Study Of Convective Boundary Layer Flow Induced By Linear Thermal Forcing

Natural convection as a common form of flow heat transfer extensively presented in various environment and industrial systems.it is a simplifiled model for many industrial applications such as solar collectors,nuclear reactors cooling and electriconic cooling devices.In order to provide a theoretical basis for improving energy efficiency in industrial applications,scaling anslysis,numerical method and direct stability analysis are employed to investigate the convective boundary layer adjacent to heated semi-infinite vertical plate,differentially heated open cavity and rectangle cavity respectively,in this paper.Firstly,for the model of heated semi-infinite vertical plate.Different heating conditions can be covered by vary the stratification factors,the value range of stratification factor under the current heating mode is 0≤s≤2.Subsequently,the nature convection flow associated with both the Pr<1 and Pr>1 fluids is analysed and quantified by power law respectively.The results demonstrate that the two flows are described by different sets of scale laws due to the dynamics of the Pr<1 and Pr>1 fluids are fundamentally different.The derived scaling relations also demonstrate that the boundary layer grow linearly and increased with stratification factor at the initial stage.The derived scaling relations are validated against the numerical simulation results and a good agreement is obtained.Secondly,for the model of differentially heated open cavity.The present scaling analysis is predominantly improved by adopting a two-dimensional decomposition of the specified thermal gradient,in which way thermal restrains are greatly eliminated.For this reason the range of stratification factor has been expend to s≥0.Meanwhile,the numerical results of Pr>1 fluids have demonstrated that the temperature difference between the overshoot and the first consecutive valley,i.e.A_lee,which is caused by LEE（Leading Edge Effect）,is not only related to Ra but also affected by s,and the A_lee reaches its maximum value when Ra is largest ans s is the smallest.It is further revealed that unlike the extensively studied homogenously heating problem,the present flow are consistently two-dimensional if a non-zero background temperature stratification presents;two flow Scenarios are identified for the intrusion and several possible flow regimes are found in each Scenario.The numerical data are compared against the scaling results.A reasonable agreement is obtained supporting the employed two-dimensional decomposition method and validating the derived scales.Lastly,for the rectangle cavity model.In order to study the convective instability and Receptivityof bounder layer,which adjacent to linear thermal plate i.e s≤0 with Pr=6.63fluids,a two-dimensional direct stability analysis is employed.The random mode calculations demonstrate that the dominant frequency shifts lower in the high frequency band（HFB）segment when Ra is higher than 1×10⁸ at s=-2.By examining the temperature profiles,it is known that this behavior is associated with the negative buoyant effect which fundamentally differentiates the present flow from the classic s=0 ones.The sinuous mode calculations demonstrate that the maximum perturbation amplitude is achieved at f_c and reveal that the relationship between f_c and Ra is f_c～Ra^7/10.In addition the propagation speed of the instability waves in the boundary layer,i.e.c_w,is obtained from the present calculations.It is revealed that the disturbance wave always travels faster than the base flow and the speed ratio ξ is larger at s=-2 than at s=0.It is further found that the maxinun Nusselt number of boundary layer achieved at f_c.