Abstract
Mixed convection of ferrofluid in square configurations having various iso‐perimetric shaped obstacles has been investigated for fluid flow and heat transfer characteristics. The iso‐perimetric shapes are allowed to vary in size and tested at three different vertical positions subject to adiabatic and isothermal conditions. Simulations have been carried out for various choices of controlling parameters using the higher order mixed finite element method. In particular, the higher order and stable finite element pair of cubic and quadratic (ℙ3/ℙ2$$ {\mathrm{\mathbb{P}}}_3/{\mathrm{\mathbb{P}}}_2 $$) approximations on the hybrid grid is utilized to achieve the discretization of the governing non‐dimensional equations of mass, momentum and energy. The adaptive Newtons method is chosen to solve the discrete system of nonlinear equations. The present solver has been tested against a well‐known open source finite element analysis tool (FEAT2) and published results in the literature. The impact of governing parameters is investigated in the ranges as nanoparticles volume fraction ϕ(0%≤ϕ≤15%$$ \phi\ \Big(0\%\le \phi \le 15\% $$), the Richardson number Ri(0.01≤Ri≤5)$$ Ri\ \left(0.01\le Ri\le 5\right) $$, the perimeter of the obstacle Γ(0.2π≤Γ≤0.6π)$$ \Gamma\ \left(0.2\pi \le \Gamma \le 0.6\pi \right) $$, and positions of the obstacles C(0.25≤C≤0.75)$$ C\ \left(0.25\le C\le 0.75\right) $$. It is concluded that an increase in the perimeter of the inner obstacles causes a weakness in the fluid flow while a good thermal enclosure is obtained. Moreover, the isothermal obstacles enhance the average Nusselt number more than the adiabatic obstacles in all cases.