Flow Instabilities and Heat Transfer in Buoyancy Driven Flows of Inelastic Non-Newtonian Fluids in Inclined Rectangular Cavities

2010 ◽  
Author(s):  
Dennis Siginer ◽  
Lyes Khezzar
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Heat Transfer Rate ◽  
Power Law ◽  
Transfer Rate ◽  
Newtonian Fluids ◽  
Two Dimensional ◽  
Aspect Ratios ◽  
Flow Configurations ◽  
Rayleigh Numbers

Steady two-dimensional natural convection in rectangular two dimensional cavities filled with non-Newtonian power law-Boussinesq fluids is numerically investigated. The conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0° and 90° and two cavity height based Rayleigh numbers, Ra = 104 and 105, a Prandtl number of Pr = 102 and two cavity aspect ratios of 1, 4. For the vertical inclination of 90°, computations were performed for two Rayleigh numbers Ra = 104 and 105 and three Prandtl numbers of Pr = 102, 103 and 104. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. A comprehensive comparison between the Newtonian and the non-Newtonian cases is presented based on the dependence of the average Nusselt number Nu on the angle of inclination together with the Rayleigh number, Prandtl number, power law index n and aspect ratio dependent flow configurations which undergo several exchange of stability as the angle of inclination O̸ is gradually increased from the horizontal resulting in a rather sudden drop in the heat transfer rate triggered by the last loss of stability and transition to a single cell configuration. Despite significant differences in the heat transfer rate and flow configurations both Newtonian and non-Newtonian fluids of the power law type exhibit qualitatively similar behavior.

Natural Convective Heat Transfer From an Inclined Narrow Isothermal Flat Plate

2008 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Abdulrahim Kalendar
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Adiabatic Surface ◽  
Plate Width

Natural convective heat transfer rate from an isothermal flat plate inclined at moderate angles to the vertical has been numerically studied. When the plate is wide compared to its height the flow can be adequately modeled by assuming two-dimensional flow. However, when the width of the plate is relatively small compared to its height, the heat transfer rate can be considerably greater than that predicted by these two-dimensional flow results. The heat transfer from a narrow isothermal plate embedded in a plane adiabatic surface, the adiabatic surface being in the same plane as the heated plate and inclined at an angle to the vertical has been numerically considered. Results for both positive and negative inclination angles have been numerically determined here. Attention was restricted to results for a Prandtl number of 0.7; this being approximately the value existing in the application that originally motivated this study. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in dimensionless form. The solution was obtained using a commercial finite element method based code, FIDAP. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, and the Prandtl number as parameters. Results have been obtained for Rayleigh numbers between 103 and 107 for ratios of the plate width to the plate height of between 0.3 and 1.5 and for angles of inclination between +45° and −45°.

A Numerical Study of Three-Dimensional Natural Convective Heat Transfer From a Plate With a “Wavy” Surface

2001 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Matt Garrett
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Wavy Surface ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
The Mean

Abstract 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 parallel to the direction of flow over the surface and have a relatively small amplitude. Two types of wavy surface have been considered here — saw-tooth and sinusoidal. Surfaces of the type considered are approximate models of situations that occur in certain window covering applications, for example, and are also sometimes used to try to enhance the heat transfer rate from the surface. The flow has been assumed to be laminar. Because the surface waves are parallel to the direction of flow, the flow over the surface will be three-dimensional. 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 type approximation. The governing equations have been written in dimensionless form, the height of the surface being used as the characteristic length scale and the temperature difference between the surface temperature and the temperature of the fluid far from the plate being used as the characteristic temperature. The dimensionless equations have been solved using a finite-element method. Although the flow is three-dimensional because the surface waves are all assumed to have the same shape, the flow over each surface thus being the same, and it was only necessary to solve for the flow over one of the surface waves. The solution has the following parameters: the Grashof number based on the height, the Prandtl number, the dimensionless amplitude of the surface waviness, the dimensionless pitch of the surface waviness, and the form of the surface waviness (saw-tooth or sinusoidal). Results have been obtained for a Prandtl number of 0.7 for Grashof numbers up to 106. The effects of Grashof number, dimensionless amplitude and dimensionless pitch on the mean heat transfer rate have been studied. It is convenient to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface. A comparison of the values of these quantities gives a measure of the effectiveness of the surface waviness in increasing the mean heat transfer rate. The results show that while surface waviness increases the heat transfer rate based on the frontal area, the modifications of the flow produced by the surface waves are such that the increase in heat transfer rate is less than the increase in surface area.

scholarly journals Maximum Heat Transfer Rate Density in Two-Dimensional Minichannels and Microchannels

2003 ◽  
Author(s):  
M. Favre-Marinet ◽  
S. Le Person ◽  
A. Bejan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Transition To Turbulence ◽  
Experimental Investigations ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Optimal Spacing

Experimental investigations of the flow and the associated heat transfer were conducted in two-dimensional microchannels in order to test possible size effects on the laws of hydrodynamics and heat transfer and to infer optimal conditions of use from the measurements. The test section was designed to modify easily the channel height e between 1 mm and 0.1 mm. Measurements of the overall friction factor and local Nusselt numbers show that the classical laws of hydrodynamics and heat transfer are verified for e > 0.4 mm. For lower values of e, a significant decrease of the Nusselt number is observed, whereas the Poiseuille number continues to have the conventional value of laminar developed flow. The transition to turbulence is not affected by the channel size. For fixed pressure drop across the channel, a maximum of heat transfer rate density is found for a particular value of e. The corresponding dimensionless optimal spacing and heat transfer rate density are in very good agreement with the predictions of Bejan and Sciubba (1992). This paper is the first time that the optimal spacing between parallel plates is determined experimentally.

Effect of a Pair of Horizontal Frame Members on the Convective Heat Transfer With Laminar and Turbulent Flow From a Recessed Window to a Room

2011 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
David Naylor
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Turbulent Flows ◽  
Heat Transfer Rate ◽  
Convective Heat ◽  
Transfer Rate ◽  
Numerical Study ◽  
Wall Functions ◽  
Inner Surface

The horizontal frame members that often protrude from the inner surface of a window can significantly effect the convective heat transfer rate from this inner surface to the room. The purpose of the present numerical study was to determine how the size of a pair of horizontal frame members effect this heat transfer rate. The flow has been assumed to be steady and conditions under which laminar, transitional, and turbulent flows occur are considered. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being dealt with using the Boussinesq approach. The governing equations have been solved using the FLUENT commercial CFD code. The k-epsilon turbulence model with standard wall functions and with buoyancy force effects fully accounted for has been used. The solution has the following parameters: the Rayleigh number, the Prandtl number, the dimensionless window recess depth, and the dimensionless width and depth of the frame members. Results have been obtained for a Prandtl number of 0.74.

A Numerical Study of Laminar and Turbulent Natural Convective Heat Transfer From an Isothermal Vertical Plate With a Wavy Surface

2010 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Convective Heat Transfer ◽  
Transfer Rate ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
Buoyancy Forces ◽  
Rayleigh Numbers

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 main purpose of the study was to examine the effect of the surface waviness on the conditions under which transition from laminar to turbulent flow occurred and to study the effect of the surface waviness on the heat transfer rate. The surface waves, which have a saw-tooth cross-sectional shape, are normal to the direction of flow over the surface and have a relatively small amplitude. The range of Rayleigh numbers considered in the present study extends from values that for a non-wavy 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 type approximation. A standard k-epsilon turbulence model with full account being taken of the effects of the buoyancy forces has been used in obtaining the solution. The solution has been obtained using the commercial CFD solver FLUENT. The solution has the following parameters: the Rayleigh number based on the plate height, the Prandtl number, the dimensionless amplitude of the surface waviness, and the dimensionless pitch of the surface waviness. Results have been obtained for a Prandtl number of 0.7 and for a single dimensionless pitch value for Rayleigh numbers between approximately 106 and 1012. The effects of Rayleigh number and dimensionless amplitude on the mean heat transfer rate have been studied. It is convenient in presenting the results to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface.

Alumina nanoparticle flow within a channel with permeable walls

2020 ◽  
Vol 31 (04) ◽  
pp. 2050050 ◽  
Author(s):  
Tran Dinh Manh ◽  
Nguyen Dang Nam ◽  
Gihad Keyany Abdulrahman ◽  
R. Moradi ◽  
Houman Babazadeh
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Power Law ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Expansion Ratio ◽  
Hydrodynamic Characteristics ◽  
Stream Velocity ◽  
Main Stream ◽  
The Impact

The application of the nanoparticles for the heat transfer augmentation has extensively increased in the scientific and industrial applications. In this research, semi-analytic method is used to disclose the heat transmission and flow feature of the fluid with nanoparticles among the two parallel sheets. In our model, one plate is warmed with specific heat flux while fluid is streamed from another plate which extends over times. Nanoparticles of Al2O3 are applied in the main fluid to obtain nanofluid flow. To obtained viscosity coefficient and heat conductivity of the base fluid with nanoparticles, Koo–Kleinstreuer–Li (KKL) formula is applied as reliable approach. Comprehensive investigations on different factors are done to disclose the impact of important aspects such as volume fraction of the nanoparticles, main stream velocity and expansion ratio on the main thermal and hydrodynamic characteristics of the nanofluid. It was found that the rate of the Nusselt number upsurges when the velocity of main stream, volume portion of the nanoparticles and power law index is increased. However, the increasing of the expansion ratio declines the heat transfer rate in our model. Our findings disclose that heat transfer rate is directly proportional with velocity of nanofluid as index of power law equals to zero.

Numerical Simulation of Natural Convection in a Two-Dimensional Enclosure Filled with Nanofluids

2012 ◽  
Vol 560-561 ◽  
pp. 1184-1187
Author(s):  
Su Fen Zhao ◽  
Xin Fang Li
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Process ◽  
Transfer Rate ◽  
Mass Fraction ◽  
Heat Transfer Process ◽  
Two Dimensional ◽  
Grashof Number ◽  
Transfer Properties

The natural convection of nanofluids in a two-dimensional enclosure is numerically simulated with Fluent software. The effect of copper particle concentration and Grashof number on heat transfer properties is investigated. The results indicate that the suspended copper nanoparticles substantially increase the heat transfer rate at any given Grashof number, and the heat transfer rate of the nanofluid increases remarkably with the mass fraction of nanoparticles. For a given initial Grashof number, as the mass fraction increases, the velocity components of nanofluid increase as a result of an increase in the energy transport through the fluid. In addition, the intensity of the streamline increase with the increases of the Grashof number, which indicate the heat transfer properties are enhanced. The heat transfer process is dominant with the heat exchange at low Gr, while the heat transfer process is dominant with the natural convection at high Gr.

Experimental Study of Free Convection Heat Transfer From a Fin Attached Cylinder Confined Between Tilt and Low Conductive Plates

2010 ◽  
Author(s):  
Amir Abbas Rezaei ◽  
Masoud Ziabasharhagh ◽  
Tooraj Yousefi ◽  
Mehran Ahmadi
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Convection Heat Transfer ◽  
Cylinder Surface ◽  
Convection Heat ◽  
Number Range ◽  
Rayleigh Numbers ◽  
Chimney Effect

Steady state and two-dimensional natural convection heat transfer flow around a horizontal and isothermal cylinder with a longitudinal fin attached to it that is located between two tilt and very low conductive plates is studied experimentally by using a Mach-Zehnder interferometer. Effects of the plates slope angel (θ) on heat transfer from the tube is investigated for Rayleigh number ranging from 1000 to 15500. Experiments are done for a fin attached cylinder placed between two low conductive plates. Two different diameter tubes with diameters of D=10 and 20mm are utilized for broad Rayleigh number range. Results specify that, heat transfer experience differs for special Rayleigh numbers. For Rayleigh numbers ranging less than 5500, rate of heat transfer amount from the cylinder surface is less than that of a lone cylinder and it’s the result of no slip boundary condition on the fin surface. For this range of Rayleigh number by the use of plates, heat transfer from the cylinder surface decreases slightly and plates leaning does not alter heat transfer speed from the cylinder surface. For Rayleigh number ranging from 5500 to 15500, heat transfer rate from the cylinder surface is lower than the heat transfer rate from the surface of an individual cylinder. Though, by adding placing the low conductive plates as plates to experimental model, heat transfer system differs and chimney effect between fin and the plates increases the heat transfer from the cylinder surface. By increasing the plates slope angel from 0° to 20°, the chimney effect between plates and fin weakens and heat transfer rate from the tube surface is going to the amount of heat transfer rate from a fin attached cylinder which is not placed between plates.

Convective Heat Transfer Augmentation in Thermal Entrance Regions by means of Thermal Instability

1979 ◽  
Vol 101 (2) ◽  
pp. 222-226 ◽  
Author(s):  
Y. Kamotani ◽  
S. Ostrach ◽  
H. Miao
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Thermal Instability ◽  
Reynolds Numbers ◽  
Channel Height ◽  
Heat Transfer Augmentation ◽  
Critical Wavelength ◽  
Visualization Experiments ◽  
Rayleigh Numbers

The effects of thermal instability on a liminar thermally developing entrance flow between two horizontal plates heated from below are studied experimentally. The experiments cover a range of Rayleigh numbers between 2.2 × 104 and 2.1 × 105, and Reynolds numbers between 50 and 300 using air. Results for the heat transfer rate and entrance length show that they are influenced not only by the Rayleigh number but also by the ratio Re2/Gr. The heat transfer rate is increased as much as 4.4 times due to thermal instability. The flow visualization experiments show that the critical wavelength is determined by the channel height, not by the thermal boundary layer thickness.

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