Table 6 Heat transfer rate \(z = \eta \theta_{y}\) at wall h for water, P/water nano fluid , P-G0/water hybrid nano fluid varying non-uniformity parameter fixing \(m_{0} = 3(sphere),\)\(x = 0.3,\gamma = 0.1.\)

From: Irreversibility effects in peristaltic transport of hybrid nanomaterial in the presence of heat absorption

\(m\)

\(M\)

\(B_{r}\)

\(\phi\)

\(\beta\)

\(Q\)

\(h_{x} \theta_{y} (x,h)\)

\(\left( \begin{gathered} \varphi_{P} = 0, \hfill \\ \varphi_{GO} = 0 \hfill \\ \end{gathered} \right)\)

\(h_{x} \theta_{y} (x,h)\)

\(\left( \begin{gathered} \varphi_{P} = 0.1, \hfill \\ \varphi_{GO} = 0 \hfill \\ \end{gathered} \right)\)

\(h_{x} \theta_{y} (x,h)\)

\(\left( \begin{gathered} \varphi_{P} = 0.1, \hfill \\ \varphi_{GO} = 0.05 \hfill \\ \end{gathered} \right)\)

\(h_{x} \theta_{y} (x,h)\)

\(\left( \begin{gathered} \varphi_{P} = 0.1, \hfill \\ \varphi_{GO} = 0.1 \hfill \\ \end{gathered} \right)\)

− 0.1

1

0.4

0.1

0.2

0.3

0.1309090

0.1569780

0.1425840

0.1313060

0.0

1

0.4

0.1

0.2

0.3

0.0877126

0.1043780

0.0946780

0.0870713

0.1

1

0.4

0.1

0.2

0.3

0.0427437

0.0508753

0.0460722

0.0423006

− 0.1

2

0.4

0.1

0.2

0.3

0.1866350

0.2100200

0.1860910

0.1671470

0.0

2

0.4

0.1

0.2

0.3

0.1275180

0.1426770

0.1261100

0.1129770

0.1

2

0.4

0.1

0.2

0.3

0.0639906

0.0711466

0.0627137

0.0560203

− 0.1

1

0.8

0.1

0.2

0.3

0.1956250

0.2408200

0.2220010

0.2077540

0.0

1

0.8

0.1

0.2

0.3

0.1309950

0.1604810

0.1466300

0.1379340

0.1

1

0.8

0.1

0.2

0.3

0.0642991

0.0783394

0.0719247

0.0670413

− 0.1

1

0.4

0.3

0.2

0.3

0.3195510

0.3721490

0.3339250

0.3036960

0.0

1

0.4

0.3

0.2

0.3

0.2745800

0.3180090

0.2846610

0.2582430

0.1

1

0.4

0.3

0.2

0.3

0.2290240

0.2637670

0.2355300

0.2131240

− 0.1

2

0.4

0.1

0.6

0.3

0.3190200

0.3562930

0.3124240

0.2768620

0.0

2

0.4

0.1

0.6

0.3

0.2148990

0.2392250

0.2094960

0.1853950

0.1

2

0.4

0.1

0.6

0.3

0.1063670

0.1179690

0.1031530

0.0911401

− 0.1

2

0.4

0.1

0.2

0.5

0.1866350

0.2100200

0.1860910

0.1671470

0.0

2

0.4

0.1

0.2

0.5

0.1275180

0.1426770

0.1261100

0.1129770

0.1

2

0.4

0.1

0.2

0.5

0.0639906

0.0711466

0.0627137

0.0560203

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