化工應(yīng)用數(shù)學(xué)-資料下載頁
2024-12-29 10:49本頁面
【正文】 ment. However, a different constant value can be taken by a property during different experiments. ? Examples – overall dimensions of the apparatus – flow rate – heat transfer coefficient – thermal conductivity – density – initial or boundary values of the depent variables 各符號(hào)之間的關(guān)係 ? A dependent variable is usually differentiated with respect to an independent variable, and occasionally with respect to a parameter. ? When a single independent variable is involved in the problem, it gives rise to ordinary differential equations. ? When more than one independent variable is needed to describe a system, the usual result is a partial differential equation. 邊界條件 (Boundary conditions) ? There is usually a restriction on the range of values which the independent variable can take and this range describes the scope of the problem. ? Special conditions are placed on the dependent variable at these end points of the range of the independent varible. These are natually called “ boundary conditions” . 常見的邊界條件 ? 熱傳 (heat transfer) – Boundary at a fixed temperature, T = T0. – Constant hear flow rate through the boundary, dT/dx = A. – Boundary thermally insulated, dT/dx = 0. – Boundary cools to the surroundings through a film resistance described by a heat transfer coefficient, k dT/dx = h (TT0). ? k is the thermal conductivity。 h is the heat transfer coefficient。 and T0 is the temperature of the surrendings. 邊界值與起始值 (Boundary value and initial value) ? Specifying conditions on a solution and its derivative at the ends of an interval (boundary value problem) is quite different from specifying the value of a solution and its derivative at a given point (initial value problem). ? Boundary value problems usually do not have unique solutions, and it is this lack of uniqueness which makes certain boundary value problems important in solving . of physics and engineering. 心得 ? 如何建立一個(gè)應(yīng)用數(shù)學(xué)問題？ – 由「假設(shè)」，將問題簡(jiǎn)化。 – 確定所要探討的目標(biāo)，找出「非獨(dú)立參數(shù)」。例如溫度、濃度等。 – 找出「獨(dú)立參數(shù)」，使得非獨(dú)立參數(shù)可經(jīng)由獨(dú)立參數(shù)表示。例如位置、時(shí)間等。 – 找出可將「獨(dú)立參數(shù)」 及「非獨(dú)立參數(shù)」的關(guān)係經(jīng)由數(shù)學(xué)式表示出的「變數(shù)」 。例如氣體流速、熱傳係數(shù)等。 – 選定一個(gè)「特殊點(diǎn)」，應(yīng)用「非獨(dú)立參數(shù)」來描述該系統(tǒng)的狀態(tài)。 – 增加微量「非獨(dú)立參數(shù)」。應(yīng)用泰勒展開式來表示該微量增加後，該系統(tǒng)的狀態(tài)。 – 應(yīng)用「守恆定律或速率方程式」來顯示增加的微量。 – 將增加的微量取極限值，建立該模型方程式。 – 將邊界條件確定。 謝謝觀看 /歡迎下載 BY FAITH I MEAN A VISION OF GOOD ONE CHERISHES AND THE ENTHUSIASM THAT PUSHES ONE TO SEEK ITS FULFILLMENT REGARDLESS OF OBSTACLES. BY FAITH I BY FAITH
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