Simulation of Natural Convection in a Complicated Enclosure with Two Wavy Vertical Walls
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1 A Mtt S, V. 6, 2012,. 57, Sut Ntu Cvt Ct Eu wt Tw Wvy Vt W P S Dtt Mtt, Futy S K K Uvty, K K 40002, T Ct E Mtt CHE, S Ayutty R., B 10400, T y 129@t. Sut Wtyu 1 Dtt Mtt, Futy S K K Uvty, K K 40002, T ut w@u..t Att Ntu vt u u v tw wvy vt w tu. A u wt u-tut u. A vty t ty tt w w w t t w ttu. T tv t tuy t t w, ttu tut t t t vty w vu Dy u, Ry u wv tu. T yz t, t v t ut uy t t FPDE 6.17 P w t t u u v. F t tuy ut, Dy Ry u t tt vt. I t, t tu ttu t tut. I t wv tu, t w tty tut y ut t t tu. Kyw: Ft Et Mt, Ntu Cvt, Pu M 1 C Aut.
2 2834 P. S S. Wtyu 1 Itut T tuy tu vt tw- u wt utut u v t ttt t y tt y t. My tuy t t u wt vu uy t. Mt t y, tu, tz tu. Du t u t t u y, t v, ut u, u ut, t ut, t., t vt t t vty tu t ut t yt. I vty wt u, B t. [1] tu t tu vt w tz u u u u t tt w u tt tw vt w t t tt ttu w t t w ut. B t. [2] vtt t t u -u t w tu vt w wt tu u. T ut u ut y ty t t y wt -ut t. K t. [3] t tu w tt w t ty w t ttu w t t w u ttu t t w. I t, tu u u t t tutu t tuy t t t. A N [4],[5] vtt t t t, Ry u t t t t vt t tu -t u u wt t y u t vu tt ut tu. P Sut [6] yz t w ttu tut tt t-tu u u tt t w t t. I t vty, D D [7],[8],[9] tu t tu vt u u v t t w wvy t vt w t, tw t uut. Fut, Ozt t. [10] tu t tu vt t t wvy-w u t t t u t t wv t y u t-vu t. Itt t t t t Ry u t tu wvy w. T t tuy tu vt u u u tt tw vt w wvy. T u-tut u t t. Btt w t ty w w t t w ttu. T tv t vtt t vt t t vty w Dy u, Ry u wv tu v y u t t t. I t 2, t tt tt u tuut t. St 3 vv t
3 Sut tu vt t u 2835 t ut u. Fy, w vut t utt ut t u u. 2 Ntt P Ctt T w tt tuut t. AR t t, AR = H/L D Dy u t u t vty ( 1 ) H t t u () L t t u () Nu Nut u u (P) P u P Pt u R Ry u T ttu (C) T H ttu t w T C ttu w u uut λ wv tu γ ty t θ ttu ν t vty ( 2 1 ) ρ ty ( 3 ) ψ t ut K ty t u u φ t ut,y Ct t () u,v,y t vty U,V,y t vty X,Y t,y t T tv t t vtt t w, ttu tut t t u t tu vt u u v tw wvy vt w. T u-tut u Nwt t u. H, u, Pt u t tt t 0.71, t u t. Bu t u tw wvy vt w, t t t wvy w v y (1) (2), tvy. 1 (y) =1 λ + λ (2π(1 y)) (1) 2 (y) =1 λ + λ (2πy). (2) Dt vu ttu t uy. Btt w t ty, T H, w w t t w ttu, T C. T ttu t tt wtt T () =T C + T [ ( )] H T C 2π 1. (3) 2 L Vty w z (u = v = 0). At t utt t z. It t t t t
4 2836 P. S S. Wtyu u = v = T = 0 H u = v = 0, T = Su L Fu 1: A vty wt tw wvy vt w uy t. vt w t t t tt w (AR = H/L). A y u u v w F.1. 3 Gv Eut Ntu vt y t ut vt, tu y ([11]). T w ut tw t y t u wt u u t tt t t ty t uyy. T v ut ty tw- tu vt w t u vty : u + v =0, (4) y u u + v u u v + v v y = 1 ρ y = 1 ρ + ν y + ν u T + v T y = α ( 2 v + 2 v 2 y 2 ( 2 u + 2 u 2 y 2 ) ( 2 T T y 2 ) ν u, (5) K ν K v + β (T T C), (6) wt w uy t: u( 1 (y),y)=u( 2 (y),y)=u(, 0) = u(, y) =0, v( 1 (y),y)=v( 2 (y),y)=v(, 0) = v(, y) =0, T ( 1 (y),y)=t( 2 (y),y)=t(, y) =T C =0, T (, 0) = T H = T C + T H T C 2 ) [ 1. (7) ( 2π L )].
5 Sut tu vt t u 2837 T v v ut t t - y u t w v: X = L, Y = y L, U = ul α, V = vl α, θ = T T C T H T C P = L2 ρα, P = ν 2 α, R = β (T H T C ) L 3 P, D = K ν 2 L. 2 T ut (4)-(7) t : U X + V Y U U X + V U Y = P ( 2 ) X + P U X + 2 U 2 Y 2 U V X + V V ( 2 ) Y = P Y + P V X + 2 V 2 Y 2 =0, (8) P U, (9) D P V + RPθ, (10) D U θ X + V θ ( 2 ) Y = θ X + 2 θ. (11) 2 Y 2 S t t w t tuy t w, t u t y y u t t ut w U = ψ ψ V =. Tu, Y X E.(8) t E.(12) 2 ψ X ψ Y 2 = U Y V X. (12) T t t u P, w u t ty t t t wt ty t γ u tt P = γ ( U + ) V X Y ([12]). Suttut P t E.(9) (10) y E.(13) (14). U U X + V U Y = γ ( U X X + V ) ( 2 ) U + P Y X + 2 U 2 Y 2 U V X + V V Y = γ Y P U, (13) D ( U X + V ) ( 2 ) V + P Y X + 2 V P 2 Y 2 D V + RPθ. (14) T t uy t : U( 1 (Y ),Y)=U( 2 (Y ),Y)=U(X, 0) = U(X, Y )=0, V ( 1 (Y ),Y)=V ( 2 (Y ),Y)=V (X, 0) = V (X, Y )=0, (15)
6 2838 P. S S. Wtyu θ( 1 (Y ),Y)=θ( 2 (Y ),Y)=θ(X, Y )=0, θ(x, 0) = 1 (1 (2πX)). 2 T vuz t t t y u w, tut tw- vt [13] 2 φ X + 2 φ 2 Y = (Uθ) (Vθ) 2 Y X. (16) Wt w uy t: φ(x, 0) = π (πx) φ( 1 (Y ),Y)=φ( 2 (Y ),Y)=φ(X, Y )=0. (17) 4 Rut Du T yz t u ut, t v ut t vuy t FPDE 6.17 P. FPDE tw w t t y t tu t t t ut yt t t t. T, t v t yt t tu utut t ut. I t t, t tt t Dy u, Ry u wv tu. T ut t vy vu t t y y t, t t w utut FPDE t w u vu. I t tuy, t t tz t t t vu D, R λ. Cutt v ut vu D = R = v w t ([1],[9]). A, t wv tu v tu ([9]). T t t,ar, u uut t 1 2, tvy. Buy t w tut v y E.(15),(16) (17). St, t t t vy tt t w t utt u ut t t t vty. F.2. w t ut D w F.2()-2() t ut D =10 2 F.2()-2() D =10 4. St utt tt u ut yt wt t t t vt t ψ =0.0 u tt t t tv vu t t tv. T t t t t u wy tt tv tv v t-w w ut tt, tvy. T w v w t t tt t w tt w D. T u vu t ut F.2() ψ =7.5 tuy t ψ =0.16
7 Sut tu vt t u 2839 w F.2(). T ttu tut t tt. I F.2(), t t t t u w t tu tut t w D w F.2(). D D y t t. Ht F.2 w tt t w t tt t t t t w t tut t t tt. t v y z A D E B C w u E : 7.50 D : 7.00 C : 6.50 B : 6.00 A : 5.50 z : 5.00 y : 4.50 : 4.00 w : 3.50 v : 3.00 : : : : : : :-6.00 : :-7.00 :-7.50 t u : 1.00 t : 0.95 : 0.90 : 0.85 : 0.80 : 0.75 : 0.70 : 0.65 :0.60 : 0.55 : 0.50 : 0.45 : 0.40 : 0.35 : 0.30 : 0.25 : 0.20 : 0.15 : 0.10 : 0.05 : 0.00 v : 3.30 u : 3.00 t : 2.70 : 2.40 : 2.10 : 1.80 : 1.50 : 1.20 : 0.90 : 0.60 : : : : : : : : : : () () () : 0.16 : 0.14 : 0.12 : 0.10 :0.08 : 0.06 : 0.04 : 0.02 : 0.00 :-0.02 :-0.04 : :-0.08 :-0.10 : :-0.14 :-0.16 u : 1.00 t : 0.95 : 0.90 : 0.85 : 0.80 : 0.75 : 0.70 : 0.65 :0.60 : 0.55 : 0.50 : 0.45 : 0.40 : 0.35 : 0.30 : 0.25 : 0.20 : 0.15 : 0.10 : 0.05 : 0.00 u t v : 3.30 u : 3.00 t : 2.70 : 2.40 : 2.10 : 1.80 : 1.50 : 1.20 : 0.90 : 0.60 : 0.30 : 0.00 : : : : : : : : : : () () () Fu 2: St (t), t () t (t) R =10 5, λ =0.05, D =10 2 (v), D =10 4 (tt). A R t 10 3 (F.3), t v tt t tty ut t t vu wt R =10 5 (F.2()). S t t D, t tu ttu t tut w R u. T ut t vy wv tu y y t (F.4). It t tt t w tw vt wvy w tt u t t t u. Mv, t w tt wt vu wv tu. F λ = 0.02, t u vu t ut ψ =9.0 ψ =5.5 w λ t 1.0.
8 2840 P. S S. Wtyu : 4.50 : 4.00 : 3.50 : 3.00 : 2.50 : 2.00 : 1.50 : 1.00 : 0.50 : 0.00 : :-1.00 :-1.50 : : : : :-4.00 : S = -2 u : 1.00 t : 0.95 : 0.90 : 0.85 : 0.80 : 0.75 : 0.70 : 0.65 : 0.60 : 0.55 : 0.50 : 0.45 : 0.40 : 0.35 : 0.30 : 0.25 : 0.20 : 0.15 : 0.10 : 0.05 : 0.00 v : 3.30 u : 3.00 t : 2.70 : 2.40 : 2.10 : 1.80 : 1.50 : 1.20 : 0.90 : 0.60 : 0.30 : 0.00 : : : : : : : : :-2.70 : () () () Fu 3: St (t), t () t (t) D =10 2, λ =0.05, R =10 3. : 9.00 : 8.00 : 7.00 : 6.00 : 5.00 : 4.00 : 3.00 : 2.00 : 1.00 : 0.00 : :-2.00 :-3.00 : : :-6.00 : :-8.00 : z t w u y v C A B C : 7.00 A : 6.00 y : 5.00 w : 4.00 u : 3.00 : 2.00 : 1.50 : 1.00 : 0.50 : 0.00 : :-1.00 : : : : : : : u t v w w : 5.50 v : 5.00 t : 4.00 : 3.00 : 2.50 : 2.00 : 1.50 : 1.00 : 0.50 : 0.00 : : : :-2.00 :-2.50 : :-4.00 :-5.00 : () () () Fu 4: St t wv tu R = 10 5, D = 10 2, λ =0.02, 0.06, 1.0, tvy. S t t t t, t ut t w. 5 Cu T t w vtt t tu vt u u u tt tw vt w wvy. T u-tut u t t. H, t u. T t tuy t t t Dy u, Ry u wv tu tu vt y t ut vt,
9 Sut tu vt t u 2841 tu y. T yz t, t v ut t tw FPDE 6.17 P. Itt ut t y y t, t t. T vu Ry Dy u v w ty. T R v I t u wt u, D u t t w t. I t v ty, t D tw St w vu t utt tt t D t tt vt. I t, t tu t t tt wt w D. I t R, t uvt t uyy v w. It v tt R t tt t u w. T wv tu t t w tty t vty, tt, t w tut y ut t t tu. T wvy w t ttu t tut. ACKNOWLEDGEMENTS. T (ty) ut y Ct E Mtt, t C H Eut, T. T ut wu t t Dtt Mtt, Futy S, K K Uvty (T) utt u y t w. R [1] T. B, S. Ry, A. S I. P, Ft t ut tu vt w tz u wt u u u t u -u t, Itt Ju Ht M T, 52 (2009), [2] T. B, S. Ry, B. K A.R. B, Ft t y tu vt w tu u u t u -u t t t w, Itt Ju Ht M T, 51 (2008), [3] A. K, H.A. Ozt Y. B, T t Pt u tu vt tu u wt z t w, Itt Ju Ht M T, 34 (2007), [4] H. A L. N, L tu vt t tu -t: u y uy t, Ey Bu, 33 (2000),
10 2842 P. S S. Wtyu [5] H. A L. N, Nu ut uyt w tu -t u wt y uy t, Ey Bu, 33 (2000), [6] P. S S. Wtyu, Nu tuy tu vt tu w t ttu ut t t, L Ju A S, 2 (2011), [7] A. D M.K. D, L tu vt t vty wt ty v w ttu, Itt Ju Ht M T, 48 (2005), [8] A. D M.K. D, Ntu vt vty wt wvy w t w uy t t t, ASME Ju Ht T, 128 (2006), [9] A. D M.K. D, Ht t t vuzt tu vt t vty, Itt Ju Ht M T, 51 (2008), [10] H.F. Ozt, E. Au-N, Y. V A. C, Ntu vt wvy u wt vut t u, Itt Ju T S, 50 (2011), [11] M. Styty, T. B, S. Ry I. P, Sty tu vt w u vty wt u u y t w(), Itt Ju Ht M T, 50 (2007), [12] J.N. Ry, A tut t t t t t, MGw-H, Nw Y, [13] T. B, G. Av S. Ry, Vuzt t w u t tu vt wt tu vt u B t t, Itt Ju Ht M T, 52 (2009), Rv: Juy, 2012
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Available online Journal of Scientific and Engineering Research, 2016, 3(6): Research Article
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