scholarly journals Development of a Mathematical Model of an Arc Plasma Discharge in Vacuum, Describing the Joint Solution of the Navier-Stokes Equations, Heat Transfer, with Equations of Plasma Theory

2020 ◽  
Vol 969 ◽  
pp. 012102
Author(s):  
I V Sitnikov ◽  
D N Trushnikov ◽  
G L Permyakov
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Stokes Equations ◽  
Plasma Discharge ◽  
Navier Stokes ◽  
Arc Plasma ◽  
Navier Stokes Equations ◽  
Joint Solution ◽  
Plasma Theory

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.

Mathematical study of a single leukocyte in microchannel flow

2018 ◽  
Vol 13 (5) ◽  
pp. 43 ◽  
Author(s):  
S. Boujena ◽  
O. Kafi ◽  
A. Sequeira
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Microchannel Flow ◽  
Navier Stokes Equations ◽  
Coupled Problem ◽  
Inflammatory Drugs ◽  
The Mathematical Model ◽  
Rate Type

The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.

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

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.

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.

Validation of a Numerical Method for Unsteady Flow Calculations

1993 ◽  
Vol 115 (1) ◽  
pp. 110-117 ◽  
Author(s):  
M. Giles ◽  
R. Haimes
Keyword(s):  
Heat Transfer ◽  
Flat Plate ◽  
Numerical Method ◽  
Stokes Equations ◽  
Companion Paper ◽  
Ideal Gas ◽  
Euler Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Loss Prediction

This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier–Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier–Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space–time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

Numerical Simulation of the Cooling Process of Cubic Shells

2011 ◽  
Author(s):  
Manabu Okura ◽  
Kiyoaki Ono
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Numerical Code ◽  
Navier Stokes ◽  
Cooling Process ◽  
Air Velocity ◽  
Navier Stokes Equations ◽  
The Difference ◽  
The Heat Transfer Coefficient

In order to keep the environment in an air-conditioned room comfortable, it is important to anticipate the air velocity and temperature fields precisely. The numerical code, solving simultaneously the Navier-Stokes equations governing flow field inside and outside the room and the heat conduction equation applying to walls, are developed. The assumption that the heat transfer coefficient between the fluid and the surface of solids is not used. This code is applied to investigate the cooling process of a cubic shell. The computational results agree with the experimental results. We also investigated the same process of the cubic shells whose walls are internally or externally insulated. The difference of the amount of heat transfer will be discussed.

scholarly journals Natural convection melting of nano-enhanced phase change material in a cavity with finned copper profile

2018 ◽  
Vol 240 ◽  
pp. 01006 ◽  
Author(s):  
Nadezhda Bondareva ◽  
Mikhail Sheremet
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Melting Process ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Dimensional Approximation ◽  
Change Material

Present study is devoted to numerical simulation of heat and mass transfer inside a cooper profile filled with paraffin enhanced with Al2O3 nanoparticles. This profile is heated by the heat-generating element of constant volumetric heat flux. Two-dimensional approximation of melting process is described by the Navier-Stokes equations in non-dimensional variables such as stream function, vorticity and temperature. The enthalpy formulation has been used for description of the heat transfer. The influence of volume fraction of nanoparticles and intensity of heat generation on melting process and natural convection in liquid phase has been studied.

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