We present numerical solutions of natural convection in a cavity of finite domain when the flow is driven by a horizontal temperature gradient between isothermal vertical walls. Only the transverse roll structure of convection is calculated by employing the pseudo spectral Chebyshev collocation method. A numerical solution of the steady flow is first obtained and, based upon it, the critical Rayleigh number (related to Grashof number) of linear transverse mode is determined. The influence of aspect ratio, on the flow and temperature patterns, is also investigated.

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