Numerical study on the effect of conduction in mixed convection flow in a rectangular cavity with a heat conducting horizontal cylinder

Abstract

Fluid flow "ith heat transfer due to the combined effect of free and forced convection (mixed convection) are often encou~teled in engineering ,ystems eg" in the design of building, air conditioning, cooling of electronic devices, nuclear reactors, ~hcmical processing equipment, lubricating grooves and industrial process float glass manufacturing etc. The simplest configurations approximating some "f these practical flow siluations ate lhc flow and heal transfer in a vented eayity, whele the flow is induced by a sl,ear force resulting from the external forced ,trcam and in a lid-driven eavity where the flow i, induced by a shear force re,,,itillg fwm the motion of a moving "ail, In lhis thesis under the title "Numerical Study on the Effect of Conduction in Mixed Conveclion Flow in a Rcctangnlar Ca,ity WIth a H~at Condueting Horizontal Cylinder", tlvo prohlems have b~cn studied. The study a, wcll depending on various flow and geometrical conditions are abstracted below. Firslly, the effect of conduction ill mixed convectioll flow in a rectangular vented eavily with a heat eondueting horizont"l (CIrcular/square) cylinder h",~ becn invcstig"ted. The right vertical wall of the cavill' is kcpt at a unifon11 consl"nl temperature, while the other walls (top, bottom and lefl vertical) arc assumed adi"balic. A heat conducting horizOlllal cyhndcr is placed some"here wilhin the cavity. An external flow cntcrs the cavity thl'Oughan opcning in the lefl vertical wnll and exits to another opening in thc opposite walL Finally, thc effect of joule heating in thc conpling of condlldion with magnctohydrodynamies (MHO) mixed com'celion flow in a lid-dri,en ca,ity along with" heat conducting horiwlltal (circular/'t]uare) cylinder have been in~estigat~d. The C"vily c(}nsists of adiabatic horizonl"l wall> and differentially heated vertical walls, bnt it also conlains a heat conducting hori7ontal cylindcr located somewhere withm thc cavity. Tempemture of thc lcll moving wall, which has constant flow speed, i, lower than that of the right vertical waiL A uniform magnelic field is applied in the horizontal direction normallo the moving wall The physical problems are represented mathcmatically by different sets of governing equations along with the corresponding boundary condition,. Usmg a elass of Vlll appropriate transformations, the governing equations along with the boundary conditions are transformed into non-dimensional form, which are then solved by employing a finite-element sehcme based on the Gaierkin method of weighted residuais. Results are presented in terms of streamlines, isothemls, average Nusselt number aiong the hot wall, average temperaturc of the fluid in the eavity and dimensionicss temperature at the cylinder center for different combinations of the gowming parameterg namely Reynolds number Re. Prandtl number Pr, solid-tluid thelmal conductivity ratio K, as well a' the size, shape and locations of the inner cylindel, cavity aspect ratio AR, locations of the inlet and outlet port (tor vented ~'\Vlty), Hartmann number Ha, and Joule heating parameter J (for lid-dliv~n cavity) at the three values of Richardson number Ri, varying frum 0,0 to 5,0. This range of Ri are selected on the basis of calculation covering pure forced convection, pure mixed convection and free eonvedion dominated regimes. Comparisons with pl~vim"ly published work are performed and the results are found to be in excellent agreement Thc result, indicate that both the flow and the thennal fidds strongly depend on the parame!crs, Reynolds number Re, the size and locations of the inncr cylinder, cavity a'l'ect ratio .-JR, location, of the inlet and outlet port (for wnted cavIty), llal tmann number Ha, and Joule heating; parameter J (for hd-driven cavity) at the three convective regime,. H is also observed that the parameters Prandtl number PI', solidfluid thennal conductivily ratio K, have imigmficant effect on the flow f,eld, and hav~ significant effect on the thcrmal fields at the three convective regimes The computational results also indicale that the average Nussclt number at the hot wall, average temperature of the fluid in the cavity and temperatUl'e at tbe ~ylmdcr center are depending on the aforementioned dimensionless parameter,_ For the pLUpOSCof comparison of the effect of cylinder shape on heat lransfer, the results In terms of average J\usselt number arc shown in tabular form, Tbe obtained resull' reveal that the averagc Nusselt number at the hot wall for the case of "Iuate cyl i nder are generally higher than that of for the case of circular cylinder.