Transp Porous Med (2011) 87:291–307 DOI 10.1007/s11242-010-9682-9 Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium I. S. Shivakumara · Jinho Lee · M. S. Malashetty · S. Sureshkumar Received: 30 September 2010 / Accepted: 2 November 2010 / Published online: 19 November 2010 © Springer Science+Business Media B.V. 2010 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 mod- ulated 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 num- ber 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. Keywords Thermal modulation · Porous medium · Walters B viscoelastic fluid · Convection I. S. Shivakumara · J. Lee (B ) School of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea e-mail: jinholee@yonsei.ac.kr I. S. Shivakumara Department of Mathematics, UGC-CAS in Fluid Mechanics, Bangalore University, Bangalore 560001, India e-mail: shivakumarais@gmail.com M. S. Malashetty Department of Mathematics, Gulbarga University, Gulbarga 585106, India e-mail: malashettyms@yahoo.com S. Sureshkumar Department of Mathematics, Siddaganga Institute of Technology, Tumkur 572103, India 123