Table 4 Variation of \(\pmb{\beta^{2}=\Upsilon}\) , \(\pmb{f''(0)}\) , \(\pmb{\theta(1)}\) and \(\pmb{-\theta'(0)}\) using 20th-order (HAM) via Mathematica package BVPh2.0 approximation when \(\pmb{\mathit {Ma}=1}\) , \(\pmb{M=1}\) , \(\pmb{\mathit {Pr}=0.2}\) , \(\pmb{\mathit {Gr}=5}\) and \(\pmb{S=0.2}\)
\(\boldsymbol{\hbar_{f}}\) | \(\boldsymbol{\hbar_{\theta}}\) | \(\boldsymbol{\beta^{2}}\) | \(\boldsymbol {f''(0)}\) | θ (1) | \(\boldsymbol{-\theta'(0)}\) |
|---|---|---|---|---|---|
K = 0.1 | |||||
−0.832780 | −0.941760 | 0.727013 | −3.16449 | 0.977408 | 0.0721367 |
−0.836000 | −0.857229 | 0.527013 | −3.11339 | 0.983654 | 0.0524063 |
−0.838367 | −0.795225 | 0.327013 | −3.06291 | 0.989878 | 0.0325884 |
−0.840192 | −0.717392 | 0.127013 | −3.01303 | 0.996077 | 0.0126844 |
−0.840993 | −0.617020 | 0.027013 | −2.98831 | 0.999166 | 0.0027005 |
K = 0.2 | |||||
−0.720505 | −0.669723 | 0.727013 | −2.98309 | 0.977904 | 0.0721543 |
−0.72187 | −0.614013 | 0.527013 | −2.93775 | 0.984014 | 0.0524153 |
−0.72276 | −0.555679 | 0.327013 | −2.89292 | 0.990101 | 0.0325917 |
−0.723643 | −0.475951 | 0.127013 | −2.84858 | 0.996164 | 0.0126848 |
−0.724163 | −0.372249 | 0.027013 | −2.82660 | 0.999185 | 0.0027003 |
K = 0.3 | |||||
−0.632928 | −0.491987 | 0.727013 | −2.84154 | 0.978332 | 0.0721680 |
−0.633377 | −0.453117 | 0.527013 | −2.80042 | 0.984325 | 0.0524221 |
−0.633868 | −0.413418 | 0.327013 | −2.75968 | 0.990294 | 0.0325937 |
−0.634495 | −0.359594 | 0.127013 | −2.71935 | 0.996239 | 0.0126836 |
−0.634866 | −0.309759 | 0.027013 | −2.69935 | 0.999201 | 0.0026989 |