(a) What temperature should you use for evaluating the fluid properties? (2%)

3. A hot solid cube (having sides of equal length) of temperature Tco is put into a pot containing cold water of temperature Two. Assume that the heat exchange only occurs between the cube and water. (20%) (a) Write down the equation for determining the final equilibrium temperature. (b) Assuming both the cube and water keep spatially uniform in temperature, write down the equation for evaluating the temperature evolution for the cube and water, respectively. (c) Consider the cube is not spatially uniform in temperature but the water is. Write down the equation and boundary conditions for evaluating the temperature distribution in the cube. (d) Consider neither the cube nor the water keeps uniform in temperature. Write down the equation and boundary conditions for evaluating the temperature distribution in the water.

4. The net radiative heat flux at the surface of an opaque medium can be evaluated using the rollowing equation if the absorptivity of the medium is cqual to its emissivity  where E is the emissivity, o the Stefan-Boltzmann constant, Ts the surface temperature and J the radiosity. This equation seems to predict a very large radiative heat flux for a blackbody that (5%) hasε = 1. Please explain.

5. What are the definitions of the following terms? (10%) (a) Friction coefficient； (b) Biot number； (c) Stanton number； (d) Nusselt number； (e) Prandtl number. [Example]: Reynolds number, ReD= puD/μ, where r: fluid density, u: flow velocity, D: tube diameter, and u: fluid viscosity.

6. Please sketch the velocity and temperature profiles of laminar and turbulent flows in a circular  tube by following the format of the example.(6%)

(b) Is it a laminar flow or turbulent flow at the midpoint (x=0.5 m)? (2%)

(c) Please calculate the local heat transfer coefficient at the midpoint (x=0.5 m) of the flow. (5%) 

題目一:【10分】 請說明彈簧之功用並各舉出一個應用實例。

題目二:【10分】 請說明機構與機械的差別。

題目三:【10分】 何謂自潤軸承?何謂無油軸承?

題目四:【10分】 何謂機械利益與機械效率?