속도 및 온도분포가 동시에 성장하고 있는 환상공간 내의 입구영역에 대한 연구

Abstract

본 연구는, 속도 및 온도분포가 동시에 성장하는 동심환형관의 입구영역에서, 층류 및 난류 비압축성 유동이 존재할 때의 운동량 및 열전달 문제들을 다루었다. 우선, 미분식들은 수치계산을 위하여 유한 차분식들로 변환했고, Prandtl 수 Pr= 0.7인 유체가 반경비 r* = 0.001, 0.01, 0.06, 0.1, 0.4, 0.9 등의 환상공간 내를 유동할 때, 수력학적 및 열적 입구영역에서 입구길이, 표면 마찰계수 및 열전달계수 등의 해를 계산하여, 다음의 주요 결과들을 얻었다. 즉, 최대속도가 존재하는 위치는, r*가 "0"에 접근할수록, 하류로 진행 함에 따라 중심으로부터 내측 벽면 쪽으로 치우치고, 수력학적 입구길이는, Re가 증가하거나 반경비가 감소할수록 증가한다. 또한 r*가 작은 경우, 내면 마찰계수 Cf.i는 하류로 진행함에 따라 감소하며 최소값 이후에는, 증가하여 완전성장 값을 갖으나, 내면 Nusselt 수 Nui는 계속 감소하며 완전 성장했다. Cf.i 또는 Nui수는 외면보다 내면이 높으며, 그 차이는 Re 가 증가할수록 감소한다. 그러나 r* 증가에 따라, Cf.i, Nui는 감소하고, Cf.o, Nuo는 증가하므로, r*=1 근처에서 서로 같은 값을 갖는다.

In this paper, we considered the problem of momentum and convective heat transfer in a concentric annulus with laminar and turbulent incompressible flow, simultaneously developing velocity and temperature distributions in teh entry region. The eifferential equations for the annulus flow are transformed into finite difference equations first, for the numerical calculation. And the solutions combined hydrodynamic and thermal entry region, such as entry length, surface friction factor and heat transfer coefficient, are found for teh fluid of Pr=0.7 an radius ratio r* = 0.001, 0.01, 0.06, 0.1, 0.4, 0.9.

The useful results are as follows; The point of maximum velocity is initially at center but tends to move toward inner tube further downstream and the hydrodynamic entry length increases as Reynolds number increase. And the inner wall friction factor for small r* tends to reach a minimum going downstream and then rise to the fully developed value, but the Nusselt number is continuously decrease in the entry region. The inner wall friction factor Cf.i and Nusselt number Nui are greater than that of outer wall, and the differences between inner surface and outer surface are decrease as Reynolds number increase. But Cf.i and Nui are decrease at inner surface and those at teh outer surface are increase as r* increase, so their differences became zero near r* =1.

In this paper, we considered the problem of momentum and convective heat transfer in a concentric annulus with laminar and turbulent incompressible flow, simultaneously developing velocity and temperature distributions in teh entry region. The eifferential equations for the annulus flow are transformed into finite difference equations first, for the numerical calculation. And the solutions combined hydrodynamic and thermal entry region, such as entry length, surface friction factor and heat transfer coefficient, are found for teh fluid of Pr=0.7 an radius ratio r* = 0.001, 0.01, 0.06, 0.1, 0.4, 0.9.

The useful results are as follows; The point of maximum velocity is initially at center but tends to move toward inner tube further downstream and the hydrodynamic entry length increases as Reynolds number increase. And the inner wall friction factor for small r* tends to reach a minimum going downstream and then rise to the fully developed value, but the Nusselt number is continuously decrease in the entry region. The inner wall friction factor Cf.i and Nusselt number Nui are greater than that of outer wall, and the differences between inner surface and outer surface are decrease as Reynolds number increase. But Cf.i and Nui are decrease at inner surface and those at teh outer surface are increase as r* increase, so their differences became zero near r* =1.