Research On Marangoni-Thermocapillary Convection In A Shallow Rectangular Liquid Pool With The Bidirectional Temperature Gradients

Natural convection exists widely in nature and social life. The buoyancy convection driven by differences of the fluid density induced by temperature gradients in the fluid, and thermocapillary convection or Marangoni convection driven by surface tension gradients induced by temperature gradients on the free surface can both be regarded as natural convection. This research focuses on the convections driven by surface tension gradient which have two kinds of formation mechanism: one is called thermocapillary convection caused by the temperature gradient parallel to the free surface; another one is called Marangoni convection caused by the temperature gradient perpendicular to the free surface.In recent years,researchers have did studied the case that one of two thermal convections exist alone, but in nature and actual industry the Marangoni-thermocapillary convection under the coupled action of the bidirectional temperature differences exists widely and its phenomenon is more complex compared with the case of unidirectional temperature difference. So this study establishes the physical model and mathematical model of Marangoni-thermocapillary convection under the coupled action of the bidirectional temperature differences in a rectangular shallow liquid pool,and discusses the steady and unsteady flow in the fluid respectively. This study also obtains the temperature fields and velocity fields in different conditions, and analysis the evolution law of different flow patterns. Additionally it discusses the effects of the horizontal temperature difference(Ma), the vertical heat flow(Q) and heat transfer conditions(Bi) on the flow in rectangular shallow liquid pool, etc. The main conclusions are as follows:Firstly, Ma number and Q both affect the form of flow. When Ma number is small and Q=0, it’s a two-dimensional steady flow in the pool. As vertical heat flux Q increases, the liquid flow develops into a two-cell flow from a single-cell flow. When it begins with a two-cell flow in the pool, as the Ma number increase, counterclockwise flow cell near the hot wall represses and shrinks, and clockwise flow cell enhances and expands, eventually flow in the pool becomes a single cell. The increase of Ma number and Q causes instability of flow and increases the frequency of the wave along different change curves. The Bi number’s increase represses the instability of flow.Secondly, when Ma number is small, Q > Qcr and Q is small, two groups of double row of symmetrical hydrothermal waves develops from the wave source at the center of the cold wall which spread to the hot wall. With the increase of vertical heat flux Q, the wave source moves from the center of cold wall toward the front wall first, and then move towards the back wall, two groups of double row of symmetrical hydrothermal waves forms near the hot wall, which coexists with the one near the cold wall when Q is large enough.Thirdly,when Ma number is relatively large, Q > Qcr and Q is small, two groups of double row of symmetrical hydrothermal waves develops from the wave source point at the center of the cold wall which spread to the hot wall. With the increase of vertical heat flux Q, the wave source keeps at the cold walls,and the waves in the pool disorder before the formation of the waves near the hot wall when Q is large enough.Finally, when Ma > Macr and Q= 0, there’s a double row oblique wave near the hot wall. With the increase of vertical heat flux Q, the wave near the hot wall disappears and two groups of double row of symmetrical hydrothermal waves appears near the cold wall, and the wave source always stays in the center of the cold wall.