Developing Fluid Flow and Heat Transfer in a Semi-Porous Square Channel

2003 ◽  
Author(s):  
Tien-Chien Jen ◽  
Tuan-Zhou Yan ◽  
S. H. Chan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Porous Channel ◽  
Navier Stokes ◽  
Axial Position ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A three-dimensional computational model is developed to analyze fluid flow in a semi-porous channel. In order to understand the developing fluid flow and heat transfer process inside the semi-porous channels, the conventional Navier-Stokes equations for gas channel, and volume-averaged Navier-Stokes equations for porous media layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain in a channel using the vorticity-velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature fields at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside semi-porous channel are also analyzed in the present study.

Numerical Computation of Fluid Flow and Heat Transfer in Microchannels

2005 ◽  
Author(s):  
Ningli Liu ◽  
Rene Chevray ◽  
Gerald A. Domoto ◽  
Elias Panides
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Time Dependent ◽  
Navier Stokes ◽  
Temperature Profiles ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A finite difference numerical approach for solving slightly compressible, time-dependent, viscous laminar flow is presented in this study. Simplified system of Navier-Stokes equations and energy equation are employed in the study in order to perform more efficient numerical calculations. Fluid flow and heat transfer phenomena in two dimensional microchannels are illustrated numerically in this paper. This numerical approach provides a complete numerical simulation of the development of the fluid flow and the temperature profiles through multi-dimensional microchannels.

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.

The Numerical Prediction of Viscous Flow and Heat Transfer in Tube Banks

1978 ◽  
Vol 100 (4) ◽  
pp. 565-571 ◽  
Author(s):  
B. E. Launder ◽  
T. H. Massey
Keyword(s):  
Heat Transfer ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Substantial Contribution ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Flow Domain ◽  
Tube Banks

A scheme for handling the numerical analysis of viscous flow and heat transfer in tube banks is presented. It involves the use of a cylindrical network of nodes in the vicinity of the tubes with a Cartesian mesh covering the remainder of the flow domain. The approach has been incorporated into the numerical solving algorithm for the Navier Stokes equations of Gasman, et al. [8]. A number of demonstration calculations is presented including a numerical simulation of the staggered square bank for which Bergelin and co-workers [4, 9] have reported experimental results for pressure drop and heat transfer rate. Agreement between predicted and measured characteristics is satisfactory when account is taken of end and entry effects that are present in the experiments but necessarily omitted from the calculations. Indeed the close agreement of the laminar predictions with measurements extends to Reynolds numbers in excess of 1000, a level at which it has hitherto been supposed that turbulent motion in the fluid made a substantial contribution to friction and heat transfer.

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

2006 ◽  
Vol 129 (1) ◽  
pp. 106-115 ◽  
Author(s):  
A. B. Rahimi ◽  
R. Saleh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Self Similar

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa2∕2υ, ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U0∕Γa, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

Cellular‐automaton fluids: A model for flow in porous media

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 509-518 ◽  
Author(s):  
Daniel H. Rothman
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Pressure Gradient ◽  
Cellular Automaton ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cellular Automaton Fluids

Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates the chief macroscopic parameters of interest—flow rate, permeability, viscosity, and pressure gradient—and may be invoked to solve for any of these parameters when the others are known. In practical situations, however, this solution may not be possible. Attention is then typically focused on the estimation of permeability, and numerous numerical methods based on knowledge of the microscopic pore‐space geometry have been proposed. Because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult, microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores, throats, and cracks. I propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries. This new method solves the Navier‐Stokes equations numerically using the cellular‐automaton fluid model introduced by Frisch, Hasslacher, and Pomeau. The cellular‐ automaton fluid is extraordinarily simple—particles of unit mass traveling with unit velocity reside on a triangular lattice and obey elementary collision rules—but is capable of modeling much of the rich complexity of real fluid flow. Cellular‐automaton fluids are applicable to the study of porous media. In particular, numerical methods can be used to apply the appropriate boundary conditions, create a pressure gradient, and measure the permeability. Scale of the cellular‐automaton lattice is an important issue; the linear dimension of a void region must be approximately twice the mean free path of a lattice gas particle. Finally, an example of flow in a 2-D porous medium demonstrates not only the numerical solution of the Navier‐Stokes equations in a highly irregular geometry, but also numerical estimation of permeability and a verification of Darcy’s law.

Heat Transfer Mode and Effect of Fluid Flow on the Morphology of the Weld Pool

2021 ◽  
Vol 406 ◽  
pp. 66-77
Author(s):  
Abdel Halim Zitouni ◽  
Pierre Spiteri ◽  
Mouloud Aissani ◽  
Younes Benkheda
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Weld Pool ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Transfer Mode ◽  
Thermal Fields ◽  
Welding Properties

In this work, the heat transfer by conduction and convection mode and effect of fluid flow on the morphology of the weld pool and the welding properties is investigated during Tungsten Inert Gas (TIG) process. In the first part, a computation code under Fortran was elaborated to solve the equations resulting from the finite difference discretization of the heat equation, taking into account the liquid-solid phase change with the associated boundary conditions. In order to calculate the velocity field during welding, the Navier-Stokes equations in the melt zone were simplified and solved considering their stream-vorticity formulation. A mathematical model was developed to study the effect of the melted liquid movement on the weld pool. The evolution of the fraction volume of the liquid and the thermal fields promoted the determination of the molten zone (MZ) and the Heat Affected Zone (HAT) dimensions, which seems to be in good agreement with literature.

A Numerical Simulation of Heat Pipe Application to the Cooling of Pulse Detonation Engines

2003 ◽  
Author(s):  
V. Dakshina Murty
Keyword(s):  
Heat Transfer ◽  
Heat Pipe ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Brinkman Model ◽  
Navier Stokes Equations ◽  
Pulse Detonation Engines ◽  
Pulse Detonation ◽  
Flow And Heat Transfer ◽  
Detonation Tube

A numerical method based on the finite elements is applied to the cooling of pulse detonation tube using heat pipe technology. Towards this end, the fluid flow and heat transfer in the wick are modeled as flow in a porous medium. The flow is described using the so called Darcy Brinkman model which has close resemblance to the Navier-Stokes equations. It is found that for Darcy numbers less than 0.0001 the results are indistinguishable from regular Darcy flows. The shape of the heat pipe is that of a fin with the proportion of the length of the evaporator section being varied. In this study two values of this ratio have been used, namely 1 and 0.5.

scholarly journals A pore scale study on fluid flow through two dimensional dual scale porous media with small number of intraparticle pores

2016 ◽  
Vol 18 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Safa Sabet ◽  
Moghtada Mobedi ◽  
Turkuler Ozgumus
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Permeability Tensor ◽  
Navier Stokes ◽  
Pore Scale ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Flow Through ◽  
Dual Scale

Abstract In the present study, the fluid flow in a periodic, non-isotropic dual scale porous media consisting of permeable square rods in inline arrangement is analyzed to determine permeability, numerically. The continuity and Navier-Stokes equations are solved to obtain the velocity and pressure distributions in the unit structures of the dual scale porous media for flows within Darcy region. Based on the obtained results, the intrinsic inter and intraparticle permeabilities and the bulk permeability tensor of the dual scale porous media are obtained for different values of inter and intraparticle porosities. The study is performed for interparticle porosities between 0.4 and 0.75 and for intraparticle porosities from 0.2 to 0.8. A correlation based on Kozeny-Carman relationship in terms of inter and intraparticle porosities and permeabilities is proposed to determine the bulk permeability tensor of the dual scale porous media.

A Numerical Study of the Influence of Disc Geometry on the Flow and Heat Transfer in a Rotating Cavity

1990 ◽  
Author(s):  
B. L. Lapworth ◽  
J. W. Chew
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Model Calculations ◽  
Flow And Heat Transfer ◽  
Rotating Cavity ◽  
Radial Outflow

Numerical solutions of the Reynolds-averaged Navier-Stokes equations have been used to model the influence of cobs and a bolt cover on the flow and heat transfer in a rotating cavity with an imposed radial outflow of air. Axisymmetric turbulent flow is assumed using a mixing length turbulence model. Calculations for the non-plane discs are compared with plane disc calculations and also with the available experimental data. The calculated flow structures show good agreement with the experimentally observed trends. For the cobbed and plane discs, Nusselt numbers are calculated for a combination of flow rates and rotational speeds; these show some discrepancies with the experiments, although the calculations exhibit the more consistent trend. Further calculations indicate that differences in thermal boundary conditions have a greater influence on Nusselt number than differences in disc geometry. The influence of the bolt cover on the heat transfer has also been modelled, although comparative measurements are not available.

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