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Homotopy simulation of micro-scale flow between rotating disks

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Abstract

The main goal of the present article is to employ the powerful analytical homotopy analysis method (HAM), in contrast to the full numerically or perturbative/asymptotically evaluated ones in the literature, to study the problem of the steady laminar flow and heat transfer generated by two infinite parallel disks separated by a gas-filled micro-gap δ in the presence of velocity slip and temperature jump conditions. Unlike the perturbation techniques, HAM is independent of any small/large physical parameters at all. Furthermore, the HAM provides us a convenient way to guarantee the convergence of solution series, different from all of other analytic techniques, so that it is valid even if nonlinearity becomes rather strong. The current HAM solution demonstrates very good correlation with those of the previously published studies. One disk rotates with angular velocity Ω and the second one with angular velocity sΩ. In addition, the lower disk is insulated and the upper disk is maintained at uniform temperature T 0. The boundary-layer governing partial differential equations (PDEs) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) consisting of the momentum and energy equations by using similarity solution. A solution based on similarity transformation is obtained and employed to investigate the effects of the governing parameters on the all velocity contours, temperature distribution, disks’ torque and power, and Nusselt number. HAM is found to demonstrate excellent potential for simulating micro-scale flow problems.

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Authors and Affiliations

  1. Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box No. 91775-1111, Mashhad, Iran

    N. Freidoonimehr & Asghar B. Rahimi

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  1. N. Freidoonimehr
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  2. Asghar B. Rahimi
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Correspondence to Asghar B. Rahimi.

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Communicated by Francisco Ricardo Cunha.

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Freidoonimehr, N., Rahimi, A.B. Homotopy simulation of micro-scale flow between rotating disks. J Braz. Soc. Mech. Sci. Eng. 38, 2333–2344 (2016). https://doi.org/10.1007/s40430-014-0286-0

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  • DOI: https://doi.org/10.1007/s40430-014-0286-0

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