Finite Analytic Solution of Convective Heat Transfer for Tube Arrays in Crossflow: Part I—Flow Field Analysis

1989 ◽  
Vol 111 (3) ◽  
pp. 633-640 ◽  
Author(s):  
Tzong-Shyan Wung ◽  
Ching Jen Chen
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Analytic Solution ◽  
Stokes Equations ◽  
Convective Motion ◽  
Field Analysis ◽  
Analytic Method ◽  
Finite Analytic Method ◽  
Tube Arrays ◽  
Local Analytic Solution

The convective motion in two types of tube array is solved numerically by the Finite Analytic Method. The Finite Analytic Method utilizes the local analytic solution of governing differential equations in obtaining its discretized algebraic representation. Both in-line tube arrays and staggered tube arrays with longitudinal and transverse pitches of 2 are studied. The geometries are expressed in boundary-fitted coordinates on which the Navier–Stokes equations and energy equation are solved. Solutions for Reynolds numbers of 40, 120, 400, and 800 are obtained. Differences in stream function, vorticity function, and location of separation and reattachment for flow past in-line tube arrays and staggered tube array are predicted and compared. The zone of separation for both arrays tends to increase with increasing Reynolds number. The predicted results on flow field and heat transfer are shown to agree with available experimental measurements.

Finite Analytic Numerical Solution Axisymmetric Navier-Stokes and Energy Equations

1983 ◽  
Vol 105 (3) ◽  
pp. 639-645 ◽  
Author(s):  
Ching-Jen Chen ◽  
Young Hwan Yoon
Keyword(s):  
Heat Transfer ◽  
Numerical Solution ◽  
Numerical Method ◽  
Stream Function ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Inlet Temperature ◽  
Local Analytic Solution

Connective heat transfer for steady-state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature, and heat transfer coefficients for flow with Reynolds numbers of 5, 100, 1000, and 2000, and Prandtl numbers of 0.1, 1.0, and 10.0 with uniform grid sizes, are reported for an axisymmetric pipe with a sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic is stable, converges rapidly, and simulates the convection of fluid flow accurately, since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values, thereby minimizing the false numerical diffusion.

The role of urban development in the formation of a “heat island”

2021 ◽  
pp. 4-14
Author(s):  
Виктория Дмитриевна Мешкова ◽  
Александр Анатольевич Дектерев ◽  
Кирилл Юрьевич Литвинцев ◽  
Сергей Анатольевич Филимонов ◽  
Андрей Анатольевич Гаврилов
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Solar Radiation ◽  
Urban Development ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Convective Motion ◽  
Surface Velocity ◽  
Heat Island ◽  
Near Surface

Для оценки роли городской застройки в формировании “острова тепла” и исследования его влияния на распространение загрязняющих веществ разработана микромасштабная математическая модель городской среды. В качестве модельной задачи рассматривалось локальное влияние городской застройки микрорайона г. Красноярска. Установлено, что наибольший вклад в формирование “острова тепла” вносят наружные стены зданий и их верхние конструкции - крыши. При учете теплообмена наблюдаются рост средней скорости воздушного потока внутри квартала и уменьшение низкоскоростных областей более чем на 0.5 м/с. Также выявлено, что при учете теплообмена наблюдается заброс загрязняющих веществ, поступающих от дороги, на б´ольшую высоту, чем без него. Разработанная математическая модель позволяет комплексно подойти к исследованию гидродинамики и прогнозированию экологической обстановки урбанизированных территорий Introduction. The configuration of modern micro districts leads to the formation of zones with low velocity, in which the accumulation of pollutants occurs. On the other hand, during the construction of cities, the surface of the Earth is covered with materials that actively absorb solar radiation, which leads to the formation of an urban heat island. Our work is devoted to the study of the local influence of urban development on the spread of pollutants, which takes into account the above mentioned factors. Mathematical model. For solving our problems we developed the microscale mathematical model based on the Reynolds-averaged Navier-Stokes equations for incompressible flows with variable density. For the correct calculation of the temperature on the surface of buildings, we used a model of conjugate heat transfer with a one-dimensional equation of thermal conductivity. As a model problem, we considered the Krasnoyarsk area with dense development and the presence of a highrise building for two seasons: winter and summer. The source of emission of pollutants was traffic. Results. The results of the calculations show a significant decrease in velocity around buildings. On the contrary, solar radiation leads to the intensification of free convective motion, especially in the surface area. That can double the near-surface velocity compared to the solution that does not account for the heat transfer. Conclusions. The developed mathematical model allows a comprehensive approach to solving hydrodynamic problems of prediction the ecological situation of cities

Finite Analytic Method in Flows and Heat Transfer

2020 ◽  
Author(s):  
Ching Jen Chen ◽  
Richard Bernatz ◽  
Kent D. Carlson ◽  
Wanlai Lin
Keyword(s):  
Heat Transfer ◽  
Analytic Method ◽  
Finite Analytic Method

scholarly journals Thermal Performance Study of a Water Tank for a Solar System With a Fresnel Lens

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
J. Chen ◽  
H. T. Xu ◽  
Z. Y. Wang ◽  
S. P. Han
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Thermal Stratification ◽  
Heating System ◽  
Fresnel Lens ◽  
Field Analysis ◽  
Water Tank ◽  
Performance Study ◽  
Shell Side ◽  
Flow Field Analysis

The heat transfer characteristics of a rectangular water tank used in a solar water heating system with a Fresnel Len were investigated qualitatively and quantitatively through the theoretical and numerical methods. The water tank is 450 mm × 400 mm × 500 mm in size and consists of 15 layers of coil pipe placed at its center. The MIX number and exergy efficiency were studied to quantify the thermal stratification of this water tank. A flow field analysis was also carried out to understand the heat transfer mechanism inside the water tank. Results indicate that the Nusselt number of shell side is increased with the growth of Reynolds number. The MIX number suggested that the thermal stratification is enhanced and then reduced with increasing flow rate. A correlation is proposed to predict the Nusselt numbers on the shell side. A detailed flow field analysis indicated that the thermal stratification is highly related to the runoff time, buoyancy force, mixing process, and geometry of the water tank.

Flow Field Analysis of Valve Plate for Hot Blast Valve

2012 ◽  
Vol 628 ◽  
pp. 523-527
Author(s):  
Ling Ling Li ◽  
Guang Pu Xu ◽  
Zhen Dong Su ◽  
Yong Ling Kang
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Valve Plate ◽  
Field Analysis ◽  
Flow State ◽  
Industry Group ◽  
Blast Valve ◽  
Flow Field Analysis ◽  
Analytical Result ◽  
Hot Blast

The valve plate of the hot blast valve is to rely on itself spiral waterway to cool. In the course of actual use, there is uneven actuality that it is cold and hot for the Valve plate of the hot blast valve. In this article, by means of COSMOSFloworks software, based on classic formula for convective heat transfer of heat transfer, we do flow field analysis for the waterway of the valve plate of DN1800 hot blast valve for certain Heavy Industry Group of our country. And analytical result indicates: Uneven distribution of water velocity in the valve plate is an important reason for causing unequal heat exchange of the valve plate and local thermal shock. In order to improve cooling uniformity, the central flow state of the type valve Plate should be altered and water cooling structure of inner water ring edge should be widen, finally the increase of the life of the valve plate can be reached.

Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Gerardo Anguiano-Orozco ◽  
Ruben Avila ◽  
Syed Shoaib Raza
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Heat Transfer Rate ◽  
Rotation Rate ◽  
Transfer Rate ◽  
Stokes Equations ◽  
Convective Motion ◽  
Maximum Temperature ◽  
Rotating Fluid ◽  
Uniform Heat

The laminar natural convection of a rotating fluid quasi-sphere in the presence of an axial gravity field and uniform heat source is presented. The influence of the Rayleigh number Ra and the Taylor number Ta on the flow pattern and heat transfer rate from the fluid quasi-sphere is discussed. The governing nonsteady, three-dimensional Navier–Stokes equations for an incompressible fluid, formulated in a Cartesian coordinate system, have been numerically solved by using the h/p spectral element method. It is shown that for a given Ta number, as the Ra number is increased, the heat transfer on the northern hemisphere is enhanced whereas the average Nusselt number on the southern hemisphere is reduced. On the other hand for a given Ra number, as the Ta number is increased, the heat transfer is a function of the convective motion intensity. It has been found that for low and high Ra numbers the heat transfer rate slightly depends on the rotation rate. However at intermediate Ra numbers, the net effect of an increased rotation rate is a reduction of the heat transfer through the wall, hence an increase of the maximum temperature of the fluid sphere is observed. We show that the net effect of the Coriolis force is to damp the convective motion and to allow a redistribution of the vorticity field.

Simultaneous Prediction of External Flow-Field and Temperature in Internally Cooled 3-D Turbine Blade Material

2000 ◽  
Author(s):  
Zhen-Xue Han ◽  
Brian H. Dennis ◽  
George S. Dulikravich
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Turbine Blade ◽  
Conjugate Heat Transfer ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Heat Fluxes ◽  
Bulk Temperature ◽  
Transfer Coefficients ◽  
Internally Cooled

A two-dimensional (2-D) and a three-dimensional (3-D) conjugate heat transfer (convection-conduction) prediction codes were developed where the compressible turbulent flow Navier-Stokes equations are solved simultaneously in the flow-field and in the solid material of the structure thus automatically predicting correct magnitudes and distribution of surface temperatures and heat fluxes. The only thermal boundary conditions are the convection heat transfer coefficients specified on the surfaces of the internal coolant flow passages and the coolant bulk temperature of internally cooled gas turbine blade. This approach eliminates the need to specify hot surface temperature or heat flux distribution. The conjugate codes use hybrid unstructured triangular/quadrilateral grids in 2-D and unstructured prismatic grids in 3-D throughout the flow-field and in the surrounding structure. The codes are capable of conjugate heat transfer prediction in arbitrarily shaped internally cooled configurations. The computer codes have been successfully tested on internally cooled turbine airfoil cascades and 3-D turbine blades by the conjugate solution of the flow-field and the temperature field inside the structure.

scholarly journals 2D-CFD Analyses of Flow Controlling Plates on Gable Roof Geometry Cross-Sections for Light Air to Strong Breeze Wind Speed Classifications-an Unsteady RANS Approach

2020 ◽  
pp. 1-18
Author(s):  
Kasra Amini ◽  
Alireza Mani
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Flow Field ◽  
Cross Sections ◽  
Bluff Body ◽  
Stokes Equations ◽  
Convective Heat Transfer Coefficient ◽  
Field Analysis ◽  
Navier Stokes ◽  
Gable Roof

The flow field analysis has been numerically performed on the effectiveness of a flow control mechanism called the Flow Controlling Plate (FCP) on buildings. For this purpose, the gable roof geometry has been considered as a common urban element in the western residential architecture. As the justification step towards the functionality of the concept of FCPs, the 2D numerical investigation of the flow field under the realistic assumptions of atmospheric boundary layer profiles for the spectrum ranging from the so-called light air to strong breeze wind speed classifications have been performed. The CFD (Computational Fluid Dynamics) field calculations have been conveyed as an unsteady case for the flow around a bluff body, using RANS (Reynolds Average Navier-Stokes) averaging methods targeting a solution of Navier-Stokes equations of the fluid flow. The results have proven the hypotheses of the contribution of the FCPs on preventing the flow separation on a partial region of the surface and improving the boundary layer development on the rest of the gable roof facades, which have led to a drastic reduction in the convective heat transfer coefficient as well as the drag force exerted on the roof

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