kindly solve the question

Consider 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.6.15 A new structural design software package is avail- able for analyzing and designing three-sided guyed towers and three- and four-sided self-supporting towers. A single-user license will cost $6000 per year. A site license has a one-time cost of $22,000. A structural engineering consulting company is trying to decide between two alternatives: buy a single-user license now and one each year for the next 3 years (which will provide 4 years of ser- vice), or buy a site license now. Determine which strategy should be adopted at an interest rate of 10% per year for a 4-year planning period using the annual worth method of evaluation. 6.16 The city council in a certain southwestern city is considering whether to construct permanent rest- rooms in 22 of its smaller parks (i.c., parks of less than 12 acres) or pay for portable toilets on a year- round basis. The cost of constructing the 22 per- manent restrooms will be $3.8 million. The 22 portable restrooms can be rented for $7500 each for 1 year. The service life of a permanent rest- room is 20 years. Using an interest rate of 6% per year and an annual worth analysis, determine if the city should build the permanent restrooms or lease the portable ones.632 The U.S. Army received two proposals for a turnkey design-build project for barracks for infantry unit sol- diers in training. Proposal A involves an off-the-shelf "bare-bones" design and standard grade construction of walls, windows, doors, and other features. With this option, heating and cooling costs will be greater, maintenance costs will be higher, and replacement will be sooner than for proposal B. The initial cost for A will be $750,000. Heating and cooling costs will average $72,000 per year, with maintenance costs averaging $24,000 per year. Minor remodeling will be required in years 5, 10, and 15 at a cost of $150,000 each time in order to render the units usable for 20 years. They will have no salvage value. Proposal B will include tailored design and construction costs of $1.1 million initially, with7.15 The Ester Municipal Water Utility issued 20-year bonds in the amount of $53 million for several high-priority flood control improvement projects. The bonds carried a 5.38%% dividend rate with the dividend payable annually. The U.S. economy was in a recession at that time, so as part of the federal stimulus program, the Utility gets a 35%% reim- bursement on the dividend it pays. [a) What is the effective dividend rate that the Utility is paying on the bonds? (b) What is the total dollar amount the Utility will sank in dividends over the life of the bands? (c) What is the future worth in year 20 of the dividend savings, if the interest rate is 8% per year? 7.16 A contract between BF Goodrich and the Steel- workers Union of America called for the company to spend $100 million in capital investment to keep the facilities competitive. The contract also re- quired the company to provide buyout packages for 400 workers. If the average buyout package is $100,000 and the company is able to reduce costs by $20 million per year, what rate of retum will the company make over a 10-year period? Assume all of the company's expenditures occur at time 0 and the savings begin 1 year later. 7.17 Rubber sidewalks made from ground up tires are said to be environmentally friendly and easier on people's knees. Rubbersidewalks, Inc. of Gardena, California, manufactures the small rubberized squares that are being installed where tree roots, freezing weather, and snow removal have required sidewalk replacement or major repairs every 3 years. The District of Columbia spent $60,000 for a rubber sidewalk in replace broken concrete in a residential neighborhood lined with towering wil- low oaks. If a concrete sidewalk costs $28 000 andIn Example 1.7, the temperature at the inner surface of the skin/fat layer was given as 35"C. In reality, this temperature depends on the existing heat transfer conditions, include ing phenomena occurring farther inside the body. Consider a region of muscle with a skin/fat layer over it. At a depth of L. = 30 mm into the muscle, the temperature can be assumed to be at the core body temperature of 7, = 37"C. The muscle thermal conductivity is k, = 0.5 W/m . K. The metabolic heat generation rate within the muscle is 4,, = 700 W/m'. The perfusion rate is w = 0.0005 s"; the blood density and specific heat are p, = 1000 kg/m' and c, = 3600 J/kg . K, respectively, and the arterial blood temperature 7, is the same as the core body temperature. The thickness, emissivity, and thermal conductivity of the skin/fat layer are as given in Example 1.7; perfusion and metabolic heat generation within this layer can be neglected. We wish to predict the heat loss rate from the body and the temperature at the inner surface of the skin/fat layer for air and water environments of Example 1.7.The walls of a refrigerator are typically constructed by sandwiching a layer of insulation between sheet metal panels. Consider a wall made from fiberglass insulation of thermal conductivity k; = 0.046 W/m . K and thick- ness L; = 50 mm and steel panels, each of thermal con- ductivity ko = 60 W/m . K and thickness Lp = 3 mm. If the wall separates refrigerated air at 7. ;= 4"C from ambient air at 7. = 25"C, what is the heat gain per unit surface area? Coefficients associated with natural convection at the inner and outer surfaces may be approximated as h; = h, = 5 W/m- . K.\f