Convection due to spatially distributed sinusoidal bump-like heating

Abstract

A fluid layer bounded by two parallel plates heated uniformly from below represents a classical system known as Rayleigh-Benard (RB) convection. It is known that this convection motion starts when the temperature difference between the plates reaches a critical value. Below this critical point the heat is transported between the plates by conduction and the temperature changes linearly across the layer. Above this critical point the heat transfer rate is increased by the thermal instability and the temperature field is strongly influenced by the presence of convective roll vortices. These roll vortices assists to augment the heat transfer process in the case of forced convection. In some applications, the bump-like heating is combined with a forced motion resulting in a mixed convection. Such convection is most likely to occur in many system of practical importance. Some of the examples of spatially distributed heating are included in the presence of ocean and land in the earth, presence of local lakes, a set of local fires, a set of computer chips, a set of electrically heated wires inserted on a surface etc. Such systems are modeled using an infinite slot subjected to periodic variation of the temperature defined by sinusoidal-bump-like function at the bottom wall. Fluid motion is driven by horizontal density gradients and occurs regardless of the intensity of the heating. Its pattern is determined by the externally imposed heating pattern unless transition to secondary states is encountered. The net heat transfer between the walls is driven by the nonlinear effects. The same heating applied to the moving fluid results in the reduction of drag experienced by this fluid. This type of heating is introduced with a presumption that the heating would create separation bubbles in the flow system so that, these bubbles isolate the moving stream from direct contact with the solid wall and thus help to reduce the overall pressure drag in the flow. This thesis deals with the flow topology and heat transfer behavior subjected to the considered heating pattern for different physical properties and flow configuration. As a result ,It has been observed that, the convective flow structures provide separation bubbles either at upper wall, at lower wall or at both walls, depending on the heating wave number, intensity of heating, and strength of external flow. These separation bubbles are more active at low Reynolds number and at low heating wave number, thereby causing more heat transfer and drag reduction in this zone. The result of this analysis also shows that, the rate of heat transfer and drag reduction is more significant in case of air rather than water.