A heated spherical ceramic object (diameter= 10cm), initially at 1200k, is held in a large enclosure whose walls are maintained at a temperature of 300k. The sphere has an emissivity of 0.7. Properties of Sphere: Density =4500 kg/m^3, heat capacity= 400 J/(kg.K); thermal conductivity= 22 W/ (m.K). Assume properties of the sphere do not vary with temperature. The rest of the enclosure is filled with stagnant nitrogen at a bulk temperature of 300 K.

a) What is the initial rate of heat transfer from sphere?
b) What are the relative contributions of radiation and convection to the rate of heat loss when the sphere is at 1200K
c) What are the relative contributions of radiation and convection to the rate of heat loss when the sphere is at 600K

Nice try!

To find the rate of heat transfer from the heated spherical ceramic object in the given scenario, we will use the equations for radiative and convective heat transfer. Let's break down the problem into parts:

a) Initial rate of heat transfer from the sphere:
To calculate this, we need to consider both the radiative heat transfer and convective heat transfer.
The radiative heat transfer can be calculated using the Stefan-Boltzmann law, which states that the power radiated by an object is proportional to the fourth power of its temperature and its emissivity. The equation is:
Radiative heat transfer = ε * σ * (T_s^4 - T_inf^4)
where ε is the emissivity of the object (0.7 in this case), σ is the Stefan-Boltzmann constant (5.67 * 10^-8 W/(m^2.K^4)), T_s is the temperature of the sphere (1200K), and T_inf is the temperature of the enclosure walls (300K).

The convective heat transfer can be calculated using Newton's law of cooling, which states that the rate of heat transfer by convection is proportional to the temperature difference between the object and the surrounding fluid. The equation is:
Convective heat transfer = h * A * (T_s - T_inf)
where h is the convective heat transfer coefficient, A is the surface area of the sphere, and T_s and T_inf are the temperatures of the sphere and the enclosure walls, respectively.

To find the initial rate of heat transfer, we need to add up the contributions from radiation and convection:
Initial rate of heat transfer = Radiative heat transfer + Convective heat transfer

b) Relative contributions of radiation and convection at 1200K:
To determine the relative contributions of radiation and convection, we need to compare their individual contributions to the total rate of heat transfer at 1200K. We can do this by dividing the heat transfer rate due to radiation by the total heat transfer rate and multiplying by 100 to express it as a percentage:
Relative contribution of radiation (%) = (Radiative heat transfer / Initial rate of heat transfer) * 100

Similarly, we can find the relative contribution of convection:
Relative contribution of convection (%) = (Convective heat transfer / Initial rate of heat transfer) * 100

c) Relative contributions of radiation and convection at 600K:
To determine the relative contributions of radiation and convection at 600K, we can repeat the calculations using the given temperature of 600K instead of 1200K.

By using the provided properties of the sphere and the given equations, we can calculate the specific values for each part of the problem.