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Table 5 Comparison solution by MDTM, FDM, and shooting method with Nu and HPM [35] for V (η) when \(\varphi\) = 0.07, δ = 2, P = 0, Ha = 0, \(\frac{1}{{R_{d} }}\) = 0, Ec = 2, 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

0.000017360000000

0.000000

2.00e−11

 − 0.8

0.0263871069970389

0.026756648117180

0.028131952780800

2.64e−02

0.026707

 − 0.6

0.0377968202181078

0.038456991519952

0.039791286425600

0.037801

0.038229

 − 0.4

0.0366455592452191

0.037449540554391

0.038657135014400

0.036652

0.037135

 − 0.2

0.0266332183474780

0.027461728992522

0.028476807859200

0.026641

0.027227

0

0.0116755798181022

0.012471144615492

0.013091000000000

0.011684

0.012360

0.2

 − 0.0044314126089784

 − 0.003695940273408

 − 0.00355835729920

 − 4.42e−03

 − 3.73e−03

0.4

 − 0.0178316240970406

 − 0.017207382328530

 − 0.01742024605440

 − 1.78e−02

 − 1.72e−02

0.6

 − 0.0243573107682773

 − 0.023940881135197

 − 0.02432671106560

 − 2.44e−02

 − 2.37e−02

0.8

0.0196282178526106

 − 0.019476674321430

 − 0.01998500942080

 − 1.96e−02

 − 1.90e−02

1

3.524349637965*^-7

0

0.000030240000000

0.000000

0.000000