Question

A spherical container with an inner radius *r*_{1} = 1 m and an outer radius *r*_{2} = 1.05 m has its inner surface subjected to a uniform heat flux of q1=7kw/m^2. The outer surface of the container has a temperature *T*_{2} = 25°C, and the container wall thermal conductivity is *k* = 1.5 W/m·K. Show that the variation of temperature in the container wall can be expressed as and determine the temperature of the inner surface of the container at *r* = *r*_{1}.

Step 1

Using differential equation for heat conduction,

Step 2

Using Fourier’s law in radial r-direction,

Step 3

Calculation:

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