Hydromagnetic stability of plane Couette flow of an upper convected Maxwell fluid |
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Authors: | Eldabe Nabil T M; El-Sabbagh M F; El-Sayed M A-S |
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Institution: |
1 Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt, 2 Department of Mathematics, Faculty of Science, Minia University, Minia, Egypt
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Abstract: | Hydrodynamic stability of plane Couette flow of an upper convectedMaxwell fluid is investigated in presence of a transverse magneticfield assuming that the magnetic Prandtl number is sufficientlysmall. The resulting equation is a modified OrrSommerfeldequation. The equations of stability are solved numericallyusing Chebyshev collocation method with QZ algorithm. The criticalvalues of Reynolds number, wave number and wave speed are computedand the results are shown through the neutral curves. By increasingthe amount of elasticity to a certain value, it is shown that,as the Hartmann number increases, the minimum critical Reynoldsnumber decreases and it does not increase again in contrastto the Newtonian case. |
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Keywords: | viscoelastic fluid hydromagnetic stability plane Couette flow Chebyshev collocation method |
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