Thermal instability in a horizontal layer of Oldroydian visco-elastic fluid in a porous medium is investigated. For porous medium the Brinkman–Darcy model is considered. A linear stability analysis based upon perturbation method and normal mode technique is used to find solution of the fluid layer confined between two free-free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically. The influence of the Brinkman–Darcy, Prandtl–Darcy number, stress relaxation parameter on the stationary and oscillatory convection is studied both analytically and graphically. The sufficient condition for the validity of PES has also been derived.
 Sharma R.C., Effect of rotation on thermal instability of a visco-elastic fluid, Acta Physica Hungrica, 1976, 40, 11–17.
 Sharma R.C., Kumar P., Thermal instability of an Oldroydian visco-elastic fluid in porous medium, Engg. Trans, 1996, 44(1), 99–109.
 Prakesh K., Chand R., Thermal instability of Oldroydian visco-elastic fluid in the presence of Finite Larmor Radius rotation and variable gravity in porous medium, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. 2002, 72(4), 373–386.
 Chand R., Effect of suspended particles on thermal instability of Maxwell visco-elastic fluid with variable gravity in porous medium, Antarctica Journal of Mathematics, 2011, 8(6), 487–497.
 Chand R., Thermal Instability of rotating Maxwell visco-elastic fluid with variable gravity in porous medium, Journal of the Indian Math. Soc., 2013, 80(1–2), 23–31.
 Chand R., Kango S.K., Thermosolutal instability of dusty rotating Maxwell visco-elastic fluid in porous medium, Advances in Applied Science Research, 2011, 2(6), 541–553.
 Chand R., Rana G.C., Dufour and Soret effects on the thermosolutal instability of Rivlin-Ericksen elastico-viscous fluid in porous medium, Z. Naturforsch., 2012, 67a, 685–691.
 Thakur R.C., Rana G.C., Effect of magnetic field on thermal instability of Oldroydian visco-elastic rotating fluid in porous medium, Int. J. of Applied Mechanics and Engineering, 2013, 18(2), 555–569.
 Chand R., Rana GC., Double diffusive convection in a layer of Maxwell viscoelastic fluid in porous medium in the presence of Soret and Dufour effects, Journal of Fluids, 2014, Article ID 479107, 7 pp., 2014.
 Yang Z., Wang S., Zhao M., Li S., Zhang Q., The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non equilibrium model, PLoS ONE, 2013, 8(11): e79956. DOI: 10.1371/journal.pone.0079956.
 Bala A., Chand R., Thermal instability in a horizontal layer of ferrofluid in Brinkman porous medium, Journal of Scientific and Eng. Research, 2014, 1(2), 25–34.