Believe it or not, this was seriously considered during the Cold War. Some manned prototypes even flew with their reactors going (albeit not to power the plane), though the problem of shielding wasn't adequately solved before progress in ICBMs made nuclear-powered bombers pointless.
Then there's Project Pluto, though that would have been less a conventional aircraft and more a terrifying drone bomber built around an unshielded nuclear ramjet the size of a bus:
The engine also acted as a secondary weapon for the missile: direct neutron radiation from the virtually unshielded reactor would sicken, injure, and/or kill living things beneath the flight path; the stream of fallout left in its wake would poison enemy territory; and its strategically selected crash site would receive intense radioactive contamination. In addition, the sonic waves given off by its passage would damage ground installations.
Note: Please see this post of mine for more on the project, my sources, and potential sources for bias.
I have written a couple of blog posts on my understanding of climate forecasting, climate change, and the Anthropogenic Global Warming (AGW) hypothesis (here and here). I also laid down the sources I was using to inform myself here.
I think one question that a number of readers may have had is: given my lack of knowledge (and unwillingness to undertake extensive study) of the subject, why am I investigating it at all, rather than relying on the expert consensus, as documented by the IPCC that, even if we're not sure is correct, is still the best bet humanity has for getting things right? I intend to elaborate on the reasons for taking a closer look at the matter, while still refraining from making the study of atmospheric science a full-time goal, in a future post.
Right now, I'm curious to hear how you formed your views on climate change. In particular, I'm interested in answers to questions such as these (not necessarily answers to all of them, or even to only these questions).