scholarly journals Finding a weak solution of the heat diffusion differential equation for turbulent flow by Galerkin's variation method using p-version finite elements

2021 ◽  
Vol 16 (2) ◽  
pp. 129-157
Author(s):  
István Páczelt
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Weak Solution ◽  
Finite Elements ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Symmetric Domain ◽  
Heat Diffusion ◽  
Variation Method ◽  
Shear Stresses

The stochastic turbulence model developed by Professor Czibere provides a means of clarifying the flow conditions in pipes and of describing the heat evolution caused by shear stresses in the fluid. An important part of the theory is a consideration of the heat transfer-diffusion caused by heat generation. Most of the heat is generated around the pipe wall. One part of the heat enters its environment through the wall of the tube (heat transfer), the other part spreads in the form of diffusion in the liquid, increasing its temperature. The heat conduction differential equation related to the model contains the characteristics describing the turbulent flow, which decisively influence the resulting temperature field, appear. A weak solution of the boundary value problem is provided by Bubnov-Galerkin’s variational principle. The axially symmetric domain analyzed is discretized by a geometrically graded mesh of a high degree of p-version finite elements, this method is capable of describing substantial changes in the temperature gradient in the boundary layer. The novelty of this paper is the application of the p-version finite element method to the heat diffusion problem using Czibere’s turbulence model. Since the material properties depend on temperature, the problem is nonlinear, therefore its solution can be obtained by iteration. The temperature states of the pipes are analyzed for a variety of technical parameters, and useful suggestions are proposed for engineering designs.

scholarly journals Effect of Prandtl number on heat transfer characteristics in an axisymmetric sudden expansion: A numerical study

2007 ◽  
Vol 11 (4) ◽  
pp. 171-178
Author(s):  
Khalid Alammar
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Study ◽  
Sudden Expansion ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Simulated Effect

Using the standard k-e turbulence model, an incompressible, axisymmetric turbulent flow with a sudden expansion was simulated. Effect of Prandtl number on heat transfer characteristics downstream of the expansion was investigated. The simulation revealed circulation downstream of the expansion. A secondary circulation (corner eddy) was also predicted. Reattachment was predicted at approximately 10 step heights. Corresponding to Prandtl number of 7.0, a peak Nusselt number 13 times the fully-developed value was predicted. The ratio of peak to fully-developed Nusselt number was shown to decrease with decreasing Prandtl number. Location of maximum Nusselt number was insensitive to Prandtl number.

The Numerical Prediction of Developing Turbulent Flow and Heat Transfer in a Square Duct

1980 ◽  
Vol 102 (1) ◽  
pp. 51-57 ◽  
Author(s):  
A. F. Emery ◽  
P. K. Neighbors ◽  
F. B. Gessner
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Algebraic Closure ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Closure Model ◽  
Constant Wall Temperature ◽  
Square Duct ◽  
Constant Wall Heat Flux ◽  
Temperature Constant

Velocity and temperature profiles were computed for developing turbulent flow in a square duct with constant wall temperature, constant wall heat flux or asymmetric heating. The computations utilized an explicit numerical differencing scheme and an algebraic closure model based upon a three-dimensional mixing length. The computed local and fully-developed shear stresses and heat transfer are shown to be in good agreement with measured data and with predictions using the k–ε closure model.

302 Study of prediction for heat transfer and mixing in complex turbulent flow via turbulence model

2016 ◽  
Vol 2016.65 (0) ◽  
pp. _302-1_-_302-2_
Author(s):  
Kenji TSUTSUI ◽  
Hirofumi HATTORI ◽  
Tomoya HOURA ◽  
Masato TAGAWA
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Turbulence Model

A Numerical Study of Unsteady Mixed Convection in a Square Cavity: Transition From Laminar to Turbulent Flow

2013 ◽  
Author(s):  
K. M. Akyuzlu
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Study ◽  
Working Fluid ◽  
Heat Transfer Characteristics ◽  
Square Cavity ◽  
Transfer Characteristics ◽  
Unsteady Mixed Convection

A study was conducted to simulate the circulation patterns and heat transfer characteristics of flows in a square cavity during transition from laminar to turbulent mixed convection conditions using numerical techniques. The cavity under study is assumed to be filled with a compressible fluid. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is assumed to be stationary initially and then pulled at constant speed for times greater than zero. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, physics based mathematical model is adopted to predict the momentum and heat transfer inside this rectangular cavity. A standard two equation turbulence model is used to model the turbulent flow inside the enclosure and the compressibility of the working fluid is represented by an ideal gas relation. The numerical solution techniques adopted in this study is a hybrid one (implicit-explicit) where the conservation equations for the velocity, temperature, and pressure are solved using an implicit technique (Coupled Modified Strongly Implicit Procedure -CMSIP) whereas the equations for the standard K-ε turbulence model are solved using an explicit (MacCormack) technique. In both techniques, a second order accurate finite difference technique is used to discretize the governing equations. Then numerical experiments were carried out to simulate the unsteady flow and heat transfer characteristics of mixed convection flow inside a square cavity filled with air (Pr = 0.72) for different Richardson numbers in the range of 0.00868–0.03470; corresponding to Reynolds numbers ranging from 2000 to 4000, respectively, when the Rayleigh number was kept constant at 105. Vertical and horizontal temperature and velocity profiles were generated while the flow goes through transition from laminar to turbulent. Changes in wall heat flux were calculated and average Nusselt numbers were determined for each parametric study.

Development of a Turbulence Model for Rectangular Passages

1984 ◽  
Vol 8 (3) ◽  
pp. 146-149
Author(s):  
S.V. Patankar ◽  
S. Acharya
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Mixing Length ◽  
Rectangular Duct ◽  
Fully Developed Turbulent Flow

A mixing length model for fully developed turbulent flow in rectangular ducts has been developed. In this model, the mixing length at any point is found from an algebraic combination of two mixing lengths, one for each set of parallel walls. The model correctly predicts the overall friction and heat transfer in a channel as well as in a rectangular duct.

scholarly journals Numerical simulation of flow dynamics and heat transfer in a rectangular channel with periodic ribs on one of the walls

2021 ◽  
Vol 2119 (1) ◽  
pp. 012028
Author(s):  
A V Barsukov ◽  
V V Terekhov ◽  
V I Terekhov
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Rectangular Channel ◽  
Flow Dynamics ◽  
Flat Channel ◽  
Optimal Model

Abstract The result of numerical simulation of a turbulent flow in a flat channel with a periodic transverse rib by the RANS and LES methods is presented. The Reynolds number, calculated from the rib height and the superficial velocity, is Re = 12600. The data obtained as a result of the study demonstrate the influence of the modeling method and the turbulence model on the quality of heat transfer prediction. The optimal model for this type of problems is presented.

Numerical Simulation of Mark Formation/Erasure in Phase Change Recording

2005 ◽  
Author(s):  
Evan Small ◽  
John Reifenberg ◽  
Yizhang Yang ◽  
Sadegh M. Sadeghipour ◽  
Mehdi Asheghi
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Temperature Distribution ◽  
Finite Elements ◽  
Phase Change ◽  
Finite Elements Method ◽  
Heat Diffusion ◽  
Recording Media ◽  
Heat Diffusion Equation ◽  
Heat Transfer Simulation

Design/optimization of the phase change recording media to create proper marks, in size, shape, and quality, needs a robust modeling tool to predict temperature distribution in the constituting layers and model the phase formation during writing/erasure of the information bits. This requires a modeling of the heat transfer (thermal performance) and the crystallization processes. The thermal modeling, which is based on the solution of the heat diffusion equation for finding temperature distribution in the multilayer media, has been done before, using the finite difference techniques. These techniques have limited potentials for modeling real phase change recording media that have a rather more complex geometry. The finite elements method has, on the other hand, the required flexibility for such applications. In this work, we are reporting on development of a numerical simulation tool that uses the finite elements method for heat transfer simulation. ANSYS is used as the source code for the heat transfer simulation, in this application, with the crystallization model then being built into this media. This code has been used to simulate mark formation during writing on grooved plain and planer patterned media. Patterning the phase change material layer looks very promising in controlling the mark size and the mark edge irregularity which lead to timing jitter.

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