This frame work is established to investigate the thermal management of free convection enclosed in trapezoidal cavity filled with the water based copper oxide (CuO) nanofluid. As nanoparticles volume fraction play a significant role to handle the thermal conductivity of any working fluid, so we have addressed the complex nature real world model that widely used at the industrial level and many other mechanisms. An identical trapezoidal shape cavity is placed inside the big trapezoidal cavity that have three various constraints at the surface (cold, insulated and heated). Since bottom wall of the outer cavity is partially heated so various heated portion tests are applied to analyze the influence of heat transfer within the entire cavity. Aspect ratio that depends upon the size of the inner cavity is also determine. Complete and compatible mathematical model is constructed in the form of nonlinear coupled partial differential equation. These set of equations are characterized under the law of conservation of mass, momentum and energy equation along with the restricted domain of the cavity. Koo and Kleinstreuer-Li (KKL) model is used for effective thermal conductivity and viscosity of the nanofluid. A Galerkin based Finite Element method (FEM) is implemented to attain the suitable results in term of stream function and isotherms within the restricted domain of the cavity. Results are also obtained for velocity and temperature of the nanofluid at vertically mean position of the cavity. The simulations are performed for nanoparticles volume fraction 0 <= phi <= 0.2 heated portion length 0 <= L-T <= 1 aspect ratio 0.5 <= AR <= 3.0, Rayleigh number 10 <= Ra <= 10(5.7), and three heated conditions (cold, adiabatic and hot) for inner trapezium. It is found that flow and thermal field are getting stronger due to increase in Rayleigh number. However, fluid velocity is decreasing with increasing nanoparticles volume fraction phi as the fluid is getting dens. Heat transfer rate is decreasing with the increase in phi and L-T due to dominant convection. (C) 2018 Elsevier Ltd. All rights reserved.