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Table 4 Comparison solution by MDTM, FDM, and shooting method with Nu and HPM [35] for V (η) when \(\varphi\) = 0.01, δ = 1, P = 0, Ha = 0, \(\frac{1}{{R_{d} }}\) = 0, Ec = 1, Pr = 6.2, and \(\alpha\) = 0

From: Radiative MHD flow of Rivlin–Ericksen nanofluid of grade three through porous medium with uniform heat source

η

Present v (η)

v (η) [35]

MDTM

FDM

Shooting method

Nu

HPM

 − 1

0

0

0.000008625000000

0

 − 1.00e−12

 − 0.8

0.0248889137406262

0.025100805859412

0.025678351456000

2.49e-02

0.024978

 − 0.6

0.0343610151313935

0.034694542987441

0.035179982872000

0.034361

0.034499

 − 0.4

0.0315996426708186

0.031972343649594

0.032362783968000

0.0316000

0.031771

 − 0.2

0.0205042979192536

0.020866193989263

0.021116768584000

0.020505

0.020717

0

0.0050363939659476

0.005367924421495

0.005374300000000

0.005037

0.005283

0.2

 − 0.0109298916536909

 − 0.010638770093157

 − 0.01088830874400

 − 1.09e−02

 − 1.07e−02

0.4

 − 0.0234796480160966

 − 0.023252896625209

 − 0.02364919452800

 − 2.35e−02

 − 2.32e−02

0.6

 − 0.0285202216294248

 − 0.028395751318524

 − 0.02883934383200

 − 2.85e−02

 − 2.83e−02

0.8

 − 0.0218952703866748

 − 0.021876616709771

 − 0.02234099241600

 − 2.19e−02

 − 2.17e−02

1

1.27761*10^-7

0

0.000013975000000

0

1.00e−12