Heat transfer enhancement inside an eccentric cylinder with an inner rotating wall using porous media: a numerical study
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Heat transfer enhancement inside an eccentric cylinder with an inner rotating wall using porous media: a numerical study Hamid Reza Talesh Bahrami1 · Hamed Safikhani2 Received: 11 February 2020 / Accepted: 7 March 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract Porous media insert is a simple technique to enhance heat transfer, which has been used in different applications. This useful passive improvement technique could be applied on the rotating/fixed inner/outer wall of a/an concentric/eccentric cylinder to improve heat transfer. This configuration has extensive applications in different fields, especially in the bearing technology. In the current study, a numerical research has been done to explore the effect of inserting a porous layer on the inner rotating wall of an eccentric cylinder on the heat transfer. The effects of different parameters including Richardson number, Rayleigh number, Darcy number, the eccentricity, and the inner wall peripheral location are investigated. The results show that using porous media with higher Darcy numbers enhances more heat transfer (for example, about 70% at Da = 10−3 with respect to 30% at Da = 10−6). Also, porous media insert improves heat transfer by about 90% in the medium Richardson numbers (Ri = 0.1). The results show that the effect of porous media insert becomes very considerable as the Rayleigh number increases. For example, porous media insert could augment heat transfer by three times at Ra = 9 × 104. Keywords Mixed convection · Concentric cylinder · Rotating cylinder · Porous media · Rayleigh number List of symbols CF Forchheimer coefficient d Normalized porous cover thickness (d* r−1 i ) d* Porous layer thickness (m) Da Darcy number e Non-dimensional porous layer thickness (m) e* Porous layer thickness (m) h Heat transfer coefficient (W m−2 K−1) K Permeability (m2) k Thermal conductivity (W m−1 K−1) keff Effective thermal conductivity (W m−1 K−1) L Specific length (m) Nu Average Nusselt number Nub Nusselt number without using porous medium Nulocal Local Nusselt number * Hamid Reza Talesh Bahrami [email protected] Hamed Safikhani h‑[email protected] 1
Department of Mechanical Engineering, Qom University of Technology, Martyred Brigadier Khodakaram Blvd, Old Qom‑Tehran Road, Qom 1519‑37195, Iran
Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak 38156‑88349, Iran
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P Dimensionless pressure P* Pressure (Pa) Pr Prandtl number PR Radial ratio r Dimensionless radial coordinate r* Radial coordinate (m) Ra Rayleigh number Rc Thermal conductivity ratio Re Reynolds number ri Inner cylinder radius (m) Ri Richardson number ro Outer cylinder radius (m) T Dimensionless temperature T* Temperature (K) Tc Inner cylinder temperature (K) Th Outer cylinder temperature (K) u*, v* Velocity component in r and theta directions, respectively u, v Dimensionless velocity component in r and theta directions, respectively V Dimensionless velocity magnitude uc Characteristic velocity (m s−1) x*
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