1. Engineering
  2. Mechanical Engineering
  3. consider radial heat conduction through a hollow sphere inside and...

Question: consider radial heat conduction through a hollow sphere inside and...

Question details

Consider radial heat conduction through a hollow sphere. Inside and outside radii and temperatures are r1, r2, T1, and T2. Thermal conductivity of the sphere wall material is k. Heat transfer is one dimensional, steady-state, and no internal heat generation. Ignore convection and thermal radiation. (a) Simplify Eq. 2.29 for heat transfer through the hollow sphere. Write the boundary conditions Eq. 2.29 is: OT r-sın ат OT (b) Integrate this equation twice and apply the two boundary conditions to obtain temperature distribution through the sphere wall (c) Apply the Fouriers Law of heat conduction at r = r1 to obtain the rate of heat transfer through the sphere wall. Apply the Fouriers Law at r r2 to obtain the rate of heat transfer again. Show that these two heat rate expressions are the same (d) Consider the following values for the parameters of this problem: r1 2 cm, r2 2.1 cm, T1- 100 C, T2- 20 C,and k - 25 W/mK. Write an MatLab code to determine and plot total heat rate vs. r2 for r2 2.1 cm to 5 cm. All other parameters remain the same

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution