Consider a composite sphere with the cross section shown

to the right. Section A has radius $r_A,$ uniform thermal

conductivity $k_A,$ and uniform internal heat generation $q^{}.$

Section B has radius $r_B$ and uniform thermal conductivity $k_B.$

Section C has radius rc and uniform thermal conductivity kc $.$

There is not internal heat generation in C or B$.$ The interface

between B and C has thermal resistance $R_{t,BC}.$ Air with

temperature $T_{}$ is blown over the sphere and the associated

convection heat transfer coefficient is $h.$ There is also

thermal radiation from the surface, with $T_{\text{S}\text{U}\text{R}}=T_{}$ and

emissivity $.$ What is the heat flux $($q$")$ at the outer surface of

the sphere? You may assume $1$D heat transfer in the radial

direction and steady state conditions. Give your answer in

terms of known values given in the question