scholarly journals Solvability of the Boussinesq Approximation for Water Polymer Solutions

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 611 ◽  
Author(s):  
Mikhail A. Artemov ◽  
Evgenii S. Baranovskii
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Boussinesq Approximation ◽  
Robin Boundary Condition ◽  
Flow Domain ◽  
The Galerkin Method ◽  
Robin Boundary ◽  
Dimensional Domain

We consider nonlinear Boussinesq-type equations that model the heat transfer and steady viscous flows of weakly concentrated water solutions of polymers in a bounded three-dimensional domain with a heat source. On the boundary of the flow domain, the impermeability condition and a slip condition are provided. For the temperature field, we use a Robin boundary condition corresponding to the classical Newton law of cooling. By using the Galerkin method with special total sequences in suitable function spaces, we prove the existence of a weak solution to this boundary-value problem, assuming that the heat source intensity is bounded. Moreover, some estimates are established for weak solutions.

Anisotropic Behavior of Different Three-Dimensional Structures Materials under Thermal Stress Effect

2019 ◽  
Vol 297 ◽  
pp. 95-104
Author(s):  
Sihem Bouzid ◽  
Nacer Hebbir ◽  
Yamina Harnane
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Three Dimensional ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Equation System ◽  
Stress Effect ◽  
Field Calculation ◽  
Heat Transfer Theory ◽  
The Galerkin Method

This work concerns the numerical modeling of stationary conduction heat transfer in a 3D three-dimensional anisotropic material subjected to an internal heat source, based on the finite element method MEF and using the Galerkin method. The field of study is a cube representing the seven crystalline systems subjected to an internal heat source and convective boundaries. The obtained equation system is solved by the LU method. The automatic mesh is managed for all the domain nodes via the program which we have written in FORTRAN language. This program allowed temperature field calculation and was applied for different crystalline systems: monoclinic, triclinic, orthorhombic, trigonal, cubic that are identified by their thermal conductivity tensors [kij]. The obtained temperature profiles obtained are in accordance with heat transfer theory and clearly illustrate the crystalline structure symmetry; this calculation permits to predict the possible thermal deformations in an anisotropic solid.

Mixed Convection of Impinging Air Cooling Over Heat Sink in Telecom System Application

2004 ◽  
Vol 126 (4) ◽  
pp. 519-523 ◽  
Author(s):  
Siddharth Bhopte ◽  
Musa S. Alshuqairi ◽  
Dereje Agonafer ◽  
Gamal Refai-Ahmed
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Mixed Convection ◽  
Heat Sink ◽  
Three Dimensional ◽  
Source Surface ◽  
Air Cooling ◽  
Transfer Rates ◽  
Nusselt Numbers ◽  
Air Jet

The current numerical investigation will examine the effect of an impinging mixed convection air jet on the heat transfer rate of a parallel flat plate heat sink. A three-dimensional numerical model was developed to evaluate the effects of the nozzle diameter d, nozzle-to-target vertical placement H/d, Rayleigh number, and the jet Reynolds number on the heat transfer rates from a discrete heat source. Simulations were performed for a Prandtl number of 0.7 and for Reynolds numbers ranging from 100 to 5000. The governing equations were solved in the dimensionless form using a commercial finite-volume package. Average Nusselt numbers were obtained, at H/d=3 and two jet diameters, for the bare heat source, for the heat source with a base heat sink, and for the heat source with the finned heat sink. The heat transfer rates from the bare heat source surface have been compared with the ones obtained with the heat sink in order to determine the overall performance of the heat sink in an impingement configuration.

Heat Transfer Enhancement in Narrow Channels Using Two and Three-Dimensional Mixing Devices

1995 ◽  
Vol 117 (3) ◽  
pp. 590-596 ◽  
Author(s):  
S. V. Garimella ◽  
D. J. Schlitz
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Prandtl Number ◽  
Heat Transfer Enhancement ◽  
Large Scale ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Transitional Flow ◽  
Transfer Enhancement ◽  
Roughness Elements

The localized enhancement of forced convection heat transfer in a rectangular duct with very small ratio of height to width (0.017) was experimentally explored. The heat transfer from a discrete square section of the wall was enhanced by raising the heat source off the wall in the form of a protrusion. Further enhancement was effected through the use of large-scale, three-dimensional roughness elements installed in the duct upstream of the discrete heat source. Transverse ribs installed on the wall opposite the heat source provided even greater heat transfer enhancement. Heat transfer and pressure drop measurements were obtained for heat source length-based Reynolds numbers of 2600 to 40,000 with a perfluorinated organic liquid coolant, FC-77, of Prandtl number 25.3. Selected experiments were also performed in water (Prandtl number 6.97) for Reynolds numbers between 1300 and 83,000, primarily to determine the role of Prandtl number on the heat transfer process. Experimental uncertainties were carefully minimized and rigorously estimated. The greatest enhancement in heat transfer relative to the flush heat source was obtained when the roughness elements were used in combination with a single on the opposite wall. A peak enhancement of 100 percent was obtained at a Reynolds number of 11,000, which corresponds to a transitional flow regime. Predictive correlations valid over a range of Prandtl numbers are proposed.

Buoyancy Effect on Developing Turbulent Flow and Heat Transfer in a Helical Pipe With Finite Pitch

2000 ◽  
Author(s):  
B. Zheng ◽  
C. X. Lin ◽  
M. A. Ebadian
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Control Volume ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Buoyancy Effect ◽  
Constant Wall Temperature ◽  
Flow And Heat Transfer ◽  
Helical Pipe ◽  
Volume Method

Abstract Numerical modeling was performed to investigate the buoyancy effect on developing turbulent flow and the heat transfer characteristics of saturated water in a helical pipe with finite pitch. The renormalization group (RNG) κ–ε model was used to account for the turbulent flow and heat transfer in the helical pipe at a constant wall temperature with or without buoyancy force effect. A control volume method with second-order accuracy was used to numerically solve the three-dimensional full elliptic governing equations for this problem. The O-type nonuniform structured grid system was adopted to discretize the computation domain. The Boussinesq approximation was applied to deal with the buoyancy. This study explored the influence of buoyancy on the developing heat transfer along the helical pipe. Based on the results of this research, the velocity, temperature, and Nusselt number are presented graphically and analyzed.

Influence Of Relative Size Of The U-Shaped Silicon Rod On Conjugate Heat Transfer In The Regime Of Gas Buayancy Induced Convection

2015 ◽  
Vol 10 (3) ◽  
pp. 76-88
Author(s):  
Vladimir Berdnikov ◽  
Konstantin Mitin ◽  
Alina Mitina
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Solid Body ◽  
Conjugate Heat Transfer ◽  
Relative Size ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Spatial Form ◽  
Section Size

The influence of relative cross-section size of an electrically heated U-shaped silicon rod which is placed in a gas-filled rectangle container with isothermal cold walls on conjugate heat transfer in the regime of buoyancy induced convection was numerically studied in three-dimensional formulation. The natural convection equations in the Boussinesq approximation in term temperature, velocity vortex and velocity vector potential were solved by the finite element method. The spatial form of convective flow and temperature fields in liquid and solid body were studied. It was show that spatial form and intensity of convective flows is significantly depends on the cross-section size of U-shaped silicon rod. This is has strong influence on the temperature field in a solid body.

Three-Dimensional Magnetohydrodynamics Slip Flow of Nanofluids Over a Slendering Stretching Sheet with Heat Source or Sink Effects

2021 ◽  
Vol 10 (3) ◽  
pp. 380-387
Author(s):  
R. Jayakar ◽  
B. Rushi Kumar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Boundary Layers ◽  
Source Parameters ◽  
Slip Flow ◽  
Three Dimensional ◽  
Current Approach ◽  
Slip Effects ◽  
Nano Fluids

Aim: The research carried out in this article is based on experimenting with a 3-D MHD nanofluid flow on a sheet as slendering stretch bearing the slip effects, thermophoresis, Brownian Motion, heat source, and sink. Water-based Cuo and Cu nano-fluids were considered for the analysis. Following the suitable techniques of similarity transformation, the partial differential equations also called the governing equations are deduced into ODE (Ordinary Differential Equations). The mathematical results were estimated by applying the Methods of Newton and Runge-Kutta. The calculations along with the graphs for different parameters were also explained. Novelty: The outcomes of novel effective graphs for different parameters of interest are shown and explained. It has been found that heat-sink/source parameters depending on the temperature and space serve as heat transfer parameters. Slip effects minimize the thermal boundary layers as well as concentration development. It is discovered that CuO-Water, as well as Cu-Water nanofluids, have homogeneous boundary layers (concentration, thermal and momentum),and as contrasted with the CuO-Water nanofluids, the mass, and the heat transfer rate is higher in Cu-Water nanofluids. The paper concludes by comparing the outcomes of the current approach with findings that already existed.

Numerical Analysis of Plume Structures of Fluids on a Horizontal Heated Plate

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
T. Praphul ◽  
P. J. Joshy ◽  
P. S. Tide
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Cube Root ◽  
Heated Plate ◽  
Steady State Model ◽  
Increasing Trend ◽  
Wall Flow ◽  
Near Wall

Numerical investigations have been carried out to predict the near-wall dynamics in indirect natural convection for air (Pr = 0.7) and water (Pr = 5.2). Near-wall flow structures appear to be line plumes. Three-dimensional laminar, steady-state model was used to model the problem. Density was formulated using the Boussinesq approximation. Flux scaling, plume spacing and plume lengths obtained numerically are found to have the same trend with the results available in the literature. Plume length and Nusselt number, Nu exhibits an increasing trend with an increase in Rayleigh number, RaH for both Pr fluids. The plume spacing is found to have an inverse relationship with RaH. The cube root of Rayleigh number based on plume spacing, Raλ1/3 is found to have a slight dependence on the dimensionless plume spacing, λ/H. Nu scales as Nu∼CRaHn, n = 0.26 for air and n = 0.3 for water. Heat transfer is thus found to be dominated by near-wall phenomenon. Nu shows a nonlinear relationship with LpH/A and is found to be an accurate representation of heat transfer.

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