Hydrothermal performance analysis of various surface roughness configurations in trapezoidal microchannels at slip flow regime

doi:10.1016/j.cjche.2020.03.028

Chinese Journal of Chemical Engineering

Volume 28, Issue 6, June 2020, Pages 1522-1532

https://doi.org/10.1016/j.cjche.2020.03.028 Get rights and content

Abstract

The effects of various surface roughness geometrical properties including roughness height (5%, 10%, 15%), number (3, 6), and shape (rectangular and triangular) on the flow and heat transfer of slip-flow in trapezoidal microchannels were investigated. The effects of mentioned parameters on the heat transfer coefficient through the microchannel, average Nusselt number and pressure drop for Reynolds number of 5, 10, 15 and 20 were examined. The obtained results showed that increasing the roughness height and number increases the pressure drop due to higher stagnation effects before and after roughness elements and decreases the Nusselt number due to higher recirculation zones effects than obstruction effects. The most reduction in Nusselt number and the most increment in pressure drop occur at the roughness height of 15%, roughness number of 6 and Reynolds number of 20 by about 10.6% and 52.8% than the smooth microchannel respectively.

Graphical abstract

Introduction

Recently, gas flows in small scale thermal engineering systems such as MEMS and NEMS have been the focus of attention amongst the connoisseurs of the field [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]. The existence of slip conditions is considered as one of the most important differences. Gas flows are categorized in four regimes including continuum where the Knudsen number is below 10⁻³, slip flow where the Knudsen number is between 10⁻³ and 10⁻¹, transition where the Knudsen number is between 10⁻¹ and 1, and free molecular regimes for Knudsen numbers above 1 [11]. The thermodynamic disequilibrium occurs on the solid boundary in slip flow regime. Previous researches confirmed that the continuum approach is inappropriate for predicting flow specifications and effects of rarefaction [12,13]. Moreover, to avoid the high expenses through an empirical study, numerical modeling has become popular amongst the connoisseurs of the field all around the world [[14], [15], [16], [17], [18], [19], [20], [21], [22], [23]], particularly at high rarefactions of gas flows [24,25].

The Navier–Stokes equations are acceptable for modeling slip flow regimes by changing the boundary conditions [26]. Aydin and Avci [27] carried out a study of forced convection in a microchannel with different conditions. They examined the effects of Brinkman number and Knudsen number on the Nusselt number. Another analytical study of convective heat transfer in a microchannel considering the effects of velocity slip and temperature jump in the slip flow regime was performed by Zhang etal. [28]. They concluded that viscose heating effects heats the fluid along the flow direction and distorts the temperature profiles. Later, Wang etal. [29], by coupling the Navier–Stokes equations with energy equation, analyzed the Newtonian fluid in a microchannel considering the slip flow regime characteristics. Their analytical analysis revealed both the dimensionless analytical expressions of velocity and temperature. Then by means of numerical simulation Qazi Zade etal. [30] studied the heat transfer and slip-flow in a microchannel using finite volume method. Their simulations showed that thermo-physical property variations have significant effects on predicting flow and heat transfer characteristics. Colin [31] studied the hydrothermal characteristics of slip flow regime both analytically and numerically. Comparing their analytical and numerical results revealed that when viscous dissipation has to be taken into account, the effect of shear work at the wall is generally not considered.

Channel geometries such as surface roughness and surface structure have an inherent effect on flow characteristics. Morini etal. [32] performed a study using Navier–Stokes equations to analyze the rarefaction effects on the pressure drop for flow through microchannels. These researchers pointed out the Knudsen number and the cross-section aspect ratio effects on the friction factor reduction due to the rarefaction effects. The same work was carried out by Duan and Muzychka [33] to develop a model for Poiseuille number prediction in elliptic microchannels. Later, Zhu etal. [34] examined the aspect ratio effects of a microchannel with arbitrary shapes on the drag coefficient in slip flow regime. They found that the second-order slip boundary condition results in higher friction factors compared to the first order-one slip boundary condition. Sadeghi etal. [35] studied the slip flow between microcylinders. Their results revealed that decreasing the Knudsen number reduces both friction factor and Nusselt number.

Furthermore, the surfaces roughness and structure play an important role in microchannels heat transfer characteristics. Koo and Kleinstreuer [36] analyzed the effects of surface roughness on thermal performance of a microtube using porous medium layer. They found that the roughness effects on hydrodynamic performance is much significant than on thermal performance. They also showed that the Nusselt number for tubular flow, relative to the thermal parallel-plate cases, is typically lower than the conventional value. Later, the roughness effects on gas flow in different microchannels structures were examined by Cao etal. [37] by means of molecular dynamics simulations. They found that by decreasing the Knudsen number and increasing the surface roughness, the friction factor increases. Same study performed by Gamrat etal. [38] numerically employing the volume averaging technique. These researchers demonstrated that the Poiseuille number and the Nusselt number increase with the relative roughness. Zhang etal. [39] , Deng etal. [40] and Rovenskaya and Croce [41] carried out an analysis of flow field in a microchannel with roughness. The authors concluded that the roughness had a notable effect on hydro-dynamical performance. Moreover, they deduced that Navier–Stokes equations coupled with the slip boundary condition provided reasonably good results for a smooth surface for Knudsen numbers higher than 0.1.

The above literature review shows that using computational fluid dynamics (CFD) analysis is a major method to analyze the microchannels in slip flow regime. Although the authors have studied the hydrothermal performance of slip-flows in microchannels by means of different numerical methods, evaluating the effects of surface roughness shape, number and height in a trapezoidal microchannel is a gap in literature review which needs to be bridged. The main objective of this study is to examine the mentioned parameters effects on rough microchannel hydrothermal performance in a slip flow regime using finite volume method. In order to consider the slip velocity and temperature jump at microchannel walls, UDF's (user defined functions) are applied to the CFD software to model the slip conditions.

Section snippets

Problem Statement

This is a numerical study of heat transfer and air flow in a counter-flow trapezoidal microchannel in slip flow regime with investigating the effect of roughness by different height, number and geometrical shape. A schematic diagram of the present study and variable parameters are shown in Fig.1, Fig. 2, respectively. In Fig.2 the geometrical parameters A, B, C, and L are fixed to 100, 25, 50, and 500 μm, respectively. The distance of the first roughness from the inlet and the distance of the

Governing equations

•
Continuity equation

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = \circ

•
Momentum equations
In x direction:

ρ (u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + w \frac{\partial u}{\partial z}) = - \frac{\partial p}{\partial x} + \frac{\partial}{\partial x} (μ \frac{\partial u}{\partial x}) + \frac{\partial}{\partial y} (μ \frac{\partial v}{\partial y}) + \frac{\partial}{\partial z} (μ \frac{\partial w}{\partial z})

In y direction: $ρ (u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z}) = - \frac{\partial p}{\partial y} + \frac{\partial}{\partial x} (μ \frac{\partial u}{\partial x}) + \frac{\partial}{\partial y} (μ \frac{\partial v}{\partial y}) + \frac{\partial}{\partial z} (μ \frac{\partial w}{\partial z})$

In z direction: $ρ (u \frac{\partial w}{\partial x} + v \frac{\partial w}{\partial y} + w \frac{\partial w}{\partial z}) = - \frac{\partial p}{\partial z} + \frac{\partial}{\partial x} (μ \frac{\partial u}{\partial x}) + \frac{\partial}{\partial y} (μ \frac{\partial v}{\partial y}) + \frac{\partial}{\partial z} (μ \frac{\partial w}{\partial z})$

•
Energy equation

(ρ c_{p}) (u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + w \frac{\partial T}{\partial z}) = \frac{\partial}{\partial x} (k \frac{\partial T}{\partial x}) + \frac{\partial}{\partial y} (k \frac{\partial T}{\partial y}) + \frac{\partial}{\partial z} (k \frac{\partial T}{\partial z})

The slip velocity and temperature jump are calculated from Eqs.(6), (7), respectively [42]. $V_{slip} = V - V_{wall} = - \frac{2 - σ}{σ} λ \frac{\partial V}{\partial n} {|_{wall} + 3 \sqrt{\frac{RT}{8 π}} \frac{λ}{T} \frac{\partial T}{\partial s}|}_{wall}$ ${T_{s} - T_{wall} = \frac{2 - σ_{T}}{σ_{T}} \frac{2 γ}{γ + 1} \frac{k}{μ c_{v}} λ \frac{\partial T}{\partial n}|}_{wall}$

Boundary conditions and data reduction

At the inlet of

Results and Discussion

At this stage, the effects of different parameters including Reynolds number, roughness height, roughness shape, and roughness number on air flow and heat transfer characteristics are investigated. For this goal, the effects of mentioned parameters on heat transfer coefficient through the microchannel, average Nusselt number and microchannel pressure drop are examined.

Fig.6 presents the heat transfer coefficient through the microchannel with roughness height of 15%, Re = 5, 1, 15, and 20 for

Conclusions

This is a three dimensional study of convective heat transfer and slip-flow in a trapezoidal microchannel evaluating the effects of various surface roughness geometrical properties including roughness height equal to 5%, 10%, 15%, roughness number equal to 3 and 6, and rectangular and triangular roughness shapes. The finite volume method is employed to solve the Navier–Stokes and energy equations. The effects of mentioned parameters on the heat transfer coefficient through the microchannel,

Nomenclature

trapezoidal channel short base, m

trapezoidal channel long base, m

trapezoidal channel height, m

C_p

specific heat capacity at constant pressure, J·kg⁻¹·K⁻¹

C_v

specific heat capacity at constant volume, J·kg⁻¹·K⁻¹

roughness height, m

heat transfer coefficient, W·m⁻²·K⁻¹

Knudsen number

thermal conductivity, W·m⁻¹·K⁻¹

length of the channel, m

Mach number

number of roughnesses

Nu_x

local Nusselt number

Nu_ave

average Nusselt number

normal vector

pressure, Pa

PEC

performance evaluation criteria

Reynolds

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ArticleHydrothermal performance analysis of various surface roughness configurations in trapezoidal microchannels at slip flow regime

Abstract

Graphical abstract

Introduction

Section snippets

Problem Statement

Governing equations

Boundary conditions and data reduction

Results and Discussion

Conclusions

Nomenclature

Adv. Powder Technol.

Appl. Therm. Eng.

Comput. Methods Prog. Biomed.

Phys. A Stat. Mech. its Appl.

Int. J. Therm. Sci.

J. Mol. Liq.

Phys. E Low-Dimensional Syst. Nanostructures

Phys. ELow-Dimensional Syst. Nanostructures

Energy

Phys. E Low-Dimensional Syst. Nanostructures

Appl. Therm. Eng.

Int. J. Therm. Sci.

Int. J. Therm. Sci.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Superlattice. Microst.

Int. J. Therm. Sci.

Int. J. Heat Mass Transf.

Int. J. Eng. Sci.

Int. J. Therm. Sci.

Phys. A Stat. Mech. Its Appl.

Int. Commun. Heat Mass Transf.

Int. J. Heat Mass Transf.

Appl. Math. Comput.

Phys. E Low-Dimensional Syst. Nanostructures

Int. Commun. Heat Mass Transf.

Comput. Math. with Appl.

Energy

Phys. A Stat. Mech. Its Appl.

Int. Commun. Heat Mass Transf.

Experimental and numerical invesitgation on turbulent flow of mwcnt-water nanofluid inside vertical coiled wire inserted tubes

Therm. Sci.

Article
Hydrothermal performance analysis of various surface roughness configurations in trapezoidal microchannels at slip flow regime