A very long 304-stainless steel rod of diameter 3.7 cm is initially at 330 ºC. Convection occurs between the surface of the rod and an adjacent fluid maintained at a temperature of 230 ºC. Radiation heat exchange also occurs with the surroundings held at 465. The convection coefficient is 20 W/m²·K and the surface of the rod has an emissivity of 15%. Refer to “TABLE A-24: Properties of solid metals” (Cengel, 2008) to determine the properties of steel. Take the density to be independent of temperature, as shown, but allow for temperature dependence in the specific heat capacity. For every 4 metres of the rod’s length, determine the following.

a. Determine the initial convective heat flux from the surface of the rod to the fluid. Answer in W/m².

b. Determine the initial net radiative heat flux from the surroundings to the surface of the rod. Answer in W/m².

c. Determine the net rate at which heat will initially be gained by that segment of rod. If heat is lost by the rod, then state your answer as a negative value. Answer in kilowatts.

d. After a very long time, what temperature will the rod eventually approach? (Hint: Temperature where radiation and convection balance out each other.) This may be approached from a variety of strategies including trail and error, iteration or plotting a suitable function. Answer in Kelvin.

e. Estimate the average heat capacity of the rod during the period that its temperature is changing. Use linear interpolation for this exercise and base your answer on the average temperature between initial and final conditions. Answer in J/kg.K.

f. Determine the total energy gained by that segment of rod after this long period of time. If energy is lost by the rod, then state your answer as a negative value. Answer in MJ.

Please and thank you.

Question

A very long 304-stainless steel rod of diameter 3.7 cm is initially at 330 ºC. Convection occurs between the surface of the rod and an adjacent fluid maintained at a temperature of 230 ºC. Radiation heat exchange also occurs with the surroundings held at 465. The convection coefficient is 20 W/m²·K and the surface of the rod has an emissivity of 15%. Refer to “TABLE A-24: Properties of solid metals” (Cengel, 2008) to determine the properties of steel. Take the density to be independent of temperature, as shown, but allow for temperature dependence in the specific heat capacity. For every 4 metres of the rod’s length, determine the following.

a. Determine the initial convective heat flux from the surface of the rod to the fluid. Answer in W/m².

b.  Determine the initial net radiative heat flux from the surroundings to the surface of the rod. Answer in W/m².

c. Determine the net rate at which heat will initially be gained by that segment of rod. If heat is lost by the rod, then state your answer as a negative value. Answer in kilowatts.

d. After a very long time, what temperature will the rod eventually approach? (Hint: Temperature where radiation and convection balance out each other.) This may be approached from a variety of strategies including trail and error, iteration or plotting a suitable function. Answer in Kelvin.

e. Estimate the average heat capacity of the rod during the period that its temperature is changing. Use linear interpolation for this exercise and base your answer on the average temperature between initial and final conditions. Answer in J/kg.K.

f. Determine the total energy gained by that segment of rod after this long period of time. If energy is lost by the rod, then state your answer as a negative value. Answer in MJ.

Please and thank you.