Chapter 2, Problem 2.24P

A transformer is to be cooled via forced air convection. To increase the effectiveness of thecooling, Alloy 1095 cast aluminum fins are attached to the top of the transformer overwhich air is blown (negligible thermal contact resistance between the transformer and thefins). The fins are 2 cm thick and 7 cm long and span the entire length of the transformer,and the transformer is 7 cm wide and 10 cm long. Air leaves the cooling fan at 25°C .a) Decide how to model the fins before performing any real analysis. Youare willing to accept some error in your analysis and so you will either model thefins as having adiabatic tips or being infinitely long. You expect the average convectioncoefficient over the heat transfer surfaces for this system to be around 50 W m2– K⁄ .Which tip condition should you use for the fins in your analysis? b) Modeling the transformer as being isothermal, determine the average convectioncoefficient over the heat transfer surfaces. Account for heat transfer from the…

4.) A 15-cm-diameter steam line carries saturated steam at 6 MPa and is located in a tunnel with stagnant air with a temperature of 50oC. The outside unit convective coefficient is 8.5 W/m2-K. The steam line is covered with 3 cm of 85% magnesia insulation. It is decided to reduce the heat loss by one-half. How much 85% magnesia insulation is required? Neglect thermal resistance of pipe and inside surface.

A 50-cm-diameter pipeline in the Arctic carries hot oil at 30◦C and is exposed to a surrounding temperature of −20◦C. A special powder insulation 5 cm thick surrounds the pipe and has a thermal conductivity of 7 mW/m · ◦C. The convection heat-transfer coefficient on the outside of the pipe is 9 W/m2 · ◦C. Estimate the energy loss from the pipe per meter of length.   (Please give step-by-step solution)