Integral Analysis of Heat Transfer on Falling Laminar Liquid Film with Constant Heat Flux

2012 ◽  
Vol 516-517 ◽  
pp. 30-35
Author(s):  
You Shun Peng ◽  
Li Yang ◽  
Yong Cheng Du
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Liquid Film ◽  
Film Flow ◽  
Constant Heat Flux ◽  
Heated Plate ◽  
Flux Boundary Condition ◽  
Integral Analysis ◽  
Characteristic Relationship

Integral analysis of heat transfer of a laminar falling liquid film along a vertical heated plate with specified heat flux boundary condition was investigated. The temperature distribution of liquid film was obtained by utilizing an integral analysis method, which was compared with numerical solution and other researcher’s results. In this analysis a new concept of thermal changing point was put forward. It’s found that the Nusselt number has a characteristic relationship with thermal changing point, which is obtained by calculation. When the film flow distance is less than thermal changing point, the Nusselt number decreases rapidly. When the film flow distance is greater than or equal to thermal changing point, the Nusselt number reaches to a fixed value. A larger Peclet number or lower initial temperature generally leads to a larger Nusselt number in entrance region, whereas the wall heat flux is found to have no influence on the Nusselt number.

Laminar Slug Flow: Heat Transfer Characteristics With Constant Heat Flux Boundary

2009 ◽  
Author(s):  
P. A. Walsh ◽  
E. J. Walsh ◽  
Y. S. Muzychka
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Heat Transfer Performance ◽  
Constant Heat Flux ◽  
Transfer Performance ◽  
Segmented Flow ◽  
Constant Heat ◽  
Flux Boundary Condition ◽  
Flow Heat

The problem of elevated heat flux in modern electronics has led to the development of numerous liquid cooling devices which yield superior heat transfer coefficients over their air based counterparts. This study investigates the use of liquid/gas slug flows where a liquid coolant is segregated into discrete slugs, resulting in a segmented flow, and heat transfer rates are enhanced by an internal circulation within slugs. This circulation directs cooler fluid from the center of the slug towards the heated surface and elevates the temperature difference at the wall. An experimental facility is built to examine this problem in circular tube flow with a constant wall heat flux boundary condition. This was attained by Joule heating a thin walled stainless steel tube. Water was used as the coolant and air as the segregating phase. The flow rates of each were controlled using high precision syringe pumps and a slug producing mechanism was introduced for segmenting the flow into slugs of various lengths at any particular flow rate. Tube flows with Reynolds numbers in the range 10 to 1500 were examined ensuring a well ordered segmented flow throughout. Heat transfer performance was calculated by measuring the exterior temperature of the thin tube wall at various locations using an Infrared camera. Nusselt number results are presented for inverse Graetz numbers over four decades, which spans both the thermally developing and developed regions. The results show that Nu in the early thermally developing region are slightly inferior to single phase flows for heat transfer performance but become far superior at higher values of inverse Gr. Additionally, the slug length plays an important role in maximizing Nusselt number in the fully developed region as Nu plateaus at different levels for slugs of differing lengths. Overall, this paper provides a new body of experimental findings relating to segmented flow heat transfer in constant heat flux tubes without boiling. Put abstract text here.

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

On Effects of Temperature Boundary Conditions on Heat Transfer in Turbulent Low-Prandtl-Number Flows

2020 ◽  
Author(s):  
Ivan Otic
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Flux Boundary Condition ◽  
Large Eddy ◽  
Heat Flux Boundary Condition ◽  
Effects Of Temperature

Abstract One important issue in understanding and modeling of turbulent heat transfer is the behavior of fluctuating temperature close to the wall. Common engineering computational approach assumes constant heat flux boundary condition on heated walls. In the present paper constant heat flux boundary condition was assumed and effects of temperature fluctuations are investigated using large eddy simulations (LES) approach. A series of large eddy simulations for two geometries is performed: First, forced convection in channels and second, forced convection over a backward facing step. LES simulation data is statistically analyzed and compared with results of direct numerical simulations (DNS) from the literature which apply three cases of heat flux boundary conditions: 1. ideal heat flux boundary condition, 2. non-ideal heat flux boundary condition, 3. conjugate heat transfer boundary condition. For low Prandtl number flows LES results show that, despite very good agreement for velocities and mean temperature, predictions of temperature fluctuations may have strong deficiencies if simplified boundary conditions are applied.

scholarly journals Convection Heat Transfer Analysis in A Vertical Porous Tube

2020 ◽  
Vol 8 (1) ◽  
pp. 31-45
Author(s):  
Hikmat N. Abdulkareem ◽  
Kifah H. Hilal
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convection Heat Transfer ◽  
Particle Diameter ◽  
Vertical Channel ◽  
Packed Bed ◽  
Constant Heat Flux ◽  
Heat Transfer Analysis ◽  
Constant Heat ◽  
Flux Boundary Condition

Forced convective heat transfer in a vertical channel symmetrically heated with a constant heat flux, and packed with saturated porous media, has been investigated experimentally in the present work. The channel was padded with spherical glass of three diameter (1, 3 and 10 mm) in a range 0.0416 < (particle diameter / inner channel radius) <0.416. The experimental setup, using a copper tube as a packed bed assembly with (48 mm) inside diameter and (1150 mm) heated length with a constant heat flux boundary condition. The test section was vertically oriented with water flowing against gravity and packed with glass spheres (1, 3 and 10 mm) diameter respectively. The results show that local Nusselt number increased at 34% with increasing Reynolds number at 65% while increased at 11% with increasing heat flux at 71%. Heat transfer rate increase as the particle diameter increase at the range of (1 – 3) mm but decrease with increasing particle diameter at the range (3 – 10) mm. Pressure drop through channel minimize at 97% as porosity increase at 23%.Many empirical relations, obtained experimentally.

scholarly journals Numerical study of combined convection heat transfer for thermally developing upward flow in a vertical cylinder

2008 ◽  
Vol 12 (2) ◽  
pp. 89-102 ◽  
Author(s):  
Hussein Mohammed ◽  
Yasin Salman
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Temperature Profile ◽  
Local Nusselt Number ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Flux Boundary Condition ◽  
Number Range ◽  
Dimensionless Velocity

The problem of the laminar upward mixed convection heat transfer for thermally developing air flow in the entrance region of a vertical circular cylinder under buoyancy effect and wall heat flux boundary condition has been numerically investigated. An implicit finite difference method and the Gauss elimination technique have been used to solve the governing partial differential equations of motion (Navier Stocks equations) for two-dimensional model. This investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m2 to 400 W/m2. The results present the dimensionless temperature profile, dimensionless velocity profile, dimensionless surface temperature along the cylinder, and the local Nusselt number variation with the dimensionless axial distance Z+. The dimensionless velocity and temperature profile results have revealed that the secondary flow created by natural convection have a significant effect on the heat transfer process. The results have also shown an increase in the Nusselt number values as the heat flux increases. The results have been compared with the available experimental study and with the available analytical solution for pure forced convection in terms of the local Nusselt number. The comparison has shown satisfactory agreement. .

scholarly journals EFFECT OF CAVITY RATIO ON HEAT TRANSFER BY FREE LOAD FROM HEATED PLATES UPWARD WITH CONSTANT HEAT FLUX

2021 ◽  
Vol 9 (12) ◽  
pp. 686-695
Author(s):  
Waleed Abdulhadiethbayah ◽  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Free Convection ◽  
Electronic Devices ◽  
Experimental Studies ◽  
Constant Heat Flux ◽  
Rate Of Change ◽  
Constant Heat ◽  
The Difference

Many engineering and industrial applications always seek to find ways to dissipate heat from heated surfaces used in these industries. As it is involved in the cooling of electronic parts and electrical transformers, as well as the design of solar collectors, in addition to being a process of heat exchange between hot surfaces and the fluids in contact with them. Since most electronic devices or their parts are cooled by removing the heat generated inside them by using air as a heat transfer medium and in a free convection way, and the fact that heat transfer by free convection occurs in many fields, so there were many studies that dealt with this topic. The free load is generated by the buoyant force (Bouncy force) As a result of the difference in the density of the fluid adjacent to the heated surface due to the difference in temperatures between the fluid and the surface. The laminar flow along surfaces has been extensively studied analytically [1,2,3,4] In the horizontal, inclined and vertical case, whether by constant heat flux or constant surface temperature, there are also many experimental studies of heat transfer by free convection from horizontal, inclined and vertical surfaces with constant heat flux or constant surface temperature [5,6,7,8]. Some experimental studies have also been conducted on heat transfer by convection from heated surfaces in the form of a disk (ring)The outcome of these studies was to extract an exponential mathematical relationship between the average of Nusselt number and the Kirchhoff number or Rayleigh number and the following formula: (Nu=C(Ra) n It is one of the most suitable formulas for heat transfer by free convection from heated surfaces in all its forms and over a wide range of Rayleigh number . It is noted that not all of these studies dealt with the study of the effect of the cavity ratio on heat transfer by free convection from square-shaped surfaces, which is the form that is more applied in electronic devices. Therefore, the current research means studying the rate of change in the average of Nusselt number, which represents a function of the rate of change in the rate of heat transfer by convection, as well as studying the thermal gradient above the surface, and this was done through using three hollow surfaces in proportions (0.25,0.5,0.75) of the total area.

Effect of non-uniform heating on conjugate heat transfer performance for nanofluid flow in a converging duct by a two-phase Eulerian–Lagrangian method

2021 ◽  
pp. 095440892110429
Author(s):  
Md. Faizan ◽  
Sukumar Pati ◽  
Pitamber R Randive
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Volume Fraction ◽  
Constant Heat Flux ◽  
Lagrangian Model ◽  
Uniform Heating ◽  
Nanofluid Flow ◽  
Two Phase

In this paper, the effect of non-uniform heating on the conjugate thermal and hydraulic characteristics for Al2O3–water nanofluid flow through a converging duct is examined numerically. An Eulerian–Lagrangian model is employed to simulate the two-phase flow for the following range of parameters: Reynolds number (100 ≤ Re ≤ 800), nanoparticle volume fraction (0% ≤  ϕ ≤ 5%) and amplitude of the sinusoidal heat flux ( A = 0, 0.5 and 1). The results reveal a similar affinity between the applied heat flux and local Nusselt number variation qualitatively, mainly at the middle of the duct. The results also indicate that there is a considerable enhancement of Nusselt number with the increase in Reynolds number and the thermal conductivity of wall materials. In addition, increasing the particle loading contributes to an enhanced rate of heat transfer. The heat transfer rate is lower for non-uniform heating when compared with the constant heat flux and the same can be compensated by the application of volume fraction of nanoparticles

Unsteady Laminar Forced-Convective Tube Flow Under Dynamic Time-Dependent Heat Flux

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
Mehdi Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Tube Flow ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow (SF) condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel's integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict (i) fluid temperature distribution inside the tube, (ii) fluid bulk temperature and (iii) the Nusselt number. A new definition, cyclic fully developed Nusselt number, is introduced and it is shown that in the thermally fully developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ansys fluent to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

A Numerical Study of the Extended Graetz Problem in a Microchannel with Constant Wall Heat Flux: Shear Work Effects on Heat Transfer

2015 ◽  
Vol 31 (6) ◽  
pp. 733-743 ◽  
Author(s):  
K. Ramadan ◽  
I. Tlili
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Flow Region ◽  
Wall Heat Flux ◽  
Flux Boundary Condition ◽  
Developing Flow ◽  
Constant Wall Heat Flux ◽  
Work Effect

ABSTRACTHeat convection of a microchannel gas flow with constant wall heat flux boundary condition is investigated numerically, considering viscous dissipation and axial conduction. The shear work due to the slipping fluid at the wall is incorporated in the analysis. An analytical solution for fully developed conditions is also derived. The effect of the shear work on heat transfer is quantified through a comparative analysis in both the entrance- and the fully developed- regions. The analysis shows that the shear work effect on heat transfer is considerable, and neglecting this term leads to an overestimation of the Nusselt number in gas heating and an underestimation in gas cooling. The over/under estimation of the Nusselt number is dependent on both the Knudsen number and the Brinkman number. The results presented also demonstrate the significance of the shear work in the developing flow region. It is shown that in the developing flow region the Nusselt number is less sensitive to viscous dissipation when the shear work is neglected. It can be concluded from this study that the shear work effect is significant and neglecting it can lead to considerable errors in microchannel flow heat transfer.

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