Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

M Qasim,N Riaz,Dianchen Lu,S Shafie

Table 1. Effects of different physical parameters on ${F}^{{\prime\prime} }\left(0\right),-{G}^{{\prime\prime} }\left(0\right),$ ${{\rm{\Theta }}}^{{\prime\prime} }\left(0\right)$ and comparison between shooting method and built-in routine bvp4c in Matlab.

$-{F}^{{\prime\prime} }\left(0\right)$ $-{G}^{{\prime\prime} }\left(0\right)$ $-{{\rm{\Theta }}}^{{\prime} }\left(0\right)$ λ ${\Pr }$ Ec δ ϵ Shooting bvp4c Shooting bvp4c Shooting bvp4c 0.0 1.2 0.6 0.2 0.5 1.569 89 1.569 62 0.784 94 0.784 75 1.823 65 1.823 55 0.5 1.2 0.6 0.2 0.5 1.271 68 1.271 24 0.806 53 0.806 12 1.932 93 1.932 77 1.0 1.2 0.6 0.2 0.5 0.996 57 0.996 18 0.823 76 0.823 45 2.015 22 2.015 09 1.5 1.2 0.6 0.2 0.5 0.735 65 0.735 44 0.838 61 0.838 36 2.080 27 2.080 11 1.2 0.3 0.6 0.2 0.5 0.591 71 0.591 49 0.865 19 0.864 87 1.007 37 1.007 23 1.2 0.7 0.6 0.2 0.5 0.773 96 0.773 64 0.843 76 0.843 42 1.556 59 1.556 41 1.2 1.2 0.6 0.2 0.5 0.890 79 0.890 47 0.829 93 0.829 78 2.042 99 2.042 81 1.2 6.7 0.6 0.2 0.5 1.171 19 1.170 98 0.803 08 0.802 73 4.752 33 4.752 02 1.2 1.0 0.0 0.2 0.5 0.892 27 0.892 06 0.829 71 0.829 65 2.033 36 2.033 22 1.2 1.0 1.0 0.2 0.5 0.827 28 0.826 95 0.837 35 0.837 19 1.760 31 1.760 17 1.2 1.0 2.0 0.2 0.5 0.771 27 0.771 13 0.843 79 0.843 52 1.524 76 1.524 61 1.2 1.0 3.0 0.2 0.5 0.722 07 0.721 95 0.849 35 0.849 14 1.316 99 1.316 71 1.2 1.0 0.5 0.0 0.5 0.887 74 0.887 55 0.830 98 0.830 65 2.129 88 2.129 69 1.2 1.0 0.5 1.0 0.5 0.765 63 0.765 48 0.843 08 0.842 88 1.375 84 1.375 77 1.2 1.0 0.5 2.0 0.5 0.683 16 0.683 03 0.852 15 0.851 94 1.081 84 1.081 69 1.2 1.0 0.5 3.0 0.5 0.622 25 0.622 11 0.859 14 0.858 92 0.916 69 0.916 52