can play more valuable role if the process under consideration can be realistically modelled into soluble mathematical relations. The mass, momentum, and energy conservation equations are exact representation of mass and energy transfer. But, there is no analytical solution for as they stand because of the non-linearity of equations, and in the case of natural convection the coupling of equations. Several numerical methods have been developed to numerically solve the conservation equations. The method followed in CFD is to discretise the governing partial differential equations into set of linear algebraic equations that can be solved by iterative numerical techniques. The most common discretisation method used in CFD is the finite-volume method. The finite- difference and finite-element methods are also frequently used. The commercial CFD code PHOENICS used in this study employs finite-volume discretisation. xn PHOENICS is an acronym standing for Parabolic, Hyperbolic Or Elliptic Numerical-Integration Code Series. PHOENICS is a finite-volume based general purpose CFD program for the solution of one or two phase, steady or unsteady fluid flow and heat transfer problems either reacting or non-reacting flows in one, two or three dimensional geometries of cartesian, polar or body-fitted coordinates. PHOENICS has three main components. These are the preprocessor called SATELLITE, the main processor called EARTH, and the post processor called PHOTON. PHOENICS has three stand-alone components called GUIDE, AUTOPLOT, and PINTO. Figure l.The layout of PHOENICS code. SATELLITE receives instructions from the user either via the input file called Ql or during an interactive session through the input device, and creates a data file called EARDAT that EARTH can understand and executes. The main processor EARTH contains the main flow simulation code. It processes the instruction supplied by the satellite via EARDAT and produces two files, namely RESULT and either Xlll PHIDA or PHI. The RESULT is a text file with crude graphics for the inspection of user. PHIDA or PHI are binary and ASCII files respectively, and are the input files containing the results and geometry information of the calculation domain for the post processing. The post-processor PHOTON visualizes the solution data provided by either of the PHI or PHIDA. The stand-alone component GUIDE provides information about PHOENICS, how to run it and CFD in general. AUTOPLOT facilitates the plotting of graphs either from PHOENICS data or of other origin. PINTO is the code that lets the transfer of PHOENICS data from one grid to another of different fineness. A schematic diagram of the components of PHOENICS and their relationship is given in the above figure. Both EARTH and SATELLITE provide an option for additional FORTRAN coding of the user. That allows the user to build in the extra modelling and property equations that are not provided as standard by the PHOENICS. These coding frameworks are called GROUND and SATLIT for earth and satellite respectively. The general transport equation solved by PHOENICS, in cartesian tensor notation has the following form. |:(p*) + ir-(poj*) = ^-(rt ?£-) + s, (i) öt dxj dXj * dXj This equation represents transport of mass when $ is replaced by 1, and conservation of the variable replacing variable § is replaced with. The terms of this differential equations are known as transient, convective, diffusive, and source terms from left to right respectively. T$ is the diffusion coefficient of variable . Any analytic solution of the general transport equation would contain continuous information on the variable <|> in space and time within the calculation domain. Since analytical solution is impossible, numerical solutions are sought for. The practice in the numerical solution of differential equations is to replace the XIV continuous information that would be contained in the exact solution with discrete values. That is achieved by transforming the differential equations into algebraic equations involving the unknown values of the variable 4> at discrete points in the calculation domain. Thus the distribution of variable <|> within the calculation domain is discretised. If the number of discrete points in space and time within the calculation domain are infinitely large the numerical solution will be the same as the exact solution. There are different ways of discretisation. The method used in PHOENICS is the finite volume discretisation. Holographic pictures have proved the existence of air cells with low velocities near the corners below and above the fins. These cells result in the reduction of the convective heat transfer coefficient. Results of the experiments have proved that as the aspect ratio (A) decreases, i.e. the interfin cavity gets deeper, these air cells grow up, forming insulating layers of air in these cavities. As a consequence, the convective heat transfer coefficient also decreases. Thus, fins with low thermal conductivity are not suitable for use at surfaces which need to be cooled effectively, as in the case of the cooling of electronic equipment. However, in case of surfaces on which reduction of natural convective heat transfer is desired, as for a solar receiver, high fins with low thermal conductivity can be effectively used. The convective heat transfer coefficients calculated by PHOENICS are approximately 10-40 % smaller than those obtained experimentally. The reason for this fact may be that in the numerical calculations, the influence of thermal radiation from the fins on natural convection from the base plate has not been considered. A best-fit regression of experimental data in the ranges, 103 < RaH < 105 and 0.25

##### Açıklama

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1997

Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1997

Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1997

##### Anahtar kelimeler

Levhalar,
Termal iletkenlik,
Plates,
Thermal conductivity