We investigate the effect of hydro-thermal convection in an aquifer system. It is assumed that the aquifer is bounded below and above by impermeable boundaries and it is heated from below. The solution of the governing system is expressed in terms of the basic steady state solution and perturbed solution. We obtain the critical Rayleigh number and critical wavenumber using Runge-Kutta method in combination of shooting method and present the marginal stability curve. The amplitude equation is derived by introducing the adjoint system. After amplitude is obtained, we compute the linear solutions for super-critical and sub-critical cases. Numerical results for various spatial and time values are presented in graphical forms.
Hydro-thermal convective solutions for an aquifer system heated from below,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
1, Article 1.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss1/1