A spherical container of inner radius r₁ = 2 m, outer radius r₂ = 2.1 m, and thermal conductivity k = 30 W/mK is filled with iced water at 0°C. The container is gaining heat by convection from the surrounding air at T = 25°C with a heat transfer coefficient of h=18 W/m²K. Assuming the inner surface temperature of the container to be 0°C, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container by solving the differential equation, and (c) evaluate the rate of heat gain to the iced water. k T₁ T. 8 11 12 h

A spherical container of inner radius r₁ = 2 m, outer radius r₂ = 2.1 m, and thermal conductivity k = 30 W/mK is filled with iced water at 0°C. The container is gaining heat by convection from the surrounding air at T = 25°C with a heat transfer coefficient of h=18 W/m²K. Assuming the inner surface temperature of the container to be 0°C, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container by solving the differential equation, and (c) evaluate the rate of heat gain to the iced water. k T₁ T. 8 11 12 h

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.16P: 3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer...

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