Buoyant and capillary natural convection in infinite horizontal liquid layers heated laterally

Solutions are presented for the equations describing natural convection in a planar, horizontal layer of liquid with a constant, linear temperature gradient along the unbounded top and bottom surfaces. Both buoyancy and capillary forces are considered to drive thermal convection. The results are compared to earlier analyses for bounded liquid layers and then applied to containerless metal melts undergoing solidification in the microgravity environment of near-earth orbit.