Research Papers: Forced Convection

Exact Solution of Electroviscous Flow and Heat Transfer in a Semi-annular Microcapillary

[+] Author and Article Information
Ali Jabari Moghadam

Associate Professor
Department of Mechanical Engineering,
University of Shahrood,
P.O. Box 316,
Shahrood 3619995161, Iran
e-mail: jm.ali.project@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 25, 2014; final manuscript received July 11, 2015; published online August 11, 2015. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 138(1), 011702 (Aug 11, 2015) (10 pages) Paper No: HT-14-1043; doi: 10.1115/1.4031084 History: Received January 25, 2014

The electro-osmotic flow (EOF) and associated heat transfer are investigated in a semi-annular microcapillary. The potential, velocity, and temperature fields are solved by analytic approaches including the eigenfunction expansion and the Green’s function methods. By selecting the potential sign of each surface of the channel, the bulk fluid may flow in two opposite directions. Effects of the key parameters governing the problem are examined. The mass flow rate increases when the hydraulic diameter is increased or the electrokinetic radius is decreased. The results reveal that surface cooling and/or surface heating (of the inner or outer walls) strongly affects the fluid temperature distributions as well as the position of the maximum/minimum temperature region inside the domain; the latter indicates temperature gradients in fluid. Also, higher thermal scale ratio leads to broaden the temperature distribution. Depending on the value of the geometric radius ratio (and for all values of the thermal scale ratio), the fully developed Nusselt number approaches a specific value as the electrokinetic radius tends to infinity.

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Grahic Jump Location
Fig. 1

The cross section of the semi-annular microchannel

Grahic Jump Location
Fig. 2

Nondimensional velocity profiles for α = 0.5, χ = 1000, Z0 = 0.5, γ = 0, M = 2.2, and E=5000: (a) β = -1, (b) β = 0, (c) β = 0.5, and (d) β = 1

Grahic Jump Location
Fig. 3

Dimensionless temperature profiles for α = 0.5, χ = 1000, Z0 = 0.5, γ = 0, M = 2.2, E=5000, and Ps = 1: (a) β = 0,βs = 1, (b) β = 0,βs = -1, (c) β = 1,βs = 1, and (d) β = 1,βs = -1

Grahic Jump Location
Fig. 4

Dimensionless temperature profiles for α = 0.5, χ = 1000, Z0 = 0.5, γ = 0, M = 2.2, E=5000, and Ps = -1: (a) β = 0,βs = 1, (b) β = 0,βs = -1, (c) β = 1,βs = 1, and (d) β = 1,βs = -1

Grahic Jump Location
Fig. 5

Dimensionless temperature profiles for α = 0.5, χ = 1000, Z0 = 0.5, M = 2.2, E=5000, and βs = 1, β = 1: (a) Ps = 2,γ = 0, (b) Ps = -2,γ = 0, (c) Ps≅-4.849 (special case),γ = 1, and (d) Ps = -6,γ = 1

Grahic Jump Location
Fig. 6

Nusselt number against electrokinetic radius for βs = 1, β = γ = 1, and three different values of the thermal scale ratio with (a) α = 0.5 and (b) α = 0.2

Grahic Jump Location
Fig. 7

Variations of dimensionless mass flow rate with electrokinetic radius for Z0=0.5, M=2.2, E=5000, β=1, γ=1, and three different values of α



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