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 $\omega $. The angles $X=30deg,90\u2009deg$, 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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June 2018

Research-Article

# 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

Muhammad Ashraf,

Muhammad Ashraf

Department of Mathematics,

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

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Almas Fatima

Almas Fatima

Department of Mathematics,

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

Search for other works by this author on:

Muhammad Ashraf

Department of Mathematics,

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

Almas Fatima

Department of Mathematics,

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

Faculty of Science,

University of Sargodha,

Sargodha 40100, Pakistan

*J. Heat Transfer*. Jun 2018, 140(6): 061701 (12 pages)

**Published Online:**February 28, 2018

Article history

Received:

May 22, 2016

Revised:

November 23, 2017

Citation

Ashraf, M., and Fatima, A. (February 28, 2018). "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." ASME. *J. Heat Transfer*. June 2018; 140(6): 061701. https://doi.org/10.1115/1.4038841

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Introduction

Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow