Natural convection in an enclosure with fins in the presence of non-uniform temperature profile at vertical wall
The development of energy instrumentation, electronic industry and energy in general is inextricably linked with the intensification of heat and mass transfer occurring in the base units and aggregates of energy systems. One of the approaches to solving this problem is to create an extended heat transfer surface by introducing a rib structure or porous inserts. This work is devoted to mathematical modeling of natural convection in an enclosure in the presence of a rib structure and nonuniform temperature profile on one of the vertical walls. The governing partial differential equations written using dimensionless non-primitive variables "stream function - vorticity - temperature" based on the Boussinesq approximation, in combination with initial and boundary conditions, have been worked out on the basis of the finite difference method. The developed computational model was varified using the mesh independence test and benchmark problems solved by other authors. Numerical investigations of unsteady natural convection of viscous fluid in a cavity with a variable temperature on the left wall under an influence of a rib structure have been carried out for the following values of governing parameters: Pr = 0.71, 10<sup>3</sup> < Ra < 10<sup>6</sup>, and the number of ribs varied from one to three. Distributions of streamlines and isotherms, as well as the dependences of the average Nusselt number and average cavity temperature, were obtained for a steady mode. As a result of the analysis, it has been found that the addition of solid ribs allows to enhance the heat transfer for low Rayleigh numbers, while for Ra > 10<sup>5</sup> one can find an attenuation of convective heat transfer. A growth of the fins heat conductivity characterizes the heat transfer enhancement.