2-90 Consider a large plate of thickness L and thermal conductivity k in which heat is generated uniformly at a rate of egn. One side of the plate is insulated, while the other side is exposed to an environment at Too With a heat transfer coefficient of h. (a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) determine the variation of temperature in the plate, and (c) obtain relations for the temperatures on both surfaces and the maximum temperature rise in the plate in terms of given parameters. FIGURE P2-90 т. gen Insulated

Heat conduction What does the assumption of one dimestional heat conduction mean? In the conduction what actual phenomena (heat transfer mechanisms) are being ignored to assume it, and where do they occur?

Derive the one-dimensional heat conduction equation for a sphere.

Q4/A 2-mm-diameter and 10-m-long electric wire is tightly wrapped with a 1-mm-thick plastic cover whose thermal conductivity is k-0.15 W/m "C. Electrical measurements indicate that a current of 10 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulated wire is exposed to a medium at Ts= 30°C with a heat transfer coefficient of h-24 W/m² C, determine the temperature at the interface of the wire and the plastic cover in steady operation. Also find the critical radius of plastic insulation. [334 T=30°C Electrical wire Insulation bale 10 m