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The characteristics of vortex instability for laminar free-convection flow over horizontal and inclinedflot plates with prescribed uniform surface heat flux are studied analytically by the linear theory. The system of linearized disturbance equations constitutes an eigenvalue problem, which is solved numerically by a Runge-Kutta integration scheme along with a shooting technique. Neutral stability curves and cn'tical Grashof numbers are presented for Prandll numbers of 0.7 and 7 over a wide range of inclination angles, from the horizontal to close to the vertical orientation. The /[OW becomes more stable to the vortex mode of instability as the angle of inclination from the horizontal increases. I t reaches an absolutely stable condition with respect to the vortex instability when the p b e is vem'cal. I n addition, fluids with a Prandtlnumber of 7 are more susceptible to instability than fluids with a Prandrl number of 0.7. The present results are also compared with available vortex instability results under the uniform wall temperature condition on the basis of equivalent Grashof and wave numbers.

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