The extended Graetz problem for a gaseous slip flow in micropipe and parallel-plate microchannel with heating section of finite length: Effects of axial conduction, viscous dissipation and pressure work

Haddout, Youssef; Lahjomri, Jawad

doi:10.1016/j.ijheatmasstransfer.2014.09.064

Cited by 28 publications

(12 citation statements)

References 35 publications

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“…In addition to the possibility of size effects rending the no-slip boundary condition, based on continuum Navier-Stokes approximations, difficult to predict and/or invalid at the nanoscales [54][55][56], we hypothesized that continuum fluid behaviors may be observed with considerable influences from microscopic mechanisms (the potential presence of slip flow). From this, we anticipate potential slip flow behavior to require a larger channel entry length than of the length determined from setting Gz -1 = 0.05 for the continuum regime; hence, to ensure full flow development inside the nanochannel, a large value of Gz -1 = 0.4 is chosen [51,57,58]. Moreover, considering the potential effects of axial conduction as well as the areas of the liquid pumping and temperature rescaling regions, the respective channel length is found to be L = 12.0 nm.…”

Section: Is the Molar Volume And Nmentioning

confidence: 99%

Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels

Marable

Shin

Nobakht

2017

International Journal of Heat and Mass Transfer

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Convection heat transfer is assessed for laminarly flowing liquid water through graphene nanochannels via molecular dynamics (MD) simulations. The use of MD simulations allows for direct assessment of the minute details and mechanisms influencing overall heat transfer behaviors within our study; despite the presence of unrealistic axial conduction from temperature resetting and periodic boundary conditions within MD, hydrodynamically and thermally fully-developed water flow conditions are observed. It is indicated that the physics of convective heat transfer deviate from traditional macroscale theory as the no-slip boundary condition is violated with dimensional sizes descending towards the nanoscale; investigation into hydrodynamic slip and thermal slip, termed microscopic mechanisms, is performed for their influence on nanoscale convective outcomes. The parameters of graphene-water interaction strength, channel height, water velocity, and wall temperature are manipulated to evaluate resultant convection behaviors while comparing the effects of differing magnitudes of microscopic mechanisms imposed under various test conditions. This study finds microscopic interfacial mechanisms to significantly augment momentum and thermal behaviors and thus the conduct of convective heat transfer. Hydrodynamic and thermal slip are strongly correlated in all test case scenarios with the exception of velocity manipulation; the influence of thermal slip is found to dominate over that of hydrodynamic slip as surface advection is insignificant in high heat flux environments. Convective performance correlation is suggested as the ratio of thermal slip length to system size.

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Section: Is the Molar Volume And Nmentioning

confidence: 99%

Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels

Marable

Shin

Nobakht

2017

International Journal of Heat and Mass Transfer

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“…By applying a self-adjoint formalism. [5], the solution for the dimensionless temperature Θ( , ) can be represented as an infinite series of eigenfunctions…”

Section: Analytical Solutionmentioning

confidence: 99%

Jeffery-Hamel slip flow in a convergent microchannel with uniform wall temperature and streamwise heat conduction

et al. 2019

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This work is devoted to the determination of the analytical solution of the problem of the laminar forced convection of the Jeffery-Hamel slip flow through a convergent microchannel. The analytical solution is obtained by using a self-adjoint formalism of the functional analysis. The solution represents an extension of the solution obtained in the conventional continuum flow by considering the boundaries slip conditions at the wall and the streamwise heat conduction. This extension has been done by using a new matrix operator of three dimensions in the Hilbert space. The results show that the thermal characteristics are strongly influenced by the Reynolds, Prandtl and Knudsen numbers, the aperture angle of the channel and the streamwise heat conduction.

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“…Specifically, Bayazitoglu et al [6], Rosa et al [7], Cetin et al [8], Cetin [9], Haddout and Lahjomri [10] and Yu and Ameel [11] observed that velocity slip increases the Nusselt number (Nu ¼ (h Â D H )/k, where h is convective and k is the conductive heat transfer coefficients of fluid), while the temperature jump has a negative effect on heat transfer in single phase microchannel flows.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly, Cetin et al [8,22] focused to extend the Graetz problem by including all three micro-scale effects. With a similar perspective, Haddout and Lahjomri [10] studied rarefaction, axial conduction and viscous dissipation effect on the Graetz problem in tube and channel geometries mostly for a case of finite heating region which is comparable with the corresponding channel height. However, there is a knowledge gap for a proper coupling of all micro-scale effects for a micro-slit convective flow.…”

Section: Introductionmentioning

confidence: 99%

The extended Graetz problem for micro-slit geometries; analytical coupling of rarefaction, axial conduction and viscous dissipation

Kalyoncu

Barışık

2016

International Journal of Thermal Sciences

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a b s t r a c tIn order to support the recent MEMS and Lab-on-a-chip technologies, we studied heat transport in micro-scale slit channel gas flows. Since the micro convection transport phenomena diverges from conventional macro-scale transport due to rarefaction, axial conduction and viscous heating, an accurate understanding requires a complete coupling of these effects. For such cases, we studied heat transfer in hydrodynamically developed, thermally developing gas flows in micro-slits at various flow conditions. The analytical solution of the energy equation considered both the heat conduction in the axial direction and heat dissipation of viscous forces. Furthermore, updated boundary conditions of velocity slip and temperature jump were applied based on Knudsen number of flow in order to account for the nonequilibrium gas dynamics. Local Nusselt number (Nu) values were calculated as a function of Peclet (Pe), Knudsen (Kn) and Brinkman (Br) numbers which were selected carefully according to possible micro-flow cases. Strong variation of Nu in thermal development length was found to dominate heat transfer behavior of micro-slits with short heating lengths for early slip flow regime. For this instance, influence of axial conduction and viscous dissipation was equally important. On the other hand, high Kn slip flow suppressed the axial conduction while viscous heating in a small surface-gas temperature difference case mostly determined the fully developed Nu and average heat transfer behavior as a function of Kn value.

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The extended Graetz problem for a gaseous slip flow in micropipe and parallel-plate microchannel with heating section of finite length: Effects of axial conduction, viscous dissipation and pressure work

Cited by 28 publications

References 35 publications

Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels

Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels

Jeffery-Hamel slip flow in a convergent microchannel with uniform wall temperature and streamwise heat conduction

The extended Graetz problem for micro-slit geometries; analytical coupling of rarefaction, axial conduction and viscous dissipation

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