Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium |
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Authors: | I S Shivakumara Jinho Lee M S Malashetty S Sureshkumar |
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Institution: | 1.School of Mechanical Engineering,Yonsei University,Seoul,South Korea;2.Department of Mathematics, UGC-CAS in Fluid Mechanics,Bangalore University,Bangalore,India;3.Department of Mathematics,Gulbarga University,Gulbarga,India;4.Department of Mathematics,Siddaganga Institute of Technology,Tumkur,India |
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Abstract: | The linear stability of Walters B viscoelastic fluid-saturated horizontal porous layer is examined theoretically when the
walls of the porous layer are subjected to time-periodic temperature modulation. Three types of boundary temperature modulations
are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held
at constant temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute
the critical values of Rayleigh number and the corresponding wave number. The shift in critical Rayleigh number is calculated
as a function of modulation frequency, viscoelastic parameter, and Prandtl number. The effect of all three types of modulations
is found to be destabilizing as compared to the unmodulated system. This result is in contrast to the system with other types
of fluids. Besides, the influence of physical parameters on the control of convective instability of the system is discussed. |
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