化工應(yīng)用數(shù)學(xué)(編輯修改稿)
2025-01-16 10:49 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 ” (t) = k2 (y2 y1) k3 y2 解數(shù)學(xué)方程式 ? How to solve? – y1(t)=1/5 cos (2t) + 6/5 cos (3t) – y2(t)=2/5 cos (2t) 3/5 cos (3t) 0)0()0(1)0(1)0(52282121212211??????????????yyyyyyyyyy 隨位置變化 Funciotn of position Mathematical Models ? Radial heat transfer through a cylindrical conductor Temperature at a is To Temperature at b is T1 Q: Determine the temperature distribution as a function of r at steady state r r +dr a b 建立數(shù)學(xué)模式 ? Considering the element with thickness ? r ? Assuming the heat flow rate per unit area = Q ? Radial heat flux ? A homogeneous second order . ))((22 rdrdrrrQ ???? ???drdTkQ ??where k is the thermal conductivity 022?? drdTdr Tdr 解數(shù)學(xué)方程式 ? Solve 1022)()(0TbTTaTdrdTdrTdr????)lnln lnln)(()( 010 ab arTTTrT ????? 流場(chǎng) (Flow systems) Eulerian ? The analysis of a flow system may proceed from either of two different points of view: – Eulerian method ? the analyst takes a position fixed in space and a small volume element likewise fixed in space ? the laws of conservation of mass, energy, etc., are applied to this stationary system ? In a steadystate condition: – the object of the analysis is to determine the properties of the fluid as a function of position. 流場(chǎng) (Flow systems) Lagrangian – the analyst takes a position astride a small volume element which moves with the fluid. – In a steady state condition: ? the objective of the analysis is to determine the properties of the fluid prising the moving volume element as a function of time which has elapsed since the volume element first entered the system. ? The properties of the fluid are determined solely by the elapsed time (. the difference between the absolute time at which the element is examined and the absolute time at which the element entered the system). – In a steady state condition: ? both the elapsed time and the absolute time affect the properties of the fluid prising the element. Eulerian 範(fàn)例 A fluid is flowing at a steady state. Let x denote the distance from the entrance to an arbitrary position measured along the centre line in the direction of flow. Let Vx denote the velocity of the fluid in the x direction, A denote the area normal to the x direction, and ? denote the fluid dens
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