Scaling Analysis and Numerical Validation of Transient Flows Near a Convectively Heated Vertical Wall for <em style="mso-bidi-font-style: normal;">Pr < ۱

Natural convection flows near a convectively heated vertical wall have significant interest in the fluid mechanics community because of their wide applications in environmental and industrial processes. The development of transient natural convection boundary layer flows near a vertical wall subjected to convective heating is investigated using scaling analysis. The scaling relations are determined by the three governing parameters: the Rayleigh number (Ra or Ray), the Prandtl number (Pr), and the non-dimensional convective heat transfer coefficient (Ci or Ciy). The transient natural convection boundary layer consists of a viscous inner layer and a thermal boundary layer and evolves through an initial stage and a steady stage. Scaling analysis reveals the flow dynamics and heat transfer characteristics of the transient natural convection boundary layer and establishes scaling relations for the boundary layer velocity, thickness, temperature, and heat transfer. In typical scaling relations, the local non-dimensional thermal boundary layer thickness is inversely proportional to Ciy۱/۵Ray۱/۵, the local non-dimensional temperature is proportional to Ciy۴/۵ and inversely proportional to Ray۱/۵, the thickness from the wall to the location of maximum velocity is inversely proportional to Ciy۱/۵Ray۱/۵, the non-dimensional velocity is proportional to Ciy۲/۵Ray۲/۵ and both the Nusselt number and the flow rate are proportional to Ci۱/۵Ra۱/۵. These scaling relations are also validated through numerical simulations.

کلیدواژه ها:

transient natural convection ، convectively heated vertical wall ، scaling analysis ، Heat transfer ، Numerical simulation