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Table 7 Comparison solution by MDTM, FDM, and shooting method with Nu and HPM [35] for θ (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 θ (η)

θ (η) [35]

MDTM

FDM

Shooting method

Nu

HPM

 − 1

0.500000000000000

0.500000000000000

0.501532200000000

5.00e−01

0.500000

 − 0.8

0.4122424546865951

0.411231537502520

0.412400824640000

0.412251

0.410966

 − 0.6

0.3184236211524941

0.319967177782257

0.320214567360000

0.318437

0.317645

 − 0.4

0.2238523181397247

0.226206920839213

0.226089794880000

0.223868

0.223923

 − 0.2

0.1285597853705173

0.129950766673386

0.130139604800000

0.128579

0.129006

0

0.0307284125447637

0.031198715284777

0.031893000000000

0.030749

0.030992

0.2

 − 0.0709204281187916

 − 0.070049233326614

 − 0.06928593696000

 − 7.09e−02

 − 7.10e−02

0.4

 − 0.1760391250819469

 − 0.173793079160787

 − 0.17377886944000

 − 0.176022

 − 0.176076

0.6

 − 0.282882693412802

 − 0.280032822217743

 − 0.28129403232000

 − 0.282871

 − 0.282354

0.8

 − 0.3900682662257274

 − 0.388768462497480

 − 0.39044705760000

 − 0.390062

 − 0.389033

1

 − 0.4999999247040331

 − 0.500000000000000

 − 0.49834180000000

 − 0.500000

 − 0.500000