The theory of constitutive equations for dipolar fluids, obtained by Bleustein and Green, is applied to investigate the Couette and Poiseuille flows between parallel plates maintained at constant but dtzerent temperatures in addition to being subjected to untform imection and suction. Explicit expressions for the velocity and the temperature fields are obtained. It is found that dtferent sets of conditions imposed on theJlow parameters lead to dtfierent expressions for the velocity distribution which are valid only for restricted ranges of the cross-flow Reynolds number R. A table showing the various conditions imposed on the parameters, the corresponding solutions and the ranges of R for which the solutions exist is presented. Velocity and temperature profiles for the dipolar and the Newtonian flows are drawn and compared to bring out the important d@erences resulting from the variations in R and B, the Brinkman number. For the dipolar CouetteJtow it is found that the value of B at which a transition from cooling to heating of the suction wall occurs always exceeds its corresponding value for Newtonian flow. Tables comparing the rates of heat transfer at the walls are providedfor several values of R and B.