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Technical Brief

Impact of Viscous Dissipation on Fully Developed Natural Convection Flow in a Vertical Microchannel

[+] Author and Article Information
Basant K. Jha

Department of Mathematics,
+234, P. M. B. 1045,
Ahmadu Bello University,
Zaria, Nigeria
e-mail: basant777@yahoo.co.uk

Babatunde Aina

Department of Mathematics,
+234, P. M. B. 005,
Bingham University,
Abuja, Nigeria
e-mail: ainavicdydx@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 20, 2017; final manuscript received March 7, 2018; published online May 22, 2018. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 140(9), 094502 (May 22, 2018) (7 pages) Paper No: HT-17-1358; doi: 10.1115/1.4039641 History: Received June 20, 2017; Revised March 07, 2018

In this research paper, fully developed natural convection flow in a vertical parallel plate's micro-channel in the presence of viscous dissipation is theoretically examined by using a perturbation series method. The effects of velocity slip and temperature jump are taken to consideration. Due to the presence of viscous dissipation, the momentum and energy equations are coupled system of ordinary differential equations. The influences of Knudsen number, fluid wall interaction parameter, and viscous dissipation on the flow formation and heat transfer aspects are demonstrated through graphs and tables. This result indicates that increasing the value of rarefaction parameter decreases the effect of viscous dissipation on the Nusselt number. Furthermore, it is found that the effects of rarefaction parameter as well as buoyancy parameter on temperature and velocity are significantly pronounced in the case of symmetric heating

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References

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Figures

Grahic Jump Location
Fig. 2

(a) Variation of velocity (U0) with βνKn and (b) variation of velocity (U1) with βνKn

Grahic Jump Location
Fig. 3

(a) Variation of velocity (U0) with ln and (b) variation of velocity (U1) with ln

Grahic Jump Location
Fig. 4

(a) Variation of velocity profile for different values of N and βνKn(ξ=1,ln=1.667), (b) variation of velocity profile for different values of N and βνKn(ξ=0,ln=1.667), and (c) variation of velocity profile for different values of N and βνKn(ξ=−1,ln=1.667)

Grahic Jump Location
Fig. 5

(a) Variation of temperature profile for different values of N and βνKn(ξ=1,ln=1.667), (b) variation of temperature profile for different values of N and βνKn(ξ=0,ln=1.667), and (c) variation of temperature profile for different values of N and βνKn(ξ=−1,ln=1.667)

Grahic Jump Location
Fig. 6:

variation of Nusselt number (Nu0) with ln(N=0.01)

Grahic Jump Location
Fig. 7

variation of Nusselt number (Nu1) with ln(N=0.01)

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