Question

In: Physics

Reacting chemicals are stored in a spherical stainless steel container of outer radius ro = 6...

Reacting chemicals are stored in a spherical stainless steel container of outer radius ro = 6 cm and of inner radius is 5 cm. The chemicals generate a uniform heat at a constant rate of ???? ̇ = 8 × 107 W m3 ⁄ . The outer surface of the container is maintained at a uniform temperature of 100 °C. Consider a steady one-dimensional heat transfer and

a. Write an appropriate form of heat conduction equation for the sphere.

b. Express the boundary conditions.

c. Obtain a relation for the variation of temperature by solving the differential equation.

d. Calculate the temperature at the center of the sphere.

Solutions

Expert Solution

genius_generous answered 2 years ago
Next > < Previous

Related Solutions

A spherical shell has in inner radius Ri and an outer radius Ro. Within the shell,...
A spherical shell has in inner radius Ri and an outer radius Ro. Within the shell, a total charge Q is uniformly distributed. Calculate: a) the charge density within the shell (if you cannot get this answer, you can proceed without it). b) the electric field strength E(r) outside the shell (r > Ro). c) the electric field strength inside the shell (r< Ri). d) the electric field within the shell (Ri < r < Ro) e) show that your...
Q1) In a food processing facility, a spherical container of inner radius r1 =41 cm, outer...
Q1) In a food processing facility, a spherical container of inner radius r1 =41 cm, outer radius r2 = 43 cm, and thermal conductivity k = 2 W/m · °C is used to store hot water and to keep it at 105°C at all times. To accomplish this, the outer surface of the container is wrapped with a 510-W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be nearly 100°C...
A disk with outer radius ro = 150 mm and inner radius ri = 25 mm...
A disk with outer radius ro = 150 mm and inner radius ri = 25 mm is press-fitted onto a shaft of radius 25.075 mm. Both members are steel with Young’s modulus, E = 205 GPa, Poisson’s ratio, ? = 0.29, and density, ? = 7845 kg·m-3. Determine and plot the radial and tangential stress distributions in the disk and shaft when it is rotating at 5000 rpm. Under the above conditions, what is the magnitude of the Von Mises...
A nonconducting spherical shell of inner radius a = 2.00 cm and outer radius b =...
A nonconducting spherical shell of inner radius a = 2.00 cm and outer radius b = 2.40 cm has (within its thickness) a positive volume charge density p = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of charge q = 4.5 x 10 ^ -14 C is located at the center of that center. Find the total charge of the shell.
A small conducting spherical shell with inner radius a and outer radius b is concentric with...
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -1q and the outer shell has a total charge of +3q. Select True or False for the following statements. 1. The total charge on the inner surface of the small shell is -4q. 2. The total charge on the outer surface of the...
A small conducting spherical shell with inner radius a and outer radius b is concentric with...
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -2q and the outer shell has a total charge of +4q. Select True or False for the following statements. The total charge on the inner surface of the small shell is zero. True False  The total charge on the inner surface of the large...
A sample of stainless steel was stored in a freezer with a temperature of -4.0°C. After...
A sample of stainless steel was stored in a freezer with a temperature of -4.0°C. After removing it from the freezer, the aluminum is placed in 1982 mL of water at room temperature (25.0°C). After several minutes thermal equilibrium is achieved at 21.4°C. What is the mass of the stainless steel sample? Please show all work with appropriate units.
For a ball bearing made out of plastic inner and outer race and a stainless steel...
For a ball bearing made out of plastic inner and outer race and a stainless steel ball, which of these materials is likely to wear? What would the wear pattern be like? Which will eventually fail first?
A solid spherical shell with a 12.0 cm inner radius and 15.0 cm outer radius is...
A solid spherical shell with a 12.0 cm inner radius and 15.0 cm outer radius is filled with water. A heater inside the water maintains the water at a constant temperature of 350 K. The outer surface of the shell is maintained at 280 K. The shell is made of Portland cement, which has a thermal conductivity of 0.29 W/(mK). (a) Starting from the basic equation for thermal conduction, derive the rate at which heat flows out of the water....
An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density...
An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density ρ=6r C/m4. (a) (2 pts.) Based on the symmetry of the situation, describe the Gaussian surface (if any) that could be used to find the electric field inside the spherical shell. (b) (3 pts.) Starting from the definition of charge enclosed, briefly derive the integral expression for the charge enclosed inside a Gaussian surface within the insulated spherical shell for the given charge density....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT