it is desired to understand the time - temperature behavior of a hot copper sphere. the sphere has a diameter D and Is buried a depth Z below the surface of the dry sand in a very large,very deep sand pit far from the edges of the pit. The initial temperature of the sphere is Ti, and the temperature at the surface of the sand is maintained at " T infinity". the difference between the temperature of the sphere and the surface, T-T infinity at any time is a function of the initial Temperature difference, Ti - Tinfinity ; the thermal conductivity of the sand, ks ; the thermal conductivity of the copper kc ; the sphere diameter D ; the depth at which it is buried Z; the elapsed time t, and the density times the specific heat Pcp of the copper. What is the best set of repeating variables for this problem? Find the appropiate functional relationship between these parameters in dimensionless form.

it is desired to understand the time - temperature behavior of a hot copper sphere. the sphere has a diameter D and Is buried a depth Z below the surface of the dry sand in a very large,very deep sand pit far from the edges of the pit. The initial temperature of the sphere is Ti, and the temperature at the surface of the sand is maintained at " T infinity". the difference between the temperature of the sphere and the surface, T-T infinity at any time is a function of the initial Temperature difference, Ti - Tinfinity ; the thermal conductivity of the sand, ks ; the thermal conductivity of the copper kc ; the sphere diameter D ; the depth at which it is buried Z; the elapsed time t, and the density times the specific heat Pcp of the copper. What is the best set of repeating variables for this problem? Find the appropiate functional relationship between these parameters in dimensionless form.

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

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

it is desired to understand the time -
temperature behavior of a hot copper sphere.
the sphere has a diameter D and Is buried a
depth Z below the surface of the dry sand in a
very large,very deep sand pit far from the edges
of the pit. The initial temperature of the sphere is
Ti, and the temperature at the surface of the
sand is maintained at "T infinity". the difference
between the temperature of the sphere and the
surface, T - Tinfinity at any time is a function of
the initial Temperature difference, Ti - Tinfinity ;
the thermal conductivity of the sand, ks ; the
thermal conductivity of the copper kc ; the
sphere diameter D ; the depth at which it is
buried Z; the elapsed time t, and the density
times the specific heat Pcp of the copper. What
is the best set of repeating variables for this
problem? Find the appropiate functional
relationship between these parameters in
dimensionless form.

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