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Research Papers

Laminar Film Condensation on a Nanosphere

[+] Author and Article Information
J. A. Esfahani

 Center of Excellence on Modelling and Control Systems (CEMCS), Mechanical Engineering Department, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iranjaesfahani@gmail.com

S. Koohi-Fayegh

 Center of Excellence on Modelling and Control Systems (CEMCS), Mechanical Engineering Department, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

J. Nanotechnol. Eng. Med 3(1), 011005 (Aug 14, 2012) (7 pages) doi:10.1115/1.4005673 History: Received May 22, 2011; Revised June 13, 2011; Published August 13, 2012; Online August 14, 2012

The present work investigates an analytical study on the problem of laminar film condensation on a nanosphere. Due to the microscale interaction, the problem is analyzed by taking into account the effects of slip in velocity and jump in temperature. A relation is derived for the liquid film thickness in the form of a nonlinear differential equation which is solved numerically using the fourth order Runge–Kutta method. Finally, the effect of velocity slip and temperature jump on different condensation parameters including the liquid film thickness, velocity and temperature profiles, Nusselt number, and liquid mass flow rate is discussed. It is found that the increase in the velocity slip and temperature jump results in a thinner liquid film and therefore increases the heat transfer coefficient.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Physical model and coordinate system for condensate film flow on a nanosphere

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Figure 2

The variation of local liquid film thickness for various Ar · Pr/Ja (α,β = 0)

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Figure 3

The variation of local liquid film thickness for various values of slip in velocity (α) and jump in temperature (β) at Ar · Pr/Ja = 1

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Figure 4

The variation of local liquid film thickness for various values of (a) slip in velocity (α) when β = 0 and (b) jump in temperature (β) when α = 0 at Ar · Pr/Ja = 1

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Figure 5

The variation of dimensionless velocity profile across the liquid film for various values of slip in velocity (α) and jump in temperature (β) in two different angles (θ = π/4 , 3π/4) at Ar · Pr/Ja = 1

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Figure 6

The variation of dimensionless temperature profile across the liquid film for various values of slip in velocity (α) and jump in temperature (β) in two different angles (θ=π/4,3π/4) at Ar · Pr/Ja = 1

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Figure 7

The effect of velocity slip and temperature jump on the local Nusselt number in two different angles (θ=π/4,3π/4) for Ar · Pr/Ja = 1

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Figure 8

The variation of local Nusselt number for various values of slip in velocity (α) and jump in temperature (β) at Ar · Pr/Ja = 1

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Figure 9

The effects of slip in velocity (α) and jump in temperature (β) on average Nusselt number for Ar · Pr/Ja = 1

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Figure 10

The effects of slip in velocity (α) and jump in temperature (β) on the liquid mass flow rate per unit width (Г) in two different angles (θ=π/4,3π/4) for Ar · Pr/Ja = 1

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Figure 11

The variation of local liquid mass flow rate per unit width (Г) for various values of slip in velocity (α) and jump in temperature (β) at Ar · Pr/Ja = 1

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