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Research Papers: Micro/Nanoscale Heat Transfer

# Entropy Generation Minimization in a Pressure-Driven Microflow of Viscoelastic Fluid With Slippage at the Wall: Effect of Conjugate Heat Transfer

[+] Author and Article Information
Rajkumar Sarma

Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India
e-mail: rajkumarsarma11@gmail.com

Pranab Kumar Mondal

Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India
e-mail: mail2pranab@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 24, 2017; final manuscript received September 8, 2017; published online January 30, 2018. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 140(5), 052402 (Jan 30, 2018) (11 pages) Paper No: HT-17-1296; doi: 10.1115/1.4038451 History: Received May 24, 2017; Revised September 08, 2017

## Abstract

We focus on the entropy generation minimization for the flow of a viscoelastic fluid through a parallel plate microchannel under the combined influences of applied pressure gradient, interfacial slip, and conjugate heat transfer. We use the simplified Phan–Thien–Tanner model (s-PTT) to represent the rheological behavior of the viscoelastic fluid. Using thermal boundary conditions of the third kind, we solve the transport equations analytically to obtain the velocity and temperature distributions in the flow field, which are further used to calculate the entropy generation rate in the analysis. In this study, the influential role of the following dimensionless parameters on entropy generation rate is examined: the viscoelastic parameter $(εDe2)$, slip coefficient $(k¯)$, channel wall thickness $(δ)$, thermal conductivity of the wall $(γ)$, Biot number $(Bi)$ and Peclet number $(Pe)$. We show that there exists a particular value of the abovementioned parameters that lead to a minimum entropy generation rate in the system. We believe the results of this analysis could be of helpful in the optimum design of microfluidic system/devices typically used in thermal management, such as micro-electronic devices, microreactors, and microheat exchangers.

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## Figures

Fig. 1

Schematic diagram depicting the physical geometry and the imposed boundary conditions for the flow of viscoelastic fluid through a parallel plate microchannel. The externally applied pressure gradient drives the flow in the axial (x) direction of the channel. The thickness of the channel walls, as well as height, is shown in the schematic.

Fig. 2

Model validation: (a) plot showing the comparison of velocity distribution across the channel between the results of the present analytical solution and the experimental results of Degré et al. The other parameters considered to obtain the variations are ΔP=52 mbar,η=0.002 Pa⋅s,λ=0.1 s,ε=0.1, and m=0.2. (b) Plot showing the comparison of temperature distribution across the channel width between the results obtained from the present analytical solution and experimental results by Hwang et al. The other parameters considered to obtain the variation are as follows: λ=0,k=0,η=0.00059 Pa⋅s,kf=0.07 Wm−1 K−1,ρ=1550 kg m−3, and cp=962 J kg−1 K−1.

Fig. 3

Variation of normalized global entropy generation rate as a function of dimensionless lower wall thickness,  δ1: (a) for k¯=0.05 and (b) for εDe2=1. The other parameters considered have the following values: Pe=0.1,Br=0.1,m=2,A=1.0,γ1=0.5,γ2=0.5,Bi1=2.0,Bi2=20.0,δ2=0.1, and Θa=5.0.

Fig. 4

Variation of normalized global entropy generation rate versus lower wall Biot number,  Bi1: (a) for k¯=0.05 and (b) for εDe2=1. The other parameters considered in plotting the above figures are: Pe=0.1,Br=0.1,m=2,A=1.0,γ1=1,γ2=1,δ1=0.1,δ2=0.1,Bi2=2, and Θa=5.0.

Fig. 5

Variation of normalized global entropy generation rate as a function of lower wall thermal conductivity,  γ1: (a) for k¯=0.05 and (b) for εDe2=1. The different other parameters considered in this plotting are as follows: Pe=0.1,Br=0.1,m=2,A=1.0,γ2=3.0,Bi1=1.0,Bi2=1.0,δ1=0.1,δ2=0.1, and Θa=5.0.

Fig. 6

Variation of global entropy generation rate with Peclet number (Pe): (a) for k¯=0.05 and (b) for εDe2=1. The other parameters considered in this plotting have the following values: Br=0.1,m=2,A=1,γ1=1.5, γ2=1.5, Bi1=5.0,Bi2=10.0, δ1=0.1,δ2=0.1, and Θa=5.0.

Fig. 7

Variation of global entropy generation rate as a function of axial temperature gradient, A: (a) for k¯=0.05 and (b) for εDe2=1. The other parameters considered in this plotting are as follows:  Pe=0.1, Br=0.1,m=2,γ1=1.5,γ2=1.5,Bi1=2.0,Bi2=20.0, δ1=0.1,δ2=0.1, and Θa=5.0.

Fig. 8

Variation of nondimensional temperature across the channel width: (a) for εDe2=0.5 and (b) for εDe2=2. The other parameters considered in plotting the above figures are: A =1.0, Br = 0.1, Pe = 0.1, k¯=0.05, m = 2, δ1=0.1,δ2=0.1, and Θa=5.0.

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