Numerical Simulation of Thermal Transport Associated With a Continuously Moving Flat Sheet in Materials Processing

1991 ◽  
Vol 113 (3) ◽  
pp. 612-619 ◽  
Author(s):  
M. V. Karwe ◽  
Y. Jaluria
Keyword(s):  
Boundary Conditions ◽  
Thermal Transport ◽  
Numerical Study ◽  
Heated Plate ◽  
Governing Equations ◽  
Flat Sheet ◽  
Conductivity Parameter ◽  
Convection Parameter ◽  
Temperature And Flow Fields ◽  
Finite Difference Techniques

The thermal transport that arises due to the continuous motion of a heated plate or sheet in manufacturing processes such as hot rolling, extrusion, continuous casting, and drawing is numerically investigated. The resulting temperature distribution in the solid is influenced by the associated flow in the ambient fluid, which is taken as stationary far from the moving surface, and is of particular interest in this work. A numerical study is carried out, assuming a two-dimensional, steady circumstance with laminar flow in the fluid. The full governing equations, including buoyancy effects, are solved, employing finite-difference techniques. The effect of various governing parameters, such as the Peclet number, Pe, the mixed convection parameter, Gr/Re2, and the conductivity parameter, Kf/Ks, which determine the temperature and flow fields, is studied in detail. Also, the effect of the boundary conditions, particularly at the location of the emergence of the plate, on the downstream thermal transport is investigated. The penetration of the conductive effects, upstream of the point of emergence, is found to be significant. The effect of buoyancy is found to be more prominent when the plate is moving vertically upward than when it is moving horizontally. The appropriate boundary conditions and their imposition in the numerical scheme are discussed for a variety of practical circumstances.

Fluid Flow and Mixed Convection Transport From a Moving Plate in Rolling and Extrusion Processes

1988 ◽  
Vol 110 (3) ◽  
pp. 655-661 ◽  
Author(s):  
M. V. Karwe ◽  
Y. Jaluria
Keyword(s):  
Numerical Study ◽  
Hot Extrusion ◽  
Physical Parameters ◽  
Manufacturing Processes ◽  
Heated Plate ◽  
Governing Equations ◽  
Moving Plate ◽  
Boundary Layer Equations ◽  
Temperature And Flow Fields ◽  
Finite Difference Techniques

The heat transfer arising due to the movement of a continuous heated plate in processes such as hot rolling and hot extrusion has been studied. Of particular interest were the resulting temperature distribution in the solid and the proper imposition of the boundary conditions at the location where the material emerges from a furnace or die. These considerations are important in the simulation and design of practical systems. A numerical study of the thermal transport process has been carried out, assuming a two-dimensional steady circumstance. The boundary layer equations, as well as full governing equations including buoyancy effects, are solved employing finite difference techniques. The effect of various physical parameters, which determine the temperature and flow fields, is studied in detail. The significance of these results in actual manufacturing processes is discussed.

scholarly journals Effect of Variable Thermal Conductivity on Buoyant Convection in a Cavity with Internal Heat Generation

2007 ◽  
Vol 12 (1) ◽  
pp. 113-122 ◽  
Author(s):  
S. Sivasankaran
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Study ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Governing Equations ◽  
Heat Transfer Characteristics ◽  
Square Cavity ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter

A numerical study has been made to analyze the effects of variable thermal conductivity on the natural convection of heat generating fluids contained in a square cavity with isothermal walls and the top and bottom perfectly insulated surfaces. The flow is assumed to be two-dimensional. Calculations are carried out by solving governing equations for different parameters. The flow pattern and the heat transfer characteristics inside the cavity are presented in the form of steady-state streamlines, isotherms and velocity profiles. The heat transfer rate is increased by an increase in the thermal conductivity parameter.

A Numerical Study of Natural Convective Heat Transfer From an Inclined Isothermal Plate Having a Square Wave Surface

2011 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Jane T. Paul
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Boussinesq Approximation ◽  
Heated Plate ◽  
Governing Equations ◽  
Cross Sectional

Natural convective heat transfer from a wide isothermal plate which has a “wavy” surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The surface waves run in the horizontal direction, i.e., are normal to the direction of flow over the surface, and have relatively small amplitude. Attention has been restricted to the case where the waves have a rectangular cross-sectional shape. The plate is, in general, inclined to the vertical, consideration only being given to inclination angles at which the heated plate is facing upwards. The range of Rayleigh numbers considered extends from values that for a non-wavy vertical plate would be associated with laminar flow to values that would be associated with fully turbulent flow. The flow has been assumed to be steady and fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq approximation. The Reynolds averaged governing equations in conjunction with a standard k-epsilon turbulence model with buoyancy force effects fully accounted for have been used in obtaining the solution. The governing equations have been solved using the commercial cfd code FLUENT. The solution has the following parameters: (i) the Rayleigh number based on the height of the heated plate, (ii) the Prandtl number, (iii) the ratios of the amplitude of the surface waviness and of the pitch of the surface waves to the height of the plate, and (iv) the angle of inclination of the plate to the vertical. Results have only been obtained for a Prandtl number of 0.74. The effects of the other dimensionless variables on the mean surface Nusselt number have been numerically studied.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

scholarly journals A numerical study of the impact perforation of sandwich panels with graded hollow sphere cores

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110094
Author(s):  
Ibrahim Elnasri ◽  
Han Zhao
Keyword(s):  
Boundary Conditions ◽  
Hollow Sphere ◽  
Sandwich Panel ◽  
Numerical Study ◽  
Sandwich Panels ◽  
Hopkinson Bar ◽  
Core Density ◽  
The Core ◽  
The Impact ◽  
Force Displacement

In this study, we numerically investigate the impact perforation of sandwich panels made of 0.8 mm 2024-T3 aluminum alloy skin sheets and graded polymeric hollow sphere cores with four different gradient profiles. A suitable numerical model was conducted using the LS-DYNA code, calibrated with an inverse perforation test, instrumented with a Hopkinson bar, and validated using experimental data from the literature. Moreover, the effects of quasi-static loading, landing rates, and boundary conditions on the perforation resistance of the studied graded core sandwich panels were discussed. The simulation results showed that the piercing force–displacement response of the graded core sandwich panels is affected by the core density gradient profiles. Besides, the energy absorption capability can be effectively enhanced by modifying the arrangement of the core layers with unclumping boundary conditions in the graded core sandwich panel, which is rather too hard to achieve with clumping boundary conditions.

scholarly journals Numerical Study of Three-Dimensional Surface Jets Emerging from a Fishway Entrance Slot

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1079
Author(s):  
Lena Mahl ◽  
Patrick Heneka ◽  
Martin Henning ◽  
Roman B. Weichert
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Free Water ◽  
Lateral Wall ◽  
Lateral Spreading ◽  
Propagation Length ◽  
Vertical Slot ◽  
Surface Jets

The efficiency of a fishway is determined by the ability of immigrating fish to follow its attraction flow (i.e., its jet) to locate and enter the fishway entrance. The hydraulic characteristics of fishway entrance jets can be simplified using findings from widely investigated surface jets produced by shaped nozzles. However, the effect of the different boundary conditions of fishway entrance jets (characterized by vertical entrance slots) compared to nozzle jets must be considered. We investigate the downstream propagation of attraction jets from the vertical slot of a fishway entrance into a quiescent tailrace, considering the following boundary conditions not considered for nozzle jets: (1) slot geometry, (2) turbulence characteristics of the approach flow to the slot, and (3) presence of a lateral wall downstream of the slot. We quantify the effect of these boundary conditions using three-dimensional hydrodynamic-numeric flow simulations with DES and RANS turbulence models and a volume-of-fluid method (VoF) to simulate the free water surface. In addition, we compare jet propagation with existing analytical methods for describing jet propagations from nozzles. We show that a turbulent and inhomogeneous approach flow towards a vertical slot reduces the propagation length of the slot jet in the tailrace due to increased lateral spreading compared to that of a jet produced by a shaped nozzle. An additional lateral wall in the tailrace reduces lateral spreading and significantly increases the propagation length. For highly turbulent flows at fishway entrances, the RANS model tends to overestimate the jet propagation compared to the transient DES model.

Numerical Study of Wave Slamming on a Rectangular Slab

2012 ◽  
Vol 204-208 ◽  
pp. 4971-4977
Author(s):  
Ya Mei Lan ◽  
Wen Hua Guo ◽  
Yong Guo Li
Keyword(s):  
Numerical Study ◽  
Navier Stokes ◽  
Governing Equations ◽  
Reflected Waves ◽  
Rans Equations ◽  
Numerical Wave Flume ◽  
Wave Flume ◽  
Wave Slamming ◽  
Numerical Wave ◽  
Rectangular Slab

The CFD software FLUENT was used as the foundation to develop the numerical wave flume, in which the governing equations are the Reynolds-averaged Navier-Stokes (RANS) equations and the standard k~ε turbulence model. The wave generating and absorbing were introduced into the RANS equations as the source terms using the relaxation approach. A new module of the wave generating and absorbing function, which is suitable for FLUENT based on the volume of fluid method (VOF), was established. Within the numerical wave flume, the reflected waves from the model within the computation domain can be absorbed effectively before second reflection appears due to the wave generating boundary. The computational results of the wave pressures on the bottom of the rectangular slab were validated for the different relative clearance by the experimental data. Good agreements were found.

Study of the Laminar Free-Convection Wake Above an Isothermal Vertical Plate

1973 ◽  
Vol 95 (3) ◽  
pp. 289-294 ◽  
Author(s):  
N. E. Hardwick ◽  
E. K. Levy
Keyword(s):  
Free Convection ◽  
Vertical Plate ◽  
Fluid Motion ◽  
Heated Plate ◽  
Two Dimensional ◽  
Wake Region ◽  
Hot Wire ◽  
Near Wake ◽  
Steady Laminar ◽  
Finite Difference Techniques

The steady, laminar, two-dimensional wake above a thin vertical isothermal heated plate cooled by free convection was investigated theoretically and experimentally. The system of partial differential equations governing the fluid motion and heat transfer in the vicinity of the plate and in the near wake region was formulated and solved using finite difference techniques. Using air, the temperature and velocity profiles in the wake region were measured experimentally using a laser holographic interferometer and a constant temperature hot wire anemometer.

Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions

2006 ◽  
Vol 5-6 ◽  
pp. 407-414 ◽  
Author(s):  
Mohammad Mohammadi Aghdam ◽  
M.R.N. Farahani ◽  
M. Dashty ◽  
S.M. Rezaei Niya
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Simple Procedure ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Differential Quadrature ◽  
Governing Equations ◽  
First Order ◽  
Various Boundary Conditions ◽  
Generalized Differential

Bending analysis of thick laminated rectangular plates with various boundary conditions is presented using Generalized Differential Quadrature (GDQ) method. Based on the Reissner first order shear deformation theory, the governing equations include a system of eight first order partial differential equations in terms of unknown displacements, forces and moments. Presence of all plate variables in the governing equations provide a simple procedure to satisfy different boundary condition during application of GDQ method to obtain accurate results with relatively small number of grid points even for plates with free edges .Illustrative examples including various combinations of clamped, simply supported and free boundary condition are given to demonstrate the accuracy and convergence of the presented GDQ technique. Results are compared with other analytical and finite element predictions and show reasonably good agreement.

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