EXAMPLE 1Aspherical container of inner radius rl = 2 m, outer radius r2 = 2.1 m,and thermal conductivity k = 30 W/m - °C 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/m2 · °C. Assumingthe inner surface temperature of the container to be 0°C,the differential equation and the boundary conditions forsteady one-dimensional heat conduction through the containerа) еxpressb) obtain a relation for the variation of temperature in the container bysolving the differential equationc) evaluate the rate of heat gain to the iced water.

Given: r1 = 2m r2 = 2.1 m k = 30 W/moC h = 18 W/m2 oC

Aspherical container of inner radius rl = 2 m, outer radius r2 = 2.1 m, and thermal conductivity k = 30 W/m · °C 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/m2 · °C. Assuming the inner surface temperature of the container to be 0°C, %3D 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 c) evaluate the rate of heat gain to the iced water.

Aspherical container of inner radius rl = 2 m, outer radius r2 = 2.1 m, and thermal conductivity k = 30 W/m · °C 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/m2 · °C. Assuming the inner surface temperature of the container to be 0°C, %3D 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 c) evaluate the rate of heat gain to the iced water.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Mechanisms of heat transfer

Heat transfer is an essential discipline in thermal engineering that deals with the transfer, conversion, usability, and creation of heat or thermal energy. Transfer of heat occurs through various mechanisms like conduction, convection, radiation, and change of phases. All these mechanisms have distinct characteristics, but these mechanisms can simultaneously occur in an identical system.

Question

EXAMPLE 1
Aspherical container of inner radius rl = 2 m, outer radius r2 = 2.1 m,
and thermal conductivity k = 30 W/m - °C 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/m2 · °C. Assuming
the inner surface temperature of the container to be 0°C,
the differential equation and the boundary conditions for
steady one-dimensional heat conduction through the container
а) еxpress
b) obtain a relation for the variation of temperature in the container by
solving the differential equation
c) evaluate the rate of heat gain to the iced water.

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A large plate of 0.5 m thickness and constant thermal conductivity of k=60 W/m⋅K in which heat is generated uniformly at a rate of 2 kW/cm3. One side of the plate is heavily insulated so that there is no heat loss from the insulated side of the plate. The other side of the plate is exposed to the environment at T∞= 25oC with convection heat transfer coefficient is 20 W/m2⋅K. a) Express the differential equation and the boundary conditions for steady operating conditions. b) Determine the variation of temperature in the plate. c) Find the inner and outer surface temperatures of plate