Mixed convection with uniform shear flow over horizontal and vertical walls

A study is made to determine similarity solutions for uniform shear flow along horizontal and vertical heated plates. For vertical walls, one momentum equation and one energy equation give rise to two similarity variables and here the temperature must decrease as the -1/3 power of the streamise coordinate along the semi-infinite plate. For horizontal walls, two momentum equations and one energy equation give rise to three similarity variables and here the temperature must increase as the 1/3 power of the streamwise coordinate.