課程名稱︰熱傳學 課程性質︰機械系大三必修 課程教師︰馬小康 開課學院：工學院 開課系所︰機械系 考試日期（年月日）︰2009/10/29 考試時限（分鐘）：110min 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 共110分 (1) Pease explain the following terms: (15%) (a) Fourier number (b) The fin efficiency (c) The temperature coefficient of thermal conductivity (d) The thermal contact resistance, Rc (e) The overall heat transfer coefficient, U (2) Consider steady one-dimensional heat conduction in a composite plane wall consists of two layers A and B in perfect contact at the interface where node 1 is. The wall is insulated at the left (node 0) and subjected to radiation at the right boundary (node 2). Using the energy balance approach, obtain the finite difference formulation of this problem for the case of insulation at the left boundary (node 0) and node 1. (15%) Insulated↓ 　　　　　╓───┬───┐ 　　　　　║　　　│　　　│ 　　　　　║　　　│　　　│ 　　　　　║　Ａ　│　Ｂ　│ 　　　　　║　　　│　　═╪═→Radiation 　　　　　║ Δx　│　　　│ 　　　　　╟───┼───┼→ 　　　　 0║　　 1│　　 2│ 　　　　　║　　　│　　　│ Tsurr 　　　　　║　　　│　　　│ 　　　　　║　　　│　　　│ 　　　　　║　　　│　　　│ 　　　　　╙───┴───┘ (3) During a picnic on a hot day, the only cold drink is at 30℃. In an effort to cool a 350 mL drink in a can, which is 13 cm high and has a diameter of 6.5 cm, a person shakes a can of drink in the iced water to cool it. The temperature of the drink can be assumed to be uniform at all times, and the aluminum can is 170 W/m^2℃. Using the properties of water for the drink, estimate how long it will take for the canned drink to cool to 4℃. (15%) 　　　　　┌───┐ 　　　　　│　　　│ Water 　　　　　│Drink │ 0℃ 　　　　　│30℃　│ 　　　　　│　　　│ 　　　　　│　　　│ 　　　　　└───┘ (4) Write down heat transfer equation (with the expression of total thermal resistance) from the insulated pipe to the surrounding air. (15%) (圖為一圓管,內側r1,T1,外側r2,無限遠處T∞,有給定k值和h值 熱阻Rins跟Rconv如圖) 　　　　　　　　　　　　　 　█ 　　　█　　　　　k 　　　　 █ 　　　 █ 　　　　　　　　　　█ 　　　 █ 　　　Rins 　　 　 █ Rconv 　　　　█──v^v^v^v^v^v^v──█──^v^v^v^v^v──● 　　　 █ 　　　　　　　　 　 █　　　　　　　　 　T∞ 　　　 █ 　　　　　　　　　　█ h 　　　█ 　　　　　　　　　　 █ 　　　 T1　　　　　　　　　 █ (局部放大圖) (5) Consider a 20-cm-thick large concrete plane wall (k=0.77 W/m^2℃) subjected to convection on both sides with T∞1 = 27℃ and h1 = 5 W/m^2℃ on the inside, and T∞2 = 8℃ and h2 = 12 W/m^2℃ on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation, (a) express the differential equations and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperatures at the inner and outer surfaces of the wall. (15%) 　　　　　　　　　h1 h2 　　　　　　　　　T∞1 T∞2 　　　　　　　　　↓ ↓ 　　　　　　　　　┌──┐ 　　　　　　　　　│　　│ 　　　　　　　　　│　　│ 　　　　　　　　　│　k │ 　　　　　　　　　│　　│ 　　　　　　　　　│　　│ 　　　　　　　　　│　　│ 　　　　　　　　　└──┘ 　　　　　　　　　├ L ┤ (6) For one-dimensional transient conduction in Cartesian coordinates in a semi-infinite medium, (a) what is the similarity variable η? and why? (b) Please derive the following partial differential equation to be an ordinary differential equation. (15%) 　　　　d^2T 1 dT 　　　　── = ─ ── 　　　　dx^2 α dt (7) Please solve the following equation by the separation variable method.(20%) 　　　d^2θ dθ 　　　── = ─ 　　　dX^2 dτ Boundary conditions ┌ dθ(0,τ) │ ──── = 0 │ dX │ dθ(1,τ) │ ──── = -Biθ(1,τ) └ dX Initial condition θ(X,0) = 1 --

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