İKİ SABİT ISI KAYNAĞIYLA ISITILMIŞ EĞİK KARE BİR KAPALI BÖLGEDE DOĞAL KONVEKSIYONLA ISI TRANSFERİ

Year 2009, Volume: 10 Issue: 1, 75 - 83, 05.08.2016

Elif Büyük Öğüt

Abstract

Bu çalışmada, üniform ısı akısıyla ısıtılmış eğik bir kare kapalı bölge içindeki doğal konveksiyonla ısı transferi, nümerik olarak incelenmiştir. Akışın iki boyutlu, daimi, laminer akış olduğu kabul edilmiştir. Nümerik çözüm için diferansiyel quadrature (DQ) yöntemi kullanılmıştır. Kapalı bölgenin iki duvarı eş sıcaklıkta, alt ve sol duvarı sabit ısı akısıyla kısmi olarak ısıtılmış olup, kalan diğer kısımlar ise adyabatik tutulmuştur. Grashof sayısı 103-106 ve kapalı bölgenin eğim açısı ise 0°? ? ?120° aralığında seçilmiştir. Isıtıcı uzunlukları ?=0.4 olarak seçilmiştir. Elde elden sonuçlara göre ısı transfer miktarı, Grashof sayısı arttıkça artmaktadır. Isıtılan alt ve sol duvarlarda ortalama Nusselt sayısının değeri, eğim açısının küçük değerlerinde, alt duvarda daha yüksek iken, eğim açısının büyük değerlerinde sol duvarda daha büyüktür. Eğim açısı 45° olduğunda, ortalama Nusselt sayısı, her iki duvar içinde eşit olmaktadır.

Keywords

Doğal konveksiyon, eğik kare kapalı bölge, ısı akısı, DQ yöntemi

NATURAL CONVECTION HEAT TRANSFER IN INCLINED SQUARE ENCLOSURE HEATED WITH TWO CONSTANT HEAT SOURCE

Abstract

Natural convection in an inclined square enclosure heated with a uniform heat flux is investigated numerically in this study. Two-dimensional, steady, laminar flow is considered. Differential Quadrature (DQ) technique was used for numerical solutions. Two walls of enclosure are isothermal and partially heated with constant heat flux and other one is adiabatic. Grashof number is chosen between 103-106 and inclination angle is chosen as 0°? ? ?120°. Length of heaters are ?=0.4. Results show that, quantitiy of heat transfer increases while Grashof number increases. Considering heated bottom and left walls, mean Nusselt number is higher at bottom wall for smaller values of inclination angle and higher at left wall for higher values of inclination angle. For 45° , average Nusselt number is equal for both walls.

Keywords

Natural convection, inclined square enclosure, heat flux, DQ method

References

• Aydin, O.,and Yang, W. J., Natural convection in enclosures with localized heating from below and symmetrical cooling from sides, Int. J. Num. Meth. Heat Fluid Flow, 10 (2000) 518-529.
• Belman, R.E., Kashef, B.G., Casti, J., Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics 10 (1972) 40-52.
• Calgagni, B., Marsili, F., Paroncini, M., Natural convective heat transfer in square enclosures heated from below, Appl. Therm. Eng. 25 (2005) 2522–2531
• Catton, I., Natural convection in enclosures, Proc. Sixth Int. Heat Transfer Conf. Toronto, Canada, 6 (1978) 13-31.
• Cheikh, N.B., Beya, B.B,. Lili, T., Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below, International Communications in Heat and Mass Transfer 34 (2007) 369–379.
• De Vahl Davis, G. Natural convection of air in a square cavity: a benchmark numerical solution, International Journal for Numerical Methods in Fluids 3 (1983) 249-264.
• Ece, M.C., Büyük, E. Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls, Fluid Dyn. Res. 38 (2006) 564-590.
• Farouk, B., Fusegi, T., Natural convection of a variable property gas in asymmetrically heated square cavities, J. Heat Transfer, 3 (1989), 85-87.
• Incropera, F.P., Convection heat transfer in electronic equipment cooling, J. Heat Transfer, 110 (1988) 1097- 1111.
• Kahveci, K., Natural convection in a partitioned vertical enclosure heated with a uniform heat flux, ASME Journal of Heat Transfer 129 (2007) 717-726.
• Kuyper, R.A., Van Der Meer, TH.., Hoogendoorn, C.J., Henkes, R.A.W.M., Numerical study of laminar and turbulent natural convection in an inclined square cavity, Int. J. Heat Mass Transfer, 36 (1993) 2899-2911.
• November, M., Nansteel, M.W., Natural convection in rectangular enclosures heated from below and cooled along one side, Int. J. Heat Mass Transfer, 30 (1987) 2433-2440.
• Sarris, I.E., Lekakis, I., Vlachos, N.S., Natural convection in rectangular tanks heated locally from bellow, Int. J. Heat Mass Transfer 47 (2004) 3549–3563.
• Sharif, M.A.R. Mohammad, T.R., Natural convection in cavities with constant flux heating at the bottom wall and isothermal cooling from the sidewalls, Int. J. Therm. Sci. 44 (2005) 865–878.
• Shu, C. Differential quadrature and its application in engineering, Springer and Verlag, 2000.
• Shu, C., Richards, B.E. Application of generalized differential quadrature to solve two–dimensional incompressible Navier Stokes equations, International Journal for Numerical Methods in Fluids 15 (1992) 791-798.
• Yang, K.T., Transitions and vifurcations in laminar buoyant flows in confined enclosures, J. Heat Transfer, 110 (1988) 1191-1204.