Baydaa Khalil Khudhair, Adel Mahmood Saleh and Ali Laftah Ekaid
Pertanika Journal of Science & Technology, Volume 31, Issue 3, April 2023
Keywords: Cylindrical annulus, heat convection, numerical validation, Rayleigh number, vertical vibration
Published on: 7 April 2023
The research looks at how heat transmission is improved when two horizontal cylinders are concentric or vertically eccentric, creating vertical motion. The inner cylinder is uniformly heated, whereas the outer cylinder is isothermal. Apart from Rayleigh’s number (102 ≥ Ra ≥ 106), eccentricity (normalized by the radius difference) at range (ϵ = 0, ±0.625 & ±0.333), and Prandtle number is fixed Pr = 0.7(air), the vibrational frequencies are changed from (ϖ = 0, 100, 1000 &10000). The steady-state, two-dimensional Navier-Stokes equations (with Boussineq approximation) are generated using central difference approximation and solved using the successive over-relaxation (LSOR) method line by line. The contour maps of streamlines and heat lines clearly illustrate the annuli’s heat and fluid flow patterns. According to the results, it is found that the vibration generally enhanced the heat transfer rate more than the stationary one for all values of frequency and different eccentricities with various rates of enhancement. Vibration thermal convection is prominent at low Rayleigh (Ra = 102, 103, 104), and the vibration significantly boosts the heat transfer rate within an annular annulus. In a high Rayleigh number situation, a high Rayleigh number situation (Ra=105 and 106), gravitational thermal convection predominates, and vibration motion does not significantly improve heat transmission. The vibration is a powerful augmentation tool for placing the inner cylinder towards the bottom of the outer cylinder (negative vertical eccentricity (ϵ = -0.625)), the heat rate enhancement more than 3.8-fold at Ra = 103, ϖ = 10000. The Nusselt number has been correlated in a dimensionless form as the Rayleigh number and the vibrational Rayleigh number.
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