Table 3.

Validation of numerical simulations in term of skin friction coefficients and heat transfer rate with published work¹⁹ when ${\mathit{ph}}_1={\mathit{ph}}_2={\mathit{ph}}_3=0,{\beta }_e=0,Pr=0.7,\beta =0$ and ${\lambda }_1=0.$

$\lambda$	Malik et al.19			Present simulations
	$-Cf{\left(R,e\right)}^{\frac{1}{2}}$	$-Cg{\left(R,e\right)}^{\frac{1}{2}}$	$-Nu{\left(R,e\right)}^{-\frac{1}{2}}$	$-Cf{\left(R,e\right)}^{\frac{1}{2}}$	$-Cg{\left(R,e\right)}^{\frac{1}{2}}$	$-Nu{\left(R,e\right)}^{-\frac{1}{2}}$
0.0	1.0253	0.6153	0.4295	1.0251320192	0.61529943250	0.4294719073
1.0	2.2007	0.8492	0.6121	2.2007397320	0.84977941223	0.6126020922
10	8.5041	1.3990	1.0097	8.5046102402	1.3995234132	1.0097023340