Conjugate natural convection in a square enclosure with inclined thin fin of arbitrary length

This work is focused on the numerical study of steady, laminar, conjugate natural convection in a square enclosure with an inclined thin fin of arbitrary length. The inclined fin is attached to the left vertical thin side of the enclosure while the other three sides are considered to have finite and equal thicknesses of arbitrary thermal conductivities. The left wall of the enclosure to which the fin is attached is assumed heated while the external sides of the other three surfaces of the enclosure are cooled. The inclined thin fin is perfectly conductive and is positioned in the middle heated surface of the enclosure. Three different fin lengths equal to 20, 35 and 50 percent of the heated surface are considered. The problem is formulated in terms of the vorticity-stream function procedure. A numerical solution based on the finite-volume method is obtained. Representative results illustrating the effects of the thin fin inclination angle and length and the thermal conductivity of the thick surfaces on the streamlines and temperature contours within the enclosure are reported. In addition, results for the local and average Nusselt numbers are presented and discussed for various parametric conditions.

[1]  K. E. Starner,et al.  An Experimental Investigation of Free-Convection Heat Transfer From Rectangular-Fin Arrays , 1963 .

[2]  Ali J. Chamkha,et al.  EFFECT OF LENGTH AND INCLINATION OF A THIN FIN ON NATURAL CONVECTION IN A SQUARE ENCLOSURE , 2006 .

[3]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[4]  E. Bilgen,et al.  Natural convection in enclosures with partial partitions , 2002 .

[5]  E. Bender.  Numerical heat transfer and fluid flow. Von S. V. Patankar. Hemisphere Publishing Corporation, Washington – New York – London. McGraw Hill Book Company, New York 1980. 1. Aufl., 197 S., 76 Abb., geb., DM 71,90 , 1981 .

[6]  Xundan Shi,et al.  Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall , 2003 .

[7]  E. Bilgen,et al.  Coupling of wall conduction with natural convection in a rectangular enclosure , 1992 .

[8]  E. K. Lakhal,et al.  Natural convection in inclined rectangular enclosures with perfectly conducting fins attached on the heated wall , 1997 .

[9]  M. Hasnaoui,et al.  Natural convection in rectangular enclosures with adiabatic fins attached on the heated wall , 1992 .

[10]  N. K. Sane,et al.  NATURAL CONVECTION HEAT TRANSFER FROM HORIZONTAL RECTANGULAR FIN ARRAYS , 1974 .

[11]  Ramón L. Frederick,et al.  Heat transfer in a square cavity with a conducting partition on its hot wall , 1989 .

[12]  E. Bilgen,et al.  Natural convection in cavities with a thin fin on the hot wall , 2005 .

[13]  V.M.K. Sastri,et al.  Natural convection in a differentially heated square cavity with a horizontal partition plate on the hot wall , 1993 .

[14]  Ricardo Scozia,et al.  NATURAL CONVECTION IN SLENDER CAVITIES WITH MULTIPLE FINS ATTACHED TO AN ACTIVE WALL , 1991 .

[15]  George N. Facas,et al.  Natural convection in a cavity with fins attached to both vertical walls , 1993 .

[16]  Raymond Viskanta,et al.  Heat transfer by conduction, natural convection and radiation across a rectangular cellular structure , 1984 .

[17]  S. Shakerin,et al.  Natural Convection in an Enclosure with Discrete Roughness Elements on a Vertical Heated Wall , 1988 .

[18]  A. Liaqat,et al.  Conjugate natural convection in a square enclosure containing volumetric sources , 2001 .

[19]  Ramón L. Frederick,et al.  Natural convection in an inclined square enclosure with a partition attached to its cold wall , 1989 .

[20]  J. Welling,et al.  Free Convection Heat Transfer Coefficients From Rectangular Vertical Fins , 1965 .

[21]  Xundan Shi,et al.  Laminar Fluid Flow and Heat Transfer in a Lid-Driven Cavity Due to a Thin Fin , 2002 .

[22]  Deborah A. Kaminski,et al.  Conjugate natural convection in a square enclosure: effect of conduction in one of the vertical walls , 1986 .