申論題

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.