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Research Papers: Forced Convection

Numerical Simulation of the Effect of Transient Shear Stress and Rate of Heat Transfer Around Different Positions of Sphere in the Presence of Viscous Dissipation

[+] Author and Article Information
Muhammad Ashraf, Almas Fatima

Department of Mathematics,
Faculty of Science,
University of Sargodha,
Sargodha 40100, Pakistan

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 22, 2016; final manuscript received November 23, 2017; published online February 28, 2018. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(6), 061701 (Feb 28, 2018) (12 pages) Paper No: HT-16-1289; doi: 10.1115/1.4038841 History: Received May 22, 2016; Revised November 23, 2017

Abstract

The present study is devoted to the problem of oscillatory convective flow in the presence of viscous dissipation around different positions of a sphere. The system of differential equations governing the flow phenomenon is transformed into dimensionless form by using suitable group of variables and then transformed into convenient form for integration by using primitive variable formulation. Numerical simulation based on finite difference method is carried out to analyze the mixed convection flow mechanism. Special focus is given on the transient shear stress and the rate of heat transfer characteristics and their dependency on various dimensionless parameters that is mixed convection parameter λ, Prandtl number Pr, dissipation parameter $N,$ and angular frequency parameter $ω$. The angles $X=30deg,90 deg$, and $360deg$ are the favorable positions around the sphere for different parameters, where the transient rate of shear stress and heat transfer is noted maximum. Later, the obtained results are presented graphically by using Tech Plot-360 and compared with the previous work given in the literature.

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Figures

Fig. 1

Coordinate system and flow configuration

Fig. 2

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of mixed convection parameter λ = 0.3, 0.5, and 0.7 when Pr = 7.0, angular frequency ω = 0.05, and viscous dissipation parameter N = 0.015 at position of the sphere X = 0 deg

Fig. 3

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of mixed convection parameter λ = 0.3, 0.5 and 0.7 when Pr = 7.0, angular frequency ω = 0.05, and viscous dissipation parameter N = 0.015 at position of the sphere X = 30 deg

Fig. 4

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of mixed convection parameter λ = 0.3, 0.5, and 0.7 when Pr = 7.0, angular frequency ω = 0.05, and viscous dissipation parameter N = 0.015 at position of the sphere X = 90 deg

Fig. 5

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of viscous dissipation parameter N = 0.01, 0.015, and 0.1 when Pr = 7.0, angular frequency ω = 0.05 and mixed convection parameter λ = 0.5 at position of the sphere X = 0 deg

Fig. 6

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of viscous dissipation parameter N = 0.01, 0.015 and 0.1 when Pr = 7.0, angular frequency ω = 0.05, and mixed convection parameter λ = 0.5 at position of the sphere X = 90 deg

Fig. 7

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of viscous dissipation parameter N = 0.01, 0.015 and 0.1 when Pr = 7.0, angular frequency ω = 0.05, and mixed convection parameter λ = 0.5 at position of the sphere X = 360 deg

Fig. 8

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of frequency parameter ω = 0.05, 0.07, 0.1 when N = 0.015, Prandtl number Pr = 7.0, and mixed convection parameter λ = 0.5 at position of the sphere X = 0 deg

Fig. 9

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of Prandtl number Pr = 5.0, 7.0, 10.0 when N = 0.015, angular frequency ω = 0.05, and mixed convection parameter λ = 0.8 at position of the sphere X = 0 deg

Fig. 10

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of Prandtl number Pr = 5.0, 7.0, 10.0 when N = 0.015, angular frequency ω = 0.05, and mixed convection parameter λ = 0.8 at position of the sphere X = 90 deg

Fig. 11

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of Prandtl number Pr = 5.0, 7.0, 10.0 when N = 0.015, angular frequency ω = 0.05, and mixed convection parameter λ = 0.8 at position of the sphere X = 360 deg

Fig. 12

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of frequency parameter ω = 0.05, 0.07, 0.1 when N = 0.015, Prandtl number Pr = 7.0, and mixed convection parameter λ = 0.5 at position of the sphere X = 90 deg

Fig. 13

Geometrical interpretation of (a) transient shear stress and (b) transient rate of heat transfer against τ for different values of frequency parameter ω = 0.05, 0.07, 0.1 when N = 0.015, Prandtl number Pr = 7.0, and mixed convection parameter λ = 0.5 at position of the sphere X = 360 deg

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