1 Introduction
Nomenclature |
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2 Geometrical Description and Governing Equations
Fig. 1 (Color online) Schematic description of the problem. |
3 Numerical Scheme
4 Stability and Convergence
5 Results and Discussion
Table 1 Properties of H2O and Ag at 25°C. |
Thermo-physical properties | H2O | Ag |
---|---|---|
p(Kg/m3) | 997.1 | 10501 |
k(W/mK) | 0.613 | 429 |
cp(J/KgK) | 4179 | 235 |
(1/K)xl0-5 | 21 | 1.8 |
Pr | 6.07 | - |
a(s/m) | 5 x 10~2 | 6.30 x 107 |
Table 2 Comparison of the variability of skin friction coefficients (cfx /cfy) and local Nusselt number Nux for different Ra at ω = 0, Vs = 1, Ts = 0, R = 0.5, M = 1, K = 1.5, Ks = 3, Kc = 0.5, Ec = 0.001, ϕ = 0.1, and Gr = 10. |
Kumar and Sood[16] | Present study | |
---|---|---|
Ra | (cfx, cfy, Nux) | (cfx, cfy, Nux) |
0.8 | (0.723 606, -0.716 842, 0.755 381) | (0.7463406, -0.7629039, 0.723 199 5) |
1.5 | (0.766 609, -0.744 827, 0.944 736) | (0.7834152, -0.7919051, 0.8998278) |
2 | (0.791274, -0.761 166, 1.063168) | (0.804 576 8, -0.808 7661, 1.009 455) |
3.5 | (0.846 564, -0.798 565, 1.363 603) | (0.851706 5, -0.847143 2, 1.284 967) |
5.1 Effect of Oscillation Frequencies ($\omega$)
Fig. 2 (Color online) Outcomes of frequency of oscillation ($\omega$). |
Fig. 3 (Color online) Outcomes of frequency of oscillation ($\omega$) against $t'$. |
5.2 Effect of Eckert Number ($Ec$)
Fig. 4 (Color online) Outcomes of Eckert number ($Ec$). |
5.3 Effect of Volume Fraction of Nanoparticles ($\phi$)
Fig. 5 (Color online) Outcomes of nanoparticles volume fraction ($\phi$). |
5.4 Effect of Homogeneous/Heterogeneous Reaction Parameters ($K_c/K_s$)
Fig. 6 (Color online) Outcomes of $K_c$ and $K_s$ on concentrations ($A$ and $B$). |
5.5 Effect of Schmidt Number ($Sc$)
Fig. 7 (Color online) Outcomes of Schmidt number ($Sc$) on concentrations on $A$ and $B$ for different $K_s$ and $K_c$. |
5.6 Effect on Skin-Friction, Reactant Sherwood Numbers and Nusselt Number
Table 3 Variability of skin friction coefficients (cfx/cfy), local Nusselt number Nux and Sherwood numbers (SHax/SHbx) for different values of M, K and R in SNF case (Vs = Ts≠ 0). |
M | K | R | (cfx,Cfy) | (Nux) | (ShAx, ShBx ) |
---|---|---|---|---|---|
3 | 3 | 1 | (0.007 3612, -0.020 193 3) | 2.433 326 | (-0.038 619 2, 0.028 477 6) |
5 | (0.0030690, -0.0132055) | 2.225 189 | (-0.036 692 1, 0.027 064 8) | ||
7 | (-0.000 118 5, -0.009 4916) | 2.161 725 | (-0.034 889 0, 0.025 714 5) | ||
9 | (-0.0025423,-0.0072348) | 2.157 807 | (-0.033 4315, 0.024 618 1) | ||
3 | 3 | 1 | (0.007 361 2, -0.020 193 3) | 2.433 326 | (-0.038 619 2, 0.028 477 6) |
5 | (0.003 253 7, -0.017 108 7) | 2.881 315 | (-0.035 566 2, 0.026 165 5) | ||
7 | (0.000 375 8, -0.014 868 1) | 3.087 055 | (-0.0336178, 0.0246968) | ||
9 | (-0.001 788 5, -0.013 173 4) | 3.186 164 | (-0.032 244 4, 0.023 664 7) | ||
3 | 3 | 0.8 | (0.007 426 0, -0.016 240 6) | 2.613 552 | (-0.039 723 3, 0.029 341 0) |
1.5 | (0.006 951 2, -0.029 473 9) | 2.000 986 | (-0.035 695 7, 0.026198 1) | ||
2.2 | (0.005 863 3, -0.040 377 6) | 1.507 200 | (-0.031 621 7, 0.023 041 5) | ||
2.9 | (0.004 374 1, -0.048 420 4) | 1.189 210 | (-0.028 070 7, 0.020 314 6) |
Table 4 Variability of skin friction coefficients (cfx/cfy), local Nusselt number (Nux) and Sherwood numbers (SHAx/SHBx) for different values of M,K and R in NSNF case (VS = Ts = 0).. |
M | K | R | (cfx, cfy ) | Nux | (ShAx, ShBx) |
---|---|---|---|---|---|
3 | 3 | 1 | (0.045 101 1, -0.024 203 7) | -2.375 846 | (-0.041 399 7, 0.030 716 5) |
5 | (0.026 255 1, -0.015 443 8) | -2.623 367 | ( -0.040 109 6, 0.029 747 7) | ||
7 | (0.011 882 7, -0.011 147 8) | -2.795 299 | (-0.038 481 6, 0.028 496 4) | ||
9 | (0.000 452 8, -0.008 642 0) | -2.890 901 | (-0.037 020 4, 0.027 372 0) | ||
3 | 3 | 1 | (0.045 101 1, -0.024 203 7) | -2.375 846 | (-0.041 399 7, 0.030 716 5) |
5 | (0.028 237 1, -0.020 725 5) | -1.356 246 | (-0.038 538 8, 0.028 486 3) | ||
7 | (0.015 826 4, -0.018 241 1) | -0.886 092 7 | (-0.036 616 4, 0.026 999 8) | ||
9 | (0.005 970 6, -0.016 373 1) | -0.6541395 | (-0.035 200 7, 0.025 911 5) | ||
3 | 3 | 0.8 | (0.045 654 8,-0.019 4512) | -1.876 567 | (-0.042 796 2, 0.031 816 8) |
1.5 | (0.042 513 4, -0.035 346 5) | -3.640 277 | (-0.037 654 8, 0.027 769 9) | ||
2.2 | (0.036 490 6, -0.048 277 0) | -5.198112 | (-0.032 306 3, 0.023 578 2) | ||
2.9 | (0.028 799 6, -0.057 539 9) | -6.247421 | ( -0.027 549 8, 0.019 877 5) |
Table 5 Variability of skin friction coefficients (cfX/cfY ), local Nusselt number (NuX) and Sherwood umbers (ShAX/ShBX) for different values of Ra, ω and Ec in SNF case (Vs = Ts ≠ 0). |
Ra | Ec | (cfx,cfy) | Nux | (ShAx, SHbx) | |
---|---|---|---|---|---|
0.4 | 0.1 | 0.01 | (0.007 3612, -0.020 193 3) | 2.433 326 | (-0.038 619 2, 0.028 477 6) |
0.8 | (0.008 089 9, -0.021 037 7) | 2.376 643 | (-0.039 506 8, 0.029 172 2) | ||
1.2 | (0.008 640 9, -0.021 689 4) | 2.287593 | (-0.040 210 4, 0.029 724 8) | ||
1.6 | (0.009 073 2, -0.022 209 5) | 2.177 142 | (-0.040 784 4, 0.030 177 0) | ||
0.4 | 0 | 0.01 | (0.001 426 6, -0.008 416 9) | 6.586 285 | (-0.042 664 5, 0.031 493 4) |
0.1 | (0.007 3612,-0.020 193 3) | 2.433 326 | (-0.038 619 2, 0.028 477 6) | ||
0.2 | (0.024 535 3, -0.007 576 3) | 77.074 29 | (-0.028 666 2, 0.021 074 7) | ||
0.3 | (0.002 929 3, 0.004 086 5) | 17.846 68 | (-0.018 548 0, 0.013 573 3) | ||
0.4 | (-0.001 454 9, 0.011 679 3) | 7.654724 | (-0.014 276 9, 0.010 407 0) | ||
0.4 | 0.1 | 0.005 | (0.005 915 3, -0.018 928 4) | 3.714268 | (-0.037 574 7, 0.027 679 0) |
0.01 | (0.007 3612,-0.020 193 3) | 2.433 326 | (-0.038 619 2, 0.028 477 6) | ||
0.015 | (0.009 189 5, -0.021 769 2) | 0.957539 | (-0.039 940 3, 0.029 488 9) | ||
0.02 | (0.011 579 5, -0.023 784 6) | -0.768 031 | (-0.041 674 2, 0.030 818 1) |
Table 6 Variability of skin friction coefficients (cfX/cfY ), local Nusselt number (NuX) and Sherwood numbers (ShAX/ShBX) for different values of Ra, ω and Ec in NSNF case (Vs = Ts = 0). |
Ra | Ec | (cfx, cfy) | Nux | (SHax , SHbx) | |
---|---|---|---|---|---|
0.4 | 0.1 | 0.01 | (0.045 101 1, -0.024 203 7) | -2.375 846 | (-0.041399 7, 0.030 716 5) |
0.8 | (0.045 619 7,-0.024 587 7) | -2.846 729 | (-0.0418108, 0.031060 6) | ||
1.2 | (0.045 9612,-0.024 864 3) | -3.283 800 | (-0.042 1175, 0.031 318 8) | ||
1.6 | (0.046 196 2,-0.025 0721) | -3.692 801 | (-0.042 355 6, 0.031520 2) | ||
0.4 | 0 | 0.01 | (0.0172209,-0.0106230) | 5.256952 | (-0.047741 3, 0.035 475 5) |
0.1 | (0.045 101 1, -0.024 203 7) | -2.375 846 | (-0.041399 7, 0.030 716 5) | ||
0.2 | (0.012 8541, 0.006 220 2) | 29.824 84 | (-0.025 944 3, 0.019 155 2) | ||
0.3 | (-0.0099312, 0.007 8093) | 13.42764 | (-0.0112600, 0.008 216 7) | ||
0.4 | (-0.033 7732,0.0176608) | -0.634210 | (-0.0078021, 0.005 619 4) | ||
0.4 | 0.1 | 0.005 | (0.040 895 9,-0.022 833 3) | 0.3041929 | (-0.040 5021, 0.029 998 5) |
0.01 | (0.045 101 1, -0.024 203 7) | -2.375 846 | (-0.041399 7, 0.030 716 5) | ||
0.015 | (0.050 912 6,-0.026 083 2) | -6.063 425 | (-0.042 5664, 0.031652 3) | ||
0.02 | (0.059 643 9,-0.028 856 7) | -11.625 26 | (-0.044 174 9, 0.032 946 1) |