qo =4x107 W/m³ heat is produced in a spherical shaped radioactive material with a diameter of R = 0.2 m. The heat produced is released from the spherical surface to the environment in a stable regime. Thus, the temperature on the surface is kept constant at T=80°C The heat transmission coefficient of the object is given as k = 15W /m° C. The temperature of the spherical body changes only in the radial direction. (T = T (r)). The distribution of temperature in a spherical body: () + -0 It is defined in the form. T. a) Obtain the temperature distribution T (r). b) Determine the boundary conditions. Find the maximum temperature. (Tmax)

A cubical piece of heat-shield-tile from the space shuttle measures 0.17 m on a side and has a thermal conductivity of 0.065 J/(s·m·C°). The outer surface of the tile is heated to a temperature of 1050°C, while the inner surface is maintained at a temperature of 23°C. (a) How much heat flows from the outer to the inner surface of the tile in 3.0 minutes? (b) If this amount of heat were transferred to 1.5 liters (1.5 kg) of liquid water, by how many Celsius degrees would the temperature of the water rise?

A steam bath center in a gym consists of a wall three different material layers. First two layers have thermal conductivity of 5 W/m K, 10 W/m K and 2*(10) W/m K respectively. All three layers have thickness of 8 cm each. The inside wall surface temperature of steam room is 80 °C whereas outside surface temperature is 25 °C. Draw this composite wall. Calculate the heat transfer per unit length of the wall.

Consider a large plane wall of thickness L = 0.2 m, thermal conductivity k = 1.2 W/mK, and surface area A = 15 m². Internally, the wall is assumed to generate heat at 500 W/m³. The left and right surfaces of the walls are exposed to convective heat transfer. On the left side (at x = 0 m), the wall temperature is maintained at 60°C. On the right surface side (at x = 0.2 m), the surface is exposed to convective heat transfer with an ambient temperature of 20°C. The convective heat transfer coefficient on the right side is assumed to be 200 W/m²K. Please answer the following questions: 1. What are the given material properties and boundary conditions? 2. What is the coordinate system used here? Please draw a schematic with proper coordinates to represent the problem 3. What are the assumptions associated with the problem? 1D, steady state, etc.? 4. Show the full heat conduction equation associated with the problem (including the unsteady term) 5. Show how to reduce it (based on…