課程名稱︰單元操作二 課程性質︰必修 課程教師︰王勝仕 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰2009.3.26 考試時限（分鐘）：160分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Part I: Close Book (75%) 1. (1) show the order of magnitude of thermal conductivities of gas, liquid, and solid(with unit) (9 points) (2) Briefly explain/define the following terms: (a) Newton's law of cooling (b) overall heat transfer coefficient (c) thermal diffusivity (d) thermal conduct- ivity (12 points) (3) Please assign the boundary conditions to the following three temperture profile (see Figure 1) (6 points) 2. (1) Please derive the Heat Conduction Equation (see below) via "differential approach" in Cartesian coordinate system (x,y,z) (Hint: the following inform- ation is for your use) [Chap. 2] (10 points) · dT <--這裡是偏微分 -▽．q + q = ρCp ----- — – dt (2) What is the equation that you would obtain when the following assumptions apply: (a) Fourier's law of heat conduction, (b) no heat generation ,(c) stea- dy-state, (d) one-dimensional distribution in x-axis (4 points) 3. If you have a sphere with insulation material outside (see Figure 2),please derive the critical insulation thickness. Please also state why the critical value exists. (Hint: steady-state, no heat generation, spherical coordinate s- ystem) [chap. 3] (10 points) 4. (1) Please describe/define two indices to evaluate the performance of a fin (specify the notations and symbols first!) (6 points) (2) In the case of steady-state infinite fin, the fin efficiency is defined k ． p as ηf = (-----------)^ (1/2), please explain the choice of fin in terms of h ． Ac the (a) material (copper or aluminum), (b) the position (liquid or gas side), and the (c) feature of its shape. [chap. 3] (6 points) 5. Please refer Figure 3 and 4 and use "Energy Balance Method" with assumptio- ns to derive the finite difference equation for the temperature of the indica- ted nodal point (m,n), Tm,n. [chap 4] (12 points) Part II: Open Book (25%) 1. Consider two long, slender rods of the same diameter but different materia- ls. One end of each rod is attached to a base surface maintained at 100°C, while the surfaces of the rods are exposed to ambient air at 20°C. By traver- sing the length of each rod with a thermocouple, it was observed that the temperatures of the rods were equal at the positions xA = 0.15 m and xB = 0.075 m, where x is measured from the base surface. (a) If you take these rods as fins, please indicate which equation (relationship) in Table 3.4 that can be used to describe the rods in this problem. (b) Please prove this equa- tion/relationship (c) If the thermal conductivity of rod A is known to be kA = 70 W/m.K, determine the value of thermal conductivity of rod B, kB(12 points) 2. The cylindrical shown has negligible variation of temperature in the r- and z- directions. Assume that △r = r0 - ri is small compared to ri and denote the length in the z- direction, normal to the page, as L. (13 points) (a) Beginning with a poorly defined control volume, using energy conservation law, and considering energy generation and storage effects, please derive the differential equation that prescribes the variation in temperature with the angular coordinate ψ. Compare your result with Equation 2.24. (b) For steady-state conditions with no internal heat generation and constant properties, determine the temperature distribution T(ψ) in terms of T1, T2, ri, and ro. Also determine the expression of the heat qψ. --

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