Using a fully coupled transient 3-dimensional numerical model, the effects of convection on the microstructural evolution of a thin sample of Ga-In25%wt. was predicted. The effects of natural convection, forced convection and thermoelectric magnetohydrodynamics were investigated numerically. A comparison of the numerical results is made to experimental results for natural convection and forced convection. In the case of natural convection, density variations within the liquid cause plumes of solute to be ejected into the bulk. When forced convection is applied observed effects include the suppression of solute plumes, preferential secondary arm growth and an increase in primary arm spacing. These effects were observed both numerically and experimentally. By applying an external magnetic field inter-dendritic flow is generated by thermoelectrically induced Lorentz forces, while bulk flow experiences an electromagnetic damping force. The former causes preferential secondary growth, while the latter slows the formation of solute plumes. This work highlights that the application of external forces can be a valuable tool for tailoring the microstructure and ultimately the macroscopic material properties.