Answer these

\fConsider a long solid tube, insulated at the outer radius r2 and cooled at the inner radius ri, with uniform heat generation q (W/m ) within the solid. 1. Obtain the general solution for the temperature distribution in the tube. 2. In a practical application a limit would be placed on the maximum temperature that is permissible at the insulated surface (r = r2). Specifying this limit as 7,2, identify appropriate boundary conditions that could be used to determine the arbitrary con- stants appearing in the general solution. Determine these constants and the correspond- ing form of the temperature distribution. 3. Determine the heat removal rate per unit length of tube. 4. If the coolant is available at a temperature 7%, obtain an expression for the convection coefficient that would have to be maintained at the inner surface to allow for operation at prescribed values of 7}2 and q.6.23 The State of Chiapas, Mexico, decided to fund a program for literacy. The first cost is $200,000 now, and an update budget of $100,000 every 7 years forever is requested. Determine the per- petual equivalent annual cost at an interest rate of 10% per year. 6.24 Calculate the perpetual equivalent annual cost (years I through infinity) of $5 million in year 0, $2 million in year 10, and $100,000 in years 11 through infinity. Use an interest rate of 10% per year 6.25 A Pennsylvania coal mining operation has in- stalled an in-shaft monitoring system for oxygen tank and gear readiness for emergencies. Based on maintenance patterns for previous systems, there are no maintenance costs for the first 2 years, they\f\f\f