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.

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.

Numerical Study of Non-Newtonian Maxwell Fluid in the Region of Oblique Stagnation Point Flow over a Stretching Sheet

2015 ◽  
Vol 32 (2) ◽  
pp. 175-184 ◽  
Author(s):  
T. Javed ◽  
A. Ghaffari
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Maxwell Fluid ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Parameter Ratio ◽  
Two Dimensional Flow

AbstractIn this article, a numerical study is carried out for the steady two-dimensional flow of an incompressible Maxwell fluid in the region of oblique stagnation point over a stretching sheet. The governing equations are transformed to dimensionless boundary layer equations. After some manipulation a system of ordinary differential equations is obtained, which is solved by using parallel shooting method. A comparison with the previous studies is made to show the accuracy of our results. The effects of involving parameters are discussed in detail and the streamlines are drawn to predict the flow pattern of the fluid. It is observed that increasing velocities ratio parameter (ratio of straining to stretching velocity) helps to decrease the boundary layer thickness. Furthermore, the velocity of fluid increases by increasing the obliqueness parameter.

A Numerical Study of Separating Supersonic Laminar Boundary Layers

1973 ◽  
Vol 40 (3) ◽  
pp. 679-684 ◽  
Author(s):  
M. J. Werle ◽  
G. D. Senechal
Keyword(s):  
Numerical Study ◽  
Supersonic Boundary Layer ◽  
Cold Wall ◽  
Governing Equations ◽  
Flat Plates ◽  
Number Range ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Implicit Finite Difference ◽  
Supersonic Laminar

A numerical study has been made of the nature of the solution to the supersonic boundary-layer equations when the flow separates from the surface. To this end, implicit finite-difference solutions to the governing equations were obtained for linearly and quadratically retarded flows over flat plates for a Mach number range of 2–15. Both extremely hot and cold-wall conditions are considered. The resutls of this study give strong evidence that all noninteracting flows are singular at separation.

scholarly journals On The Numerical Solutions of Boundary Layer Equations of Williamson Fluid Past a Moving Plate

2020 ◽  
Vol 8 (2) ◽  
pp. 75-80
Author(s):  
Manisha Patel ◽  
Jayshri Patel ◽  
M.G.Timol
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Flow Problem ◽  
Governing Equations ◽  
Moving Plate ◽  
Williamson Fluid ◽  
Boundary Layer Equations ◽  
Reduced Equations ◽  
Layer Flow ◽  
Graphical Presentation

Laminar boundary layer flow of Williamson fluid over a moving plate is discussed in this paper. The governing equations of the flow problem are transformed into similarity equations using similarity technique. The reduced equations are numerically solved by finite difference method. The graphical presentation is discussed.

scholarly journals Numerical Solution for Mixed Convection Heat Transfer from a Vertical Heated Plate Embedded in a Sparsely Packed Porous Medium

2011 ◽  
Vol 10 (2) ◽  
pp. 37-52
Author(s):  
N. Nalinakshi ◽  
P.A. Dinesh ◽  
I.S. Shivakumara ◽  
D.V. Chandrashekar
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Mixed Convection ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Heated Plate ◽  
Similarity Transformations ◽  
Layer Flow

An improved numerical study on mixed convection from a heated vertical plate embedded in a Newtonian fluid saturated sparsely packed porous medium is undertaken by considering the variation of permeability, porosity and thermal conductivity. The boundary layer flow in the porous medium is governed by Lapwood – Forchheimer – Brinkman extended Darcy model. Similarity transformations are employed and the resulting ordinary differential equations are solved numerically by using shooting algorithm with Runge – Kutta – Fehlberg integration scheme to obtain velocity and temperature distributions. Besides, skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence in decreasing the flow field, whereas its influence is reversed on the rate of heat transfer for all values of permeability considered. Further, the obtained results under the limiting conditions were found to be in good agreement with the existing ones.

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 The analysis of the suction/injection on the MHD Maxwell fluid past a stretching plate in the presence of nanoparticles by Lie group method

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Limei Cao ◽  
Xinhui Si ◽  
Liancun Zheng ◽  
Huihui Pang
Keyword(s):  
Lewis Number ◽  
Maxwell Fluid ◽  
Elastic Parameter ◽  
Group Method ◽  
Physical Parameters ◽  
Governing Equations ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Runge Kutta Method ◽  
Stretching Plate

AbstractIn this paper, the magnetohydrodynamic (MHD) Maxwell fluid past a stretching plate with suction/ injection in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations are solved numerically using Bvp4c with MATLAB, which is a collocation method equivalent to the fourth order mono-implicit Runge-Kutta method. The effects of some physical parameters, such as the elastic parameter K, the Hartmann number M, the Prandtl number Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le, on the velocity, temperature and nanoparticle fraction are studied numerically especially when suction and injection at the sheet are considered.

scholarly journals Numerical Solution of MHD Nanofluid Over a Stretching Surface with Chemical Reaction and Viscous Dissipation

2020 ◽  
Vol 21 (1) ◽  
pp. 36-45
Author(s):  
G Narender ◽  
Santoshi Misra ◽  
K Govardhan
Keyword(s):  
Boundary Layer ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Physical Parameters ◽  
Engineering Research ◽  
Boundary Layer Equations ◽  
State Boundary ◽  
Layer Flow

The main objective of this paper is to focus on a numerical study of chemical reaction and viscous dissipation effects on the steady state boundary layer flow of MHD nanofluid past the horizontally stretching sheet with the existence of nanoparticles. A proper similarity transformation is utilized to convert the boundary layer equations into the nonlinear and coupled ordinary differential equations. These ODEs are sorted out numerically by applying the shooting mechanism. Graphical representations are also included to explain the effect of evolving parameters against the above-mentioned distributions. Significance of different physical parameters on dimensionless velocity, temperature and concentration are elaborated through graphs and tables. For increasing values of Eckert number, the temperature profile increases whereas the chemical reaction parameter increases, the boundary layer thickness decreases. Chemical Engineering Research Bulletin 21(2019) 36-45

A numerical study of hybrid nanofluids near an irregular 3D surface having slips and exothermic effects

2021 ◽  
pp. 095440892110647
Author(s):  
Mumtaz Khan ◽  
Amer Rasheed
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Skin Friction ◽  
Numerical Study ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Slip Effects ◽  
Hybrid Nanofluids

The current article presents a comprehensive investigation of MHD viscous flow of hybrid-nanofluids (Al2O3 − Ag/ water and (Al2O3 − Cu/) over a horizontally irregular 3D plane with non-uniform thickness combined with slip effects. The foremost aim of conducting this study is to enhance thermal transportation. Based on the following novelties, the subject study holds tremendous significance: i. A comparative analysis of two hybrid nanofluids with hybrid-base fluid together with slip effects ii. An exclusive study where the Tiwari and Das nanofluid model is employed combined with Fourier's heat flux model iii. Development of finite-difference code which implements the three-stage Lobatto IIIa approach for the designed problem. We have used suitable scaling transformations to convert the three-dimensional conservation equations of mass, momentum, and energy into a dimensionless system of boundary layer equations. The numerical solution of the coupled non-linear boundary layer problem is determined using the built-in finite-difference code designed to employ the three-stage Lobatto IIIa formula. A comprehensive assessment is carried out in how the velocity components, temperature, skin friction, and heat transfer rate are affected by the physical parameters of interest. The same is presented through graphs and in tabular form to offer a pictorial overview. The fluctuating trends of skin friction coefficients (x, y-directions) and Nusselt number are investigated to explore the physical landscape of the current study. The findings of this study offer a noticeable contrast to their existing counterparts.

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

2017 ◽  
Vol 6 (10) ◽  
pp. 116
Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Transfer Flow

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

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