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Bio-Heat and Mass Transfer

# Magnetohydrodynamic Nonlinear Peristaltic Flow in a Compliant Walls Channel With Heat and Mass Transfer

[+] Author and Article Information

Department of Mathematical Sciences,  Fatima Jinnah University, Rawalpindi 46000, Pakistanquaidan85@yahoo.com

Tasawar Hayat

Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan; Department of Mathematics, Faculty of Science,  King Abdul Aziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Saleem Asghar

Department of Mathematics, Faculty of Science,  King Abdul Aziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia; Department of Mathematics, CIIT, H-8, Islamabad 44000, Pakistan

Department of Mathematics, Faculty of Science,  King Abdul Aziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

1

Corresponding author.

J. Heat Transfer 134(7), 071101 (May 24, 2012) (7 pages) doi:10.1115/1.4006100 History: Received July 15, 2011; Revised November 18, 2011; Published May 24, 2012; Online May 24, 2012

## Abstract

This paper discusses the effects of magnetic field and heat and mass transfer on the peristaltic flow of an incompressible fluid in a channel with compliant walls. Mathematical formulation for the fourth grade fluid is presented. Relations of stream function, temperature, concentration field, and heat transfer coefficient are derived. The variations of the interesting parameters entering into the problem are carefully analyzed.

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## Figures

Figure 4

(a) Variation of M on Z when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; Γ = 0.01; Br = 1; t = 0.1. (b) Variation of Γ on Z when E1 = 1; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; M = 2.5; Br = 0.5; t = 0.1. (c) Variation of Br on Z when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; M = 1.5; Γ = 0.1; t = 0.1.

Figure 3

(a) Variation of M on φ when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.6; ε=0.15; Br = 5; Sr = 1; Sc = 1; Γ = 0.1; x = 0.2; t = 0.1. (b) Variation of Γ on φ when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; Br = 4; Sr = 1; Sc = 1; M = 1.5; x = 0.2; t = 0.1. (c) Variation of Br on φ when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; Γ = 0.1; M = 1.5; Sr = 1; Sc = 1; x = 0.2; t = 0.1. (d) Variation of Sc on φ when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; M = 1.5; x = 0.2; Br = 1; Sr = 1; t = 0.1. (e) Variation of compliant wall parameters on φ when Br = 2; Sr = 1; Sc = 1; ε=0.15; M = 1.5; x = 0.2; t = 0.1.

Figure 2

(a) Variation of M on θ when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.6; ε=0.15; Γ = 0.1; x = 0.2; t = 0.1; Br = 5. (b) Variation of Γ on θ when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; M = 1.5; x = 0.2; t = 0.1; Br = 4. (c) Variation of Br on θ when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; ε=0.15; Γ = 0.1; x = 0.2; t = 0.1; M = 1.5. (d) Variation of compliant wall parameters on θ when Γ = 0.1; ε=0.15; M = 1.5; x = 0.2; t = 0.1; Br = 2.

Figure 1

(a) Variation of M on u when E1  = 0.5; E2  = 0.2; E3  = 0.1; E4  = 0.01; E5  = 0.1; ε=0.2; Γ = 0.1; x = 0.3; t = 0.1. (b) Variation of Γ on u when E1 = 0.5; E2 = 0.4; E3 = 0.1; E4 = 0.01; E5 = 0.6; ε=0.2; M = 0.5; x = −0.3; t = 0.1. (c) Variation of ε on u when E1 = 0.2; E2 = 0.1; E3 = 0.01; E4 = 0.01; E5 = 0.2; M = 2; Γ = 0.01; x = −0.3; t = 0.1 and (d) Variation of compliant wall parameters on u when Γ = 0.01; ε=0.2; M = 2; x = −0.3; t = 0.1.

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