Uniform Flow Over a Bi-axial Stretching Surface

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Numerical Integration ◽  
Stokes Equations ◽  
Uniform Flow ◽  
Navier Stokes ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Similarity Transform ◽  
Axial Stretching

The uniform flow over a bi-axial stretching surface is studied by similarity transform of the Navier–Stokes equations and an efficient numerical integration of the resulting ordinary differential equations. The uniform flow induces a net shear stress (and drag), which is increased by lateral stretching. Heat transfer from the surface is also determined.

Melting From a Horizontal Rotating Disk

1989 ◽  
Vol 56 (1) ◽  
pp. 47-50 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Heat Transfer ◽  
Numerical Integration ◽  
Stokes Equations ◽  
Rotating Disk ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Relative Importance ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Transfer Rates

Melting of a disk is facilitated by rotation. The problem is governed by a nondimensional parameter α which represents the relative importance of injection (melt) rate and rotation times viscosity. The nonlinear governing equations are solved by perturbations for small α and numerical integration for arbitrary α. Torque and heat transfer rates are found. The solution is one of the rare exact similarity solutions of the Navier-Stokes equations.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Reynolds Numbers ◽  
Drop Impact ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Viscous Drop

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.

Modeling and analysis of solar air channels with attachments of different shapes

2019 ◽  
Vol 29 (5) ◽  
pp. 1815-1845 ◽  
Author(s):  
Younes Menni ◽  
Ahmed Azzi ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Research Work ◽  
Convection Heat Transfer ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Modeling And Analysis ◽  
Air Channels

Purpose This paper aims to report the results of numerical analysis of turbulent fluid flow and forced-convection heat transfer in solar air channels with baffle-type attachments of various shapes. The effect of reconfiguring baffle geometry on the local and average heat transfer coefficients and pressure drop measurements in the whole domain investigated at constant surface temperature condition along the top and bottom channels’ walls is studied by comparing 15 forms of the baffle, which are simple (flat rectangular), triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, double V (or W), Z, T, G and epsilon (or e)-shaped, with the Reynolds number changing from 12,000 to 32,000. Design/methodology/approach The baffled channel flow model is controlled by the Reynolds-averaged Navier–Stokes equations, besides the k-epsilon (or k-e) turbulence model and the energy equation. The finite volume method, by means of commercial computational fluid dynamics software FLUENT is used in this research work. Findings Over the range investigated, the Z-shaped baffle gives a higher thermal enhancement factor than with simple, triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, W, T, G and e-shaped baffles by about 3.569-20.809; 3.696-20.127; 3.916-20.498; 1.834-12.154; 1.758-12.107; 7.272-23.333; 6.509-22.965; 8.917-26.463; 8.257-23.759; 5.513-18.960; 8.331-27.016; 7.520-26.592; 6.452-24.324; and 0.637-17.139 per cent, respectively. Thus, the baffle of Z-geometry is considered as the best modern model of obstacles to significantly improve the dynamic and thermal performance of the turbulent airflow within the solar channel. Originality/value This analysis reports an interesting strategy to enhance thermal transfer in solar air channels by use of attachments with various shapes

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

Measurement and Calculation of Nozzle Guide Vane End Wall Heat Transfer

1998 ◽  
Author(s):  
Neil W. Harvey ◽  
Martin G. Rose ◽  
John Coupland ◽  
Terry Jones
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Guide Vane ◽  
Correction Method ◽  
Navier Stokes ◽  
Design Data ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Transfer Rates ◽  
Nozzle Guide

A 3-D steady viscous finite volume pressure correction method for the solution of the Reynolds averaged Navier-Stokes equations has been used to calculate the heat transfer rates on the end walls of a modern High Pressure Turbine first stage stator. Surface heat transfer rates have been calculated at three conditions and compared with measurements made on a model of the vane tested in annular cascade in the Isentropic Light Piston Facility at DERA, Pyestock. The NGV Mach numbers, Reynolds numbers and geometry are fully representative of engine conditions. Design condition data has previously been presented by Harvey and Jones (1990). Off-design data is presented here for the first time. In the areas of highest heat transfer the calculated heat transfer rates are shown to be within 20% of the measured values at all three conditions. Particular emphasis is placed on the use of wall functions in the calculations with which relatively coarse grids (of around 140,000 nodes) can be used to keep computational run times sufficiently low for engine design purposes.

The turning couples on an elliptic particle settling in a vertical channel

1994 ◽  
Vol 271 ◽  
pp. 1-16 ◽  
Author(s):  
Peter Y. Huang ◽  
Jimmy Feng ◽  
Daniel D. Joseph
Keyword(s):  
Shear Stress ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Vertical Channel ◽  
Navier Stokes ◽  
Front Face ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Back Face ◽  
The One

We do a direct two-dimensional finite-elment simulation of the Navier–Stokes equations and compute the forces which turn an ellipse settling in a vertical channel of viscous fluid in a regime in which the ellipse oscillates under the action of vortex shedding. Turning this way and that is induced by large and unequal values of negative pressure at the rear separation points which are here identified with the two points on the back face where the shear stress vanishes. The main restoring mechanism which turns the broadside of the ellipse perpendicular to the fall is the high pressure at the ‘stagnation point’ on the front face, as in potential flow, which is here identified with the one point on the front face where the shear stress vanishes.

Utilizing Schlieren Imaging to Visualize Heat Transfer Studies

2014 ◽  
Author(s):  
Jacob C. Kaessinger ◽  
Kramer C. Kors ◽  
Jordan S. Lum ◽  
Heather E. Dillon ◽  
Shannon K. Mayer
Keyword(s):  
Heat Transfer ◽  
Undergraduate Students ◽  
Cfd Simulation ◽  
Stokes Equations ◽  
Imaging System ◽  
Empirical Science ◽  
Navier Stokes ◽  
Schlieren Imaging ◽  
Navier Stokes Equations ◽  
Imaging Device

Convective heat transfer beyond explicit solutions to the Navier Stokes equations is often an empirical science. Schlieren imaging is one of the only fluid imaging systems that can directly visualize the density gradients of a fluid using collimated light and refractive properties. The ability to visualize fluid densities is useful in both research and educational fields. A Schlieren imaging device has been constructed by undergraduate students at the University of Portland. The device is used for professorial heat transfer and fluid dynamics research and to help undergraduates visualize and understand natural convection. This paper documents the design decisions, design process, and the final specifications of the Schlieren system. A simple 2-D heated cylindrical model is considered and evaluated using Schlieren imaging, OpenFOAM C.F.D. simulation, and convection analysis using a Nusselt correlation. Results are presented for the three analysis techniques and show excellent verifications between the CFD simulation, Nusselt correlation, and Schlieren imaging system.

scholarly journals Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions

2013 ◽  
Vol 45 (3) ◽  
pp. 742-772
Author(s):  
G. N. Milstein ◽  
M. V. Tretyakov
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Weak Sense ◽  
Periodic Boundary Conditions ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Probabilistic Nature

We propose and study a number of layer methods for Navier‒Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic.

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