Forced Convection Heat Transfer of a Giesekus Fluid in Circular Micro-Channels Subjected to a Constant Wall Temperature

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
M. Norouzi ◽  
M. R. Rezaie
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Constitutive Equation ◽  
Wall Temperature ◽  
Micro Channel ◽  
Slip Coefficient ◽  
Constant Wall Temperature ◽  
Mobility Factor ◽  
Micro Channels ◽  
Giesekus Fluid

Abstract In this paper, an exact analytical solution for forced convective heat transfer of nonlinear viscoelastic fluid in isothermal circular micro-channel is presented. The nonlinear Giesekus constitutive equation is used to model the Giesekus fluid heat transfer in micro-channel with constant wall temperature, which is the main innovative aspect of the current study. This constitutive equation is a powerful tool and able to model the fractional viscometric functions, extensional viscosity, and elastic property. The solution of temperature profile and Nusselt number is obtained based on the Frobenius method. The effects of Weissenberg number, mobility factor, slip coefficient, and Navier index on temperature distribution, velocity profile, and Nusselt number are investigated in detail. The results show that the increases in both slip coefficient and Navier index cause the increases in slip velocity and maximum dimensionless temperature at the wall and the micro-channel center, respectively. Moreover, the Nusselt number has an upward trend with increases in slip coefficient and Navier index parameters. The results are indicated that the flow and temperature fields have a complex relation with mobility factor which controls the level of the nonlinearity of the Giesekus model. Additionally, three correlations for Nusselt number of Giesekus flow in micro-channel are presented.

On the Convective Heat Transfer in a Tube of Elliptic Cross Section Maintained Under Constant Wall Temperature

1986 ◽  
Vol 108 (1) ◽  
pp. 33-39 ◽  
Author(s):  
M. A. Ebadian ◽  
H. C. Topakoglu ◽  
O. A. Arnas
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Wall Temperature ◽  
Elliptic Cross Section ◽  
Constant Wall Temperature ◽  
Elliptic Cross

The convective heat transfer problem along the portion of a tube of elliptic cross section maintained under a constant wall temperature where hydrodynamically and thermally fully developed flow conditions prevail is solved in this paper. The successive approximation method is used for the solution utilizing elliptic coordinates. Analytical expressions for temperature distribution and Nusselt number corresponding to the first cycle of approximation are obtained in terms of the ellipticity of the cross section. In the case of a circular section, the first cycle approximation of the Nusselt number is obtained as 3.7288 compared to the exact value of 3.6568. Representative temperature distribution curves are plotted and compared to those corresponding with constant wall heat flux conditions.

Heat Transfer Coefficient in Ducts With Constant Wall Temperature

1983 ◽  
Vol 105 (4) ◽  
pp. 878-883 ◽  
Author(s):  
A. Haji-Sheikh ◽  
M. Mashena ◽  
M. J. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Numerical Calculation ◽  
Transfer Coefficient ◽  
Cross Sections ◽  
Wall Temperature ◽  
Constant Wall Temperature ◽  
Circular Pipes ◽  
The Heat Transfer Coefficient

An analytical method for the numerical calculation of the heat transfer coefficient in arbitrarily shaped ducts with constant wall temperature at the boundary is presented. The flow is considered to be laminar and fully developed, both thermally and hydrodynamically. The method presented herein makes use of Galerkin-type functions for computation of the Nusselt number. This method is applied to circular pipes and ducts with rectangular, isosceles triangular, and right triangular cross sections. A three-term or even a two-term solution yields accurate solutions for circular ducts. The situation is similar for right triangular ducts with two equal sides. However, for narrower ducts, a larger number of terms must be used.

scholarly journals Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1

2001 ◽  
Vol 124 (2) ◽  
pp. 356-364 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou ◽  
Olga Simek
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Flow Regime ◽  
Wall Temperature ◽  
Slip Flow ◽  
Constant Wall Temperature ◽  
Slip Flow Regime ◽  
Axial Heat ◽  
Axial Heat Conduction

We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions. Our investigation covers both the slip-flow regime 0⩽Kn⩽0.1, and most of the transition regime 0.1<Kn⩽10, where Kn, the Knudsen number, is defined as the ratio between the molecular mean free path and the channel height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0⩽Kn⩽0.2, and a stochastic molecular simulation technique known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in the range 0.02<Kn<2. Inclusion of the effects of axial heat conduction in the continuum model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Kn⩽0.1, but also remains a good approximation beyond its expected range of applicability. We also show that the Nusselt number decreases monotonically with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Kn=0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes.

Slip-Flow Constant-Wall-Temperature Nusselt Number in Circular Tubes in the Presence of Axial Heat Conduction

2001 ◽  
Author(s):  
Olga Simek ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Wall Temperature ◽  
Slip Flow ◽  
Small Scale ◽  
Constant Wall Temperature ◽  
Circular Tubes ◽  
Axial Heat ◽  
Axial Heat Conduction

Abstract We present an investigation of slip-flow constant-wall-temperature convective heat transfer in circular tubes under hydrodynamically and thermally fully developed conditions. Our analysis includes the contribution of axial heat conduction (finite Peclet number) which is important in small scale flows, and has not been included in previous investigations of slip-flow heat transfer. The Nusselt number is found to decrease with increasing Knudsen number for all Peclet numbers in the fully accommodating case, as expected. The effect of axial heat conduction is found to be most important at Kn = 0, and results in an increase in the Nusselt number of the order of 15%; as Kn increases, the effect of axial heat conduction decreases.

scholarly journals Effect of Taper Manifolds with Different Slopes in Microchannel Heat Sink

2019 ◽  
Vol 8 (12) ◽  
pp. 3988-3992
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Pressure Drop ◽  
Heat Sink ◽  
Microchannel Heat Sink ◽  
Micro Channel ◽  
Flow And Heat Transfer ◽  
Micro Channels ◽  
Upward Direction ◽  
Degree Slope

In this analysis, the liquid flow and heat transfer in micro channel heat sink (MCHS) to find the pressure drop are experimentally investigated by three degree slope in manifolds in addition to the arrangement of micro channels. This experimental analysis is executed with respect to the Nusselt Number and Heat transfer characteristics for three manifolds with different arrangement. We are working on this experiment at three different arrangement manifolds: Arrangement (A) is the three-degree slope in manifolds downward and upward, Arrangement (B) is the three-degree slope in manifolds upward and downward and Arrangement (C) is the three-degree slope in upward direction of the manifolds are selected. In this investigation we are using the Reynolds number ranging from 705-1411 for micro channel heat sink. The Arrangement (A) is the greater heat transfer coefficient within the increase Nusselt number and velocity and low pressure drop in comparison to Arrangement (B) and (C) type manifolds

scholarly journals Numerical analysis of forced convection heat transfer in a rectangular micro-channel totally filled with Ag/ water nano fluid in slip flow regime using the lattice Boltzmann method

2021 ◽  
Vol 321 ◽  
pp. 04008
Author(s):  
Kaouther Ben Ltaifa ◽  
Annunziata D’Orazio ◽  
Arash Karimipour ◽  
Hacen Dhahri
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Temperature Jump ◽  
Micro Channel ◽  
Slip Coefficient ◽  
Nano Fluid ◽  
Boltzmann Method

Numerical simulation reported on heat transfer and fluid flow in a two-dimensional rectangular micro channel totally filled with Ag/water. The first –order slip/jump boundary conditions were uniformly imposed to the up and bottom walls. The governing conservation equations are translated in dimensionless form using the thermal Single Relaxation Time (T-SRT) modified Lattice Boltzmann Method (LBM) with double distribution functions (DDFs). The viscous dissipations effects are adopted into the energy equation. Effects of nanoparticle volume fraction φ, slip coefficient, B, on the flow of Nano fluid and heat transfer were studied. The results were interpreter in terms of slip velocity; temperature jump and Nusselt number. Based on the results found, it can be concluded that decreasing the values of slip coefficient enhances the convective heat transfer coefficient and consequently the Nusselt number (Nu) but increases the slip velocity at the wall and temperature jump values.

Heat Transfer Characteristics of Gaseous Flows in Micro-Channels With Constant Wall Temperature: Cooled From Walls

2006 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako
Keyword(s):  
Heat Transfer ◽  
Incompressible Flow ◽  
Wall Temperature ◽  
Heat Transfer Characteristics ◽  
Transfer Coefficients ◽  
Constant Wall Temperature ◽  
Gaseous Flow ◽  
Heat Transfer Coefficients ◽  
Micro Channels ◽  
Gaseous Flows

Two-dimensional compressible momentum and energy equations are solved to obtain the heat transfer characteristics of gaseous flows in micro-channels with CWT (constant wall temperature) whose temperature is lower than the inlet temperature. The combined effect of viscous dissipation and compressibility is also investigated. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The stagnation temperature is fixed at 300K and the computations were done for the wall temperature of 250K, 280K, and 290K. The bulk temperature based on the static temperature and the total temperature are compared with those of the heated case and also compared with those of the incompressible flow in a conventional sized channel. The identical heat transfer coefficients are obtained for both heated and cooled cases of the incompressible flow. However, in the case of the gaseous flow in micro-channels, different heat transfer coefficients are obtained for each heated and cooled case. A correlation for the prediction of the heat transfer rate of the gaseous flow in the micro-channel is proposed.

Two-Phase Flow and Heat Transfer in Rectangular Micro-Channels

2003 ◽  
Author(s):  
Weilin Qu ◽  
Seok-Mann Yoon ◽  
Issam Mudawar
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Flow Pattern ◽  
Two Phase Flow ◽  
Flow Patterns ◽  
Heat Sinks ◽  
Phase Flow ◽  
Micro Channel ◽  
Two Phase ◽  
Micro Channels

Knowledge of flow pattern and flow pattern transitions is essential to the development of reliable predictive tools for pressure drop and heat transfer in two-phase micro-channel heat sinks. In the present study, experiments were conducted with adiabatic nitrogen-water two-phase flow in a rectangular micro-channel having a 0.406 × 2.032 mm cross-section. Superficial velocities of nitrogen and water ranged from 0.08 to 81.92 m/s and 0.04 to 10.24 m/s, respectively. Flow patterns were first identified using high-speed video imaging, and still photos were then taken for representative patterns. Results reveal that the dominant flow patterns are slug and annular, with bubbly flow occurring only occasionally; stratified and churn flow were never observed. A flow pattern map was constructed and compared with previous maps and predictions of flow pattern transition models. Annual flow is identified as the dominant flow pattern for conditions relevant to two-phase micro-channel heat sinks, and forms the basis for development of a theoretical model for both pressure drop and heat transfer in micro-channels. Features unique to two-phase micro-channel flow, such as laminar liquid and gas flows, smooth liquid-gas interface, and strong entrainment and deposition effects are incorporated into the model. The model shows good agreement with experimental data for water-cooled heat sinks.

The Infrared Characteristics of the Wall Temperature of Boiling Heat Transfer in Microchannel

2011 ◽  
Vol 383-390 ◽  
pp. 811-815
Author(s):  
Hu Gen Ma ◽  
Jian Mei Bai ◽  
Rong Jian Xie ◽  
Wen Jing Tu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Temperature ◽  
Boiling Heat Transfer ◽  
Transfer Test ◽  
Axial Direction ◽  
Transfer Model ◽  
Micro Channel ◽  
Vapor Quality ◽  
Test Rig

In this paper, the boiling heat transfer test rig was designed and built, while the characteristics of boiling Heat Transfer of refrigerants in micro-channel was researched. The wall temperature of micro-channel was measured by TH5104 Infrared thermography. The results showed that there were obvious variations for wall temperature of micro-channel along the axial direction when boiling heat transfer occurred in the micro-channel. The temperature distribution affected obviously by the heat flux, mass flow rate; vapor quality and heat transfer model.

Enhancement of Heat Transfer of Rectangular Saw Tooth Shaped Micro Channel Heat Sink with Water Nano Fluid/Aluminium Oxide

2015 ◽  
Vol 813-814 ◽  
pp. 685-689
Author(s):  
M. Vijay Anand Marimuthu ◽  
B. Venkatraman ◽  
S. Kandhasamy
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Pressure Drop ◽  
Heat Sink ◽  
Micro Channel ◽  
Performance Curve ◽  
Theoretical Level ◽  
Enhancement Of Heat Transfer ◽  
Nano Fluid

This paper investigates the performance and characteristics of saw tooth shape micro channel in the theoretical level. If the conduct area of the nano fluid increases the heat transfer also increases. The performance curve has drawn Reynolds number against nusselt number, heat transfer co efficient. Pressure drop plays an important role in this device. If pressure drop is high the heat transfer increases. The result in this experiment shows clearly that the heat transfer is optimized.

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