Free convective heat transfer of a non-Newtonian fluid in a cavity containing a thin flexible heater plate: an Eulerian–Lagrangian approach

In the present study, the free convection heat transfer of a power-law non-Newtonian fluid is considered in a cavity containing a flexible hot thin heater. The sidewalls of the square cavity are maintained at cold temperatures, while the hot heater is placed inside the cavity. The top and bottom walls of the cavity are kept insulated. The thin heater plate can undergo large deformations due to the interaction between the fluid flow and the heater. The arbitrary Lagrangian–Eulerian moving mesh method is employed to track the displacement of the heater in the fluid domain. Appropriate non-dimensional parameters are utilized to transform the governing equations into a general non-dimensional form. The equations governing fluid flow and heat transfer are solved using the finite element method with an automatic time-stepping scheme. The effect of control parameters such as the non-Newtonian power index (0.6 < n<1.4), the Rayleigh number (10⁴ < Ra < 10⁶), the element location and length is studied on the hydraulic and thermal behavior of the cavity and element displacement. The results indicate that raising the power-law index (n) from the pseudoplastic behavior (n < 1) to the dilatant (n > 1) behavior reduces the fluid circulation and heat transfer rate in the cavity, but it increases the magnitude of the exerted tensions on the element. Moreover, raising Ra from 10⁴ to 10⁶ enhances the average heat transfer the value of Nu_av by up to 3.5 times in pseudoplastic fluids and by 1.5 times in dilatant ones. In addition, it is found that shifting the heater upward deteriorates the heat transfer rate by suppressing the convection flow intensity. A 35% rise in the average heater can be obtained when the height of the plate was divided by 4 in the cse of dilatant fluid, and an increase by up to 100% is found for pseudoplastic fluids. Increasing the length of the element is also found to reduce the average Nusselt number and to increase the tensions in the heater. The average Nusselt number can be doubled when the length of the plate is reduced seven times.