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Research Papers: Forced Convection

Entropy Generation Minimization in an Electroosmotic Flow of Non-Newtonian Fluid: Effect of Conjugate Heat Transfer

[+] Author and Article Information
Prakash Goswami

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India

Pranab Kumar Mondal

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India;
Advanced Technology Development Center,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India

Anubhab Datta

Department of Mechanical Engineering,
Jadavpur University,
Kolkata, West Bengal 700032, India

Suman Chakraborty

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India;
Advanced Technology Development Center,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India
e-mail: suman@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 13, 2015; final manuscript received December 22, 2015; published online February 3, 2016. Assoc. Editor: Oronzio Manca.

J. Heat Transfer 138(5), 051704 (Feb 03, 2016) (9 pages) Paper No: HT-15-1030; doi: 10.1115/1.4032431 History: Received January 13, 2015; Revised December 22, 2015

We investigate the entropy generation characteristics of a non-Newtonian fluid in a narrow fluidic channel under electrokinetic forcing, taking the effect of conjugate heat transfer into the analysis. We use power-law model to describe the non-Newtonian fluid rheology, in an effort to capture the essential thermohydrodynamics. We solve the conjugate heat transfer problem in an analytical formalism using the thermal boundary conditions of third kind at the outer surface of the walls. We bring out the alteration in the entropy generation behavior as attributable to the rheology-driven alteration in heat transfer, coupled with nonlinear interactions between viscous dissipation and Joule heating originating from electroosmotic effects. We unveil optimum values of different parameters, including both the geometric as well as thermophysical parameters, which lead to the minimization of the entropy generation rate in the system. We believe that the inferences obtained from the present study may bear far ranging consequences in the design of various cooling and heat removal devices/systems, for potential use in microscale thermal management.

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Figures

Grahic Jump Location
Fig. 1

Schematic depicting the physical dimensions of the problem. The external applied electric field Ex actuates the flow in the positive x -direction. The walls of the channel are kept at unequal temperatures.

Grahic Jump Location
Fig. 2

Comparison between the approximate analytical and numerical solutions for the normalized velocity distribution obtained for different values of power-law index: n=0.8, 1.0, and  1.2. We take κ¯=10 for this plot. The analytical solutions show a good agreement with the numerical results for all the values of n considered.

Grahic Jump Location
Fig. 3

Plot of normalized global entropy generation versus δU, for three different values of n=0.8,1.0, and 1.2, respectively, while κ¯=10 and J=1. The parameter δU used as a x -axis variable is the upper wall thickness (dimensionless). The other parameters considered are: Pe=0.01, B=1, δL=0.1, BiL=2, BiU=20, and λL=λU=0.5. The global entropy generation rate in the system initially decreases, attains a minimum value, and finally shows an increasing trend for all the cases of power-law fluids considered.

Grahic Jump Location
Fig. 4

Plot of normalized global entropy generation as a function of λU, for three different values of n=0.8, 1.0, and 1.2, while κ¯=10 and J=1. The x -axis variable λU is the ratio of wall to fluid thermal conductivity at the upper wall. We have taken the following values of the other parameters: Pe=0.01, B=1, δL=δU=0.1, BiL=BiU=2, and λL=10. The variations predict an optimum value of λU,opt, leading to a minimum entropy generation rate in the system. A careful observation of the figure reveals that a change in fluid rheology alters the λU,opt value.

Grahic Jump Location
Fig. 5

Normalized entropy generation rate (normalized by its value when BiU=0) as a function of BiU is plotted, for three different values of n=0.8, 1.0, and 1.2. Note that the x -axis variable BiU is the Biot number at the upper wall of the channel. We have consider κ¯=10 and J=1. The other parameters are as follows: Pe=0.01, B=1, δL=δU=0.1, λL=λU=2, and BiL=4. We observe an optimum value of BiU,opt from the figure, leading to a minimum entropy generation rate in the system, which changes with a change in rheological behavior of the fluid.

Grahic Jump Location
Fig. 6

Variation of global entropy generation with B, while three different values of n=0.8, 1.0, and 1.2 have been considered. The x -axis variable B represents the axial temperature gradient. We have taken κ¯=10 and J=1. The other parameters considered have the following values: Pe=0.01, δL=δU=0.1, BiL=2, BiU=20, and λL=λU=10. The optimum value of axial temperature gradient Bopt exists that minimizes the irreversibility associated to the present system, for all the values of n considered.

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