Hello,

You asked for the temperature distribution profile for the solid cylinder.

It is fully elaborated below:

the temperature distribution of solid and hollow cylinders when the thermal  conductivity  is assumed  constant and  variable. The  reason of  using  two  different cases is to give more understanding about the effect of thermal conductivity property on the temperature  distribution for  different  geometries. It is known that the temperature distribution of a solid cylinder for Iron, Aluminum, and Copper corresponding to the constant and  variable  thermal  conductivity,  respectively.  It  can  be  seen   that  the maximum value of temperature occurred in Iron because of Iron's thermal conductivity is less than the other selected materials. This fact will be made the amount of heat transfer in this material is  slower than that  the other  materials. On the  other hand, the  minimum value of temperature observed in Copper, due to its high thermal conductivity which makes the heat transfers  through  this  material  is  fast.  Stay  in  this  pattern,  the  temperature  distribution depends upon the radius of the cylinder and there is no change in the circumference direction due to the symmetry in the load and geometry. The value of temperature is constant within a certain radius; this is explained the conical shape of the temperature distribution. It can  be noticed  the same  behavior which can be   demonstrated. The  slight difference in  the maximum  temperature gets  it from  this  temperature distribution for both cases. The effect of variation in thermal conductivity seems clearly in the high-temperature (>150C) surface of a cylinder.

Hope this helps  !!