Heat Transfer in the Slip Flow with Axial Heat Conduction in a Microchannel with Walls Having a Constant Temperature

Haddout, Youssef; Oubarra, Abdelaziz; Lahjomri, Jawad

doi:10.1007/s10891-020-02158-9

Cited by 6 publications

(10 citation statements)

References 27 publications

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“…The first-order slip-velocity and temperature jump models are used, and the fixed constant pressure drop along the streamwise direction per unit length condition is considered. Therefore, the results of the effects of the Knudsen number and the degree of temperature jump on heat transfer are presented differently from those found in the case of a fixed average velocity condition (Larrodé et al, 2000;Tunc and Bayazitoglu, 2001;Çetin et al, 2008;Çetin and Zeinali, 2014;Barişik et al, 2015;Kalyoncu and Barişik, 2016;Haddout et al, 2020;Sun et al, 2020). The obtained analytical solution is directly applied without introducing the spatial rescaling factor (Larrodé et al, 2000), which is used for a fixed average velocity.…”

Section: Introductionmentioning

confidence: 98%

“…Many investigations studied the coupling of axial heat conduction, viscous dissipation, and rarefaction effects on the Graetz problem in microchannels and microtubes, and to the best of our knowledge, all of them used the fixed average velocity condition Çetin et al, 2008;Çetin and Zeinali, 2014;Barişik et al, 2015;Kalyoncu and Barişik, 2016;Haddout et al, 2020;Sun et al, 2020). However, for optimization problems or energy efficiency maximization, the variation of the pressure drop along the streamwise direction per unit length in the microchannel or microtube is as important as the variation of the Nusselt number.…”

Section: Introductionmentioning

confidence: 99%

“…Kalyoncu and Barişik (2016) found that the convective heat transfer coefficient increases with decreasing flow dimensions despite the reduction of the Nusselt number. Haddout et al (2020) used the self-adjoint formalism method involving the decomposition of the energy equation into a system of two first-order partial differential equations. It was concluded that heat transfer increases as the Péclet number and the Knudsen number decrease; at the same time, for large Péclet numbers, the Knudsen number does not affect the temperature gradient near-wall layer, while for small Péclet numbers, this effect becomes important.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytical Solution of the Extended Graetz Problem in Microchannels and Microtubes With Fixed Pressure Drop

Shaimi¹,

Khatyr²,

Naciri³

2023

Front. Heat Mass Transf.

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This paper presents an exact analytical solution to the extended Graetz problem in microchannels and microtubes, including axial heat conduction, viscous dissipation, and rarefaction effects for an imposed constant wall temperature. The flow in the microchannel or microtube is assumed to be hydrodynamically fully developed. At the same time, the first-order slip-velocity and temperature jump models represent the wall boundary conditions. The energy equation is solved analytically, and the solution is obtained in terms of Kummer functions with expansion constants directly determined from explicit expressions. The local and fully developed Nusselt numbers are calculated in terms of the Péclet number, Brinkman number, Knudsen number, and thermal properties of the fluid. The constant pressure drop along the streamwise direction per unit length is imposed at a constant value and independent of the flow parameters, unlike the usual practice of fixing the average velocity. This solution can be used as the reference solution for optimization problems to enhance heat transfer using a fixed pressure drop. It is found that for no viscous dissipation and negligible axial heat conduction, the local Nusselt number is larger for imposed pressure drop compared to imposed average velocity. The thermal entrance length increases as the Knudsen number or the degree of temperature jump increases for imposed pressure drop, while it is approximately unchangeable for imposed average velocity. The quantitative differences between the cases of imposed pressure drop and imposed average velocity in the average Nusselt number over the largest thermal entrance length are reduced with the increase of axial heat conduction or viscous dissipation effects. The fully developed Nusselt number is the same for imposed pressure drop and imposed average velocity.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Solution of the Extended Graetz Problem in Microchannels and Microtubes With Fixed Pressure Drop

Shaimi¹,

Khatyr²,

Naciri³

2023

Front. Heat Mass Transf.

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“…Wang et al 24 explored the flow method in laminar and heat transfer improvement in a microchannel heat sink. In a micro‐channel, axial heat conduction with forced convection with slip effect by Haddout et al 25 …”

Section: Introductionmentioning

confidence: 99%

“…Wang et al 24 explored the flow method in laminar and heat transfer improvement in a microchannel heat sink. In a micro-channel, axial heat conduction with forced convection with slip effect by Haddout et al 25 Gong et al 26 examined the impact of hydraulic diameter and slip length on the hydraulic entrance length of laminar fluid flow in superhydrophobic microchannels. Ma et al 27 have explored the Reynolds number significantly, which impacts the local Nusselt quantity in the thermally evolving region, particularly at a lower Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

Exploration of radiative heat on the Jeffery fluid flow in a microchannel for the impact of suction/injection

Krishna¹,

Ramanuja²,

Mishra

et al. 2022

Heat Trans

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The purpose of the present paper is to investigate the flow and heat transfer of thermal radiation on the Jeffery fluid flow within a microchannel for the effects of the superhydrophobic surface (SHS) within suction/injection. The governing differential equations of motion and heat transfer are transformed into nonlinear coupled ordinary differential equations (ODEs) using appropriate similarity transformations. The ODEs are solved along with boundary conditions by adopting Runge–Kutta with shooting technique. Symbolic computational software such as MATLAB, the solver bvp4c syntax examines the behavior of the relevant physical parameters. However, some effective emerging parameters on the flow problem reveal that the microchannel walls within the suction/injection parameter increase the temperature, and the SHS is heated. In contrast, without slip, the opposite behavior is rendered. It is clearly shown that the velocity profile diminishes with increasing the Prandtl number. Furthermore, it is noticed that velocity decreases for increasing values of Hartmann number. Comparison with available results for particular cases is an excellent agreement.

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Effects of Viscous Dissipation and Pressure Work on the Extended Graetz Problem for a Gaseous Slip Flow in a Microchannel with Walls Having a Constant Temperature

Haddout¹,

Essaghir

Oubarra

et al. 2022

J Eng Phys Thermophy

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Heat Transfer in the Slip Flow with Axial Heat Conduction in a Microchannel with Walls Having a Constant Temperature

Cited by 6 publications

References 27 publications

Analytical Solution of the Extended Graetz Problem in Microchannels and Microtubes With Fixed Pressure Drop

Analytical Solution of the Extended Graetz Problem in Microchannels and Microtubes With Fixed Pressure Drop

Exploration of radiative heat on the Jeffery fluid flow in a microchannel for the impact of suction/injection

Effects of Viscous Dissipation and Pressure Work on the Extended Graetz Problem for a Gaseous Slip Flow in a Microchannel with Walls Having a Constant Temperature

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