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Forced Convection

# Multiple Analytic Solutions of Heat and Mass Transfer of Magnetohydrodynamic Slip Flow for Two Types of Viscoelastic Fluids Over a Stretching Surface

[+] Author and Article Information
Mustafa Turkyilmazoglu

Department of Mathematics,  Hacettepe University, Beytepe, Ankara-06532, Turkeyturkyilm@hacettepe.edu.tr

J. Heat Transfer 134(7), 071701 (May 18, 2012) (9 pages) doi:10.1115/1.4006165 History: Received September 11, 2010; Revised January 05, 2012; Published May 17, 2012; Online May 18, 2012

## Abstract

This paper focuses on the magnetohydrodynamic (MHD) slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is to analytically investigate the structure of the solutions and determine the thresholds beyond which multiple solutions exist or the physically pure exponential type solution ceases to exist. In the case of the presence of multiple solutions, closed-form formulae for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walter’s liquid B fluids. Heat transfer analyzes are also carried out for two general types of boundary heating processes, either by a prescribed quadratic power law surface temperature or by a prescribed quadratic power law surface heat flux. The flow field is affected by the presence of several physical parameters, whose influences on the unique/multiple solutions of velocity and temperature profiles, and Nusselt numbers are examined and discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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## Figures

Figure 1

The solution domain for λ at different values of k1 (curves from bottom to top for k1  = −500, −5, −1, −1/2, −1/20, −1/50, −1/100, and 0, respectively) as a function of the mass suction parameter s. (a) M = 0 and (b) M = 5. For each pair shown, the lower corresponds to L = 0 and the upper corresponds to L = 50, respectively.

Figure 2

The solution domain for λ at different values of k1 as a function of the mass suction parameter s. (a) L = M = 0, (b) L = M − 3 = 0, (c) L − 50 = M = 0, and (d) L − 50 = M − 3 = 0. Curves correspond to dotted k1  = 500, dotted-dashed k1  = 5, dashed k1  = 1/2, long-dashed k1  = 1/10, and thick k1  = 1/100, respectively.

Figure 3

Double velocity profiles f and f′. Upper curves are the first branches and the lower ones are the second branches, respectively. (a) k1  =  − 1/20, M = 1, and s = 3/2, (b) k1  = 1/2, M = 1, and s =  − 4. Solid L = 0 and dashed L = 1.

Figure 4

Temperature profiles for the values of k1  =  − 1/20 with Pr = 3, M = 1, Ec = 0.1, R = 1, χ = 0, and s = 3/2. (a) θ in PST case and (b) φ in PHF case. Curves correspond to thin L = 0, dashed L = 1, and dotted asymptotic formula 22, respectively, and the upper curves are for the first branches and the lower ones are for the second branches.

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