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The paper consists of the study of an elongated cavity filled with a viscoelestic fluid in a porous medium that is heated from below at a fixed temperature. If we have this system without flow it will experience natural convection and if the fluid flow exists, mixed convection rules over the system. In both cases the temperature difference creates different instabilities. At the present study we are interested in conducting calculations for Boger fluid that is considered a viscoelastic fluid with constant viscosity. Generally, the Oldroyd B model is used to describe the behavior of viscoelastic fluids. In the presence of fluid flow, Peclet number is a non-zero value and in this study the Peclet number is varied to check the influence of fluid flow on the instabilities. By the use of temporal and spatiotemporal methods to solve the equations the effect of the fluid flow on the weakly and highly viscoelastic zones has been checked. In addition, the effect of the relaxation time on the instabilities has been studied by comparison of results for different relaxation times. Hence, we fix Γ and vary Peclet number to plot the critical Rayleigh number curve as a function of Peclet number to see the effect of relaxation time on the instabilities and to compare the temporal and spatiotemporal methods simultaneously.
