Abstract This paper reports the results of a numerical study on the heat transfer during process of conduction dominated solidification of copper–water nanofluid in isosceles trapezoidal cavity under controlled temperature and concentration gradients. The suspended nanoparticles have proven to increase the heat transfer rate substantially. The horizontal walls of the cavities are insulated while side walls are kept at constant but different temperatures. The total solidification time of pure fluid and nanofluid filled in the cavity is investigated for three different inclinations of side walls and the results are compared with square cavity. Results revealed that the total solidification time for pure fluid as well for nanofluid for all nano particle concentrations decreases. The effects of Grashof number (105–107) on the heat transfer phenomenon and solid–liquid interface are also numerically investigated and presented graphically. The enthalpy–porosity technique is used to trace the solid–liquid interface. Inclination angle can be used efficiently to control the solidification time. In addition, average Nusselt number along the hot wall for different angles, nanoparticles volume fractions, and Grashof number is presented graphically. The proposed predictions are very helpful in developing improved latent heat thermal energy storage for solar heat collector and for casting and mold design.