A New Spectral-Homotopy Perturbation Method and Its Application to Jeffery-Hamel Nanofluid Flow with High Magnetic Field

Table 1

Comparison of the numerical results against the SHPM approximate solutions for 𝐹(𝜂) and 𝐹^′′(𝜂) when Re = 10, Ha=200, and 𝛼=5.

	𝜂	𝐹(𝜂)			𝐹^′′(𝜂)
		2nd order	3rd order	Numerical	2nd order	3rd order	Numerical
𝜙=0.1	0.0	1	1	1	−1.97361423	−1.97361423	−1.97361423
	0.1	0.99013256	0.99013258	0.99013258	−1.97286367	−1.97286367	−1.97286367
	0.2	0.96053716	0.96053725	0.96053725	−1.97132614	−1.97132614	−1.97132614
	0.3	0.91122738	0.91122758	0.91122758	−1.97114172	−1.97114171	−1.97114172
	0.4	0.84220211	0.84220246	0.84220246	−1.97587434	−1.97587434	−1.97587434
	0.5	0.75340988	0.75341039	0.75341039	−1.99052431	−1.99052431	−1.99052431
	0.6	0.64469883	0.64469947	0.64469947	−2.02157959	−2.02157959	−2.02157959
	0.7	0.51575172	0.51575242	0.51575242	−2.07714031	−2.07714032	−2.07714032
	0.8	0.36600474	0.36600533	0.36600533	−2.16716308	−2.16716309	−2.16716309
	0.9	0.19454749	0.19454782	0.19454782	−2.30388760	−2.30388760	−2.30388760
	1.0	0	0	0	−2.50253230	−2.50253230	−2.50253230
𝜙=0.4	0.0	1	1	1	−1.97636754	−1.97636754	−1.97636754
	0.1	0.99011749	0.99011749	0.99011749	−1.97717852	−1.97717852	−1.97717852
	0.2	0.96046170	0.96046171	0.96046171	−1.97979610	−1.97979610	−1.97979610
	0.3	0.91100600	0.91100602	0.91100602	−1.98477509	−1.98477509	−1.98477509
	0.4	0.84169981	0.84169985	0.84169985	−1.99304375	−1.99304375	−1.99304375
	0.5	0.75245937	0.75245942	0.75245942	−2.00591025	−2.00591025	−2.00591025
	0.6	0.64315460	0.64315467	0.64315467	−2.02507402	−2.02507402	−2.02507403
	0.7	0.51359211	0.51359218	0.51359218	−2.05264442	−2.05264442	−2.05264442
	0.8	0.36349409	0.36349415	0.36349415	−2.09116967	−2.09116967	−2.09116968
	0.9	0.19247275	0.19247278	0.19247278	−2.14368045	−2.14368045	−2.14368046
	1.0	0	0	0	−2.21375299	−2.21375298	−2.21375298