it is desired to understand the time - temperature behavior of a hot copper sphere. the sphere has a diameter D and Is buried a depth Z below the surface of the dry sand in a very large,very deep sand pit far from the edges of the pit. The initial temperature of the sphere is Ti, and the temperature at the surface of the sand is maintained at " T infinity". the difference between the temperature of the sphere and the surface, T-T infinity at any time is a function of the initial Temperature difference, Ti - Tinfinity ; the thermal conductivity of the sand, ks ; the thermal conductivity of the copper kc ; the sphere diameter D ; the depth at which it is buried Z; the elapsed time t, and the density times the specific heat Pcp of the copper. What is the best set of repeating variables for this problem? Find the appropiate functional relationship between these parameters in dimensionless form.

Since the correlation given in the textbook is so complicated, Dr. Roy wants to come up with a new correlation for convection over a sphere. He proposes the correlation to be NUD D=2+C Re" Pr3 He used a steel sphere (conductivity of 42 W/m-K) of 20 cm diameter that generates steady 40 W heat. He placed it in air flow with 1 m/s where air temperature is 20°C. He then measured the steady state tempera- ture of the sphere surface to be 30°C. 31'8 w/m² K Based on his measurements, what is the convection coefficient? Using properties at film temperature, what should the value of C be as per Dr. Roy's calculations if he assumes m = 0.8? O'142 What is the temperature at the center of the sphere? 30 38 C

The 12ft x 14 foot room illustration in figure 1.6a has an exterior wall at a surface temperature of 60°F, a window surface temperature of 40°F (double glazing on a cold day). The two interior wall surfaces are a temperature of 72°F. Determine the MRT sensation of a person standing in the center of the room. (See figure 1.6 below) Round your values to the nearsest hundreth decimal place (0.00).  You will need to upload your mathematical work in question 4.

Consider you have four long, 2 cm diameter rods, one each made of copper, steel, wood, and glass. They are to be cooled from a high temperature for 10 minutes. If you want to describe how the temperature changes with time, what approach is best for each of these rods. Balance solution accuracy against efficiency and justify with rules of thumb given