A Solution of Freezing of Liquids of Low Prandtl Number in Turbulent Flow Between Parallel Plates

1977 ◽  
Vol 99 (1) ◽  
pp. 20-24 ◽  
Author(s):  
A. A. Shibani ◽  
M. N. O¨zis¸ik
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Freezing Temperature ◽  
Axial Position ◽  
Parallel Plates ◽  
Uniform Temperature

The steady-state freezing of liquids of low Prandtl number in turbulent flow between parallel plates, the walls of which are kept at uniform temperature lower than the freezing temperature of the liquid, is solved by matched asymptotic technique. The location of the liquid-solid interface and the heat transfer rate are established as a function of the axial position along the channel.

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.

Transient Freezing of Liquids in Turbulent Flow inside Tubes

1979 ◽  
Vol 101 (3) ◽  
pp. 465-468 ◽  
Author(s):  
Chul Cho ◽  
M. N. O¨zis¸ik
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Circular Tube ◽  
Freezing Temperature ◽  
Liquid Interface ◽  
Wall Heat Flux ◽  
Uniform Temperature ◽  
Solid Liquid Interface ◽  
Solid Liquid

The problem of freezing of a liquid in turbulent flow inside a circular tube whose wall is kept at a uniform temperature lower than the freezing temperature of the liquid is solved. The radius of the solid-liquid interface and the local wall heat flux are determined as a function of time and position along the tube for several different values of the Prandtl number and the freezing parameter.

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.

Heat transfer from hypersonic turbulent flow at a wedge compression corner

1972 ◽  
Vol 56 (4) ◽  
pp. 741-752 ◽  
Author(s):  
G. T. Coleman ◽  
J. L. Stollery
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Turbulent Flow ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Separated Flows ◽  
Rate Distribution ◽  
Compression Corner

A hypersonic gun tunnel has been used to measure the heat-transfer-rate distribution over a compression corner under turbulent boundary-layer conditions. Attached, incipient and separated flows are considered. The results are compared with other experimental data and with the predictions of a simple theory.

scholarly journals Non-linear radiation influence on oblique stagnation point flow of Maxwell fluid

2018 ◽  
Vol 64 (4) ◽  
pp. 420 ◽  
Author(s):  
Abuzar Ghaffari ◽  
T. Javed ◽  
I. Mustafa
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Maxwell Fluid ◽  
Stagnation Point Flow ◽  
Non Linear ◽  
Linear Radiation

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged through streamlines graphs. It is also observed that oblique stagnation point flow behaves like orthogonal stagnation point flow, when free stream velocity is very large as compared to stretching velocity.

scholarly journals Natural Convection from Four Circular Cylinders in Across Arrangement within Horizontal Annular Space

2020 ◽  
Vol 14 (2) ◽  
pp. 98-102
Author(s):  
Houssem Laidoudi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Prandtl Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Initial Conditions ◽  
Fluid Motion ◽  
Circular Cylinders ◽  
Thermal Buoyancy

AbstractNumerical investigation is accomplished to study the roles of governing parameters of natural convection on the fluid motion and heat transfer rate of four heated circular cylinders placed inside a circular enclosure of cold surface. The cylinders are positioned in across arrangement. The representative results are obtained within the ranges of initial conditions as: Prandtl number (Pr = 7.1 to 1000) and Rayleigh number (Ra = 103 to 105). The average Nusselt number of each inner cylinder is computed. The effects of thermal buoyancy strength on the fluid motion and temperature are also illustrated. It was found that the heat transfer rate of cylinders depends significantly on the position inside the enclosure. Moreover, the role of Prandtl number on flow and thermal patterns is negligible. The values of Nusselt number are also given, which can be useful for some engineering applications.

Numerical Study of the Heat Transfer Rate in a Helical Static Mixer

2006 ◽  
Vol 128 (8) ◽  
pp. 769-783 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Numerical Study ◽  
Three Dimensional ◽  
Static Mixer ◽  
Flow Conditions ◽  
Modern Approach ◽  
Static Mixers

In chemical processing industries, heating, cooling, and other thermal processing of viscous fluids are an integral part of the unit operations. Static mixers are often used in continuous mixing, heat transfer, and chemical reactions applications. In spite of widespread usage, the flow physics of static mixers is not fully understood. For a given application, besides experimentation, the modern approach to resolve this is to use powerful computational fluid dynamics tools to study static mixer performance. This paper extends a previous study by the authors on an industrial helical static mixer and investigates heat transfer and mixing mechanisms within a helical static mixer. A three-dimensional finite volume simulation is used to study the performance of the mixer under both laminar and turbulent flow conditions. The turbulent flow cases were solved using k−ω model. The effects of different flow conditions on the performance of the mixer are studied. Also, the effects of different thermal boundary conditions on the heat transfer rate in static mixer are studied. Heat transfer rates for a flow in a pipe containing no mixer are compared to that with a helical static mixer.

Enhancement and Prediction of Heat Transfer Rate in Turbulent Flow Through Tube With Perforated Twisted Tape Inserts: A New Correlation

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. U. Ahamed ◽  
M. A. Wazed ◽  
S. Ahmed ◽  
Y. Nukman ◽  
T. M. Y. S. Tuan Ya ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Circular Tube ◽  
Twisted Tape ◽  
Pumping Power ◽  
Plain Tube ◽  
Flow Through

An experimental investigation has been carried out for turbulent flow in a tube with perforated twisted tape inserts. The mild steel twisted tape inserts with circular holes of different diameters (i.e., perforation) are used in the flow field. An intensive laboratory study is conducted for heat transfer and pressure drop characteristics in the tubes for turbulent flow with various airflow rates. Heat transfer and pressure drop data are engendered for a wide range Reynolds number (1.3×104–5.2×104). Tube wall temperature, pressure drop, air velocity, and its temperature are measured both for plain tube and for tube with perforated twisted tape inserts. Heat transfer coefficients, Nusselt number, pumping power, and heat transfer effectiveness are calculated for both cases. Experimental results showed that perforated twisted inserts of different geometry in a circular tube enhanced the heat transfer rate with an increase in friction factor and pumping power for turbulent flow. The pumping power, heat transfer coefficient, and effectiveness in the tube with the twisted tape inserts are found to increase up to 1.8, 5.5, and 4.0 times of those for the plain tube for same Reynolds number, respectively. Finally, a correlation is developed for prediction of the heat transfer rate for turbulent flow through a circular tube with perforated twisted tape inserts.

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