Ok, so here's the deal. You have an enclosed space. Ansys Workbench is unable to handle convection in enclosed space without using APDL command snippets. A word of warning, though, this is easier with ANSYS Classic.
I recently posted an example of how to do convection to ambient in Workbench here:
In my opinion, modelling pure conduction into the air will not accurately capture the behavior. You need to apply convective coefficients to calculate the heat transfer between the air surface and the air. Mind you, this analysis uses some advanced features.
The model will need to determine the air temperature inside the box. How? You'll need to insert a space node somewhere in the model and attach it to surface effect elements. Ansys will then calculate the air temperature when the model is run. Before you start, have the ANSYS Command Reference, Element Manual, and Thermal Analysis Guide in front of you. The process goes something like this:
1. Create named selections (in Classic they're called "Components") on the interior of the box and the exterior of the cylinder.
2. You'll then need to create a "space node" to convect the convection elements ([tt]N,NODE_NUMBER,X,Y,Z[/tt]). You do this by inserting an APDL Command Object in your boundary conditions
3. Define a new element type, real constant number, and material number
4. Set keyopts 5 to 1 and keyopt 6 to 1; I'd also recommend setting keyopt 7 to 1 and keyopt 8 to 2 in order to apply a parametric heat transfer coefficient. You'll also want to set real constant 13... probably equal to 1/3. The film coefficients may be input as a material property (see the MPTEMP and MPDATA commands). In Ansys terminology, HTC = (film coef)*|T1-T2|^n.
5. Set your element type and real constant number ([tt]TYPE[/tt] and [tt]REAL[/tt] commands)
5. Select the surface nodes ([tt]NSEL,S,NODE,my_NAMEDSELECTION[/tt]) and create a surface mesh, being sure to connect it to the space node ([tt]ESURF,NODE(X,Y,Z)[/tt]).
6. Select your newly created surface elements ([tt]ESEL,S,TYPE,my_TYPE[/tt]) and apply your film coefficients with the following command ([tt]SFE,ALL,1,CONV,1,-my_MATERIAL[/tt]).
The last thing to take care of is surface-to-surface radiation. As of ANSYS 13, it's available within the GUI, although I haven't tried it. The other way is to use command objects. The following document explains how to apply radiation with command objects.
Be SURE to include symmetry (RSYMM) otherwise your results will be incorrect.
Now, there are a couple of tricky things involved. Firstly, the lack of a command line makes it tough to apply all of those boundary conditions. Ansys Workbench runs has to run the entire analysis, which makes testing out commands difficult. Secondly, you can't see the elements or the space node that you create with command line scripts in Workbench. Thirdly, it is not possible to see that your boundary conditions were applied correctly without outputting still images with more APDL scripting.
Again, this analysis would be much easier to do in Ansys/Mechanical APDL. The other option is a CFD analysis... but that's its own can of worms.