- 4 5 Imagine A Solid Sphere With Radius Rs Hung By A Very Thin String In The Center Of A Closed Cylindrical Recipient F 1 (91.81 KiB) Viewed 62 times
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4.5) Imagine a solid sphere with radius Rs, hung by a very thin string in the center of a closed cylindrical recipient full of a fluid initially at 50 °C, as depicted in the figure below. The air that surrounds the cylinder is at 25 °C, and its temperature remains invariable over time. The solid sphere was at 100 °C before being immersed in the cylinder. It can be assumed that all properties of the fluid and of the sphere do not change over time. Assume that the temperature of the fluid is homogeneous along the entire cylinder. Teny = 25°C Rs Rc (a) Consider that the sphere is made of a very conductive material and that its radius R, is very small; in a way, the temperature profiles inside the sphere are neglectable. Develop an energy balance for the sphere and for the fluid, and obtain the two differential equations that represent this system over time. Define the initial conditions. (b) Now consider that the sphere is made of a material with very low thermal conductivity, and its radius R, is big enough to make the radial temperature profiles inside it significant. Develop the energy balances for this new situation, and define all initial/boundary conditions. Is the energy balance for the fluid different in this case?