That’s my question. What would that be liable to look like at a high level? Uranium pellets separated by some sort of radiation shielding filler?
In order to maintain the fuel in a supercritical configuration for an arbitrary period of time, you’d need to remove heat fast enough to keep the pellets from melting. So the upper temperature of your coolant can’t exceed the melting temp of the fuel, and in fact would need to be substantially less than that. In terms of power rate, at some point you are limited by the thermal conductivity of the fuel pellet itself; if you can’t get heat out of the pellet fast enough, it will melt. It would take a nuclear physicist to tell you how small the pellets can be while still allowing a supercritical configuration to be made.
The smaller the pellets, the better the surface-area-to-volume ratio, and the more power you can get out of them without melting. But your coolant’s temperature must still be less than the fuel’s melting temp.
In a nuclear power plant, water (for cooling) is pressurized to prevent boiling, or else liquid sodium is used. These are impractical for delivering destructive heat to a target. Your coolant, since you intend to interact with the surrounding environment, would need to be air.
In terms of your OP, youre device won’t create the kind of shock waves that knock buildings off off foundations. At best, you’ll create the world’s most extreme bonfire.
As it happens, this was done already once, though not on purpose. The Windscale nuclear facility was a pair of air-cooled nuclear reactors that actually caught fire.
I hope you realized I was kind of joking when I said “mere” engineering problem. It is utterly beyond the capabilities of any conceivable materials.
For some quick numbers:
A normal fuel rod in a nuclear reactor produces about 20kW heating power per meter for 40,000 hours, giving a burnup of 66MWd/kgU (I take about 0.5 kgU per meter of fuel rod).
To burn that up in 10 minutes, we’re looking at a heating power of 4.8 GIGAwatts out of that tiny, one meter long, 1 centimeter diameter rod. An areal heat flux of 77 Gigawatts/sq.m.
You’d need a water stream of 40 cubic meters per SECOND to cool it down with a temperature rise of 30 degC.
That’s 250,000 people taking a hot shower simultaneously.
All that water would have to be directed past that rod in close contact.
Don’t know how to visualize this better, it’s utterly inconceivable.
There’s a form of criticality accident that can occur in handling nuclear materials that can become self-sustaining for a considerable period of time. This would emit disabling and lethal radiation in a local area over the period of criticality, so it somewhat resembles what Wells imagined.
The poster child for this sort of accident is Tokaimura.
Note that the criticality continued to operate and emit deadly radiation for about 20 hours, albeit intermittently.
The consequences were also somewhat grenade-like:
For a hand grenade, you might consider a one centimeter length of fuel rod.
It could sustain 2500 hot showers simultaneously for 10 minutes with its heating power.
Maybe someone can calculate the surface temperature of a 1 centimeter radiating body radiating that amount of heat as a blackbody spectrum?
I’m fairly sure it would melt. Maybe even evaporate.
I imagined water flowing across the rod in a layer 5mm thick across either side of it. So 40 cubic meters per second, through a flow area of 1 * (0.005 * 2) = .01 m^2, works out to a water velocity of 4 km per second. You’d have to use all the energy you harvested to power pumps to make that flow happen. 
The OP has already declined to consider this kind of intense radiation/omni-directional death ray (hat-tip JRDelirious). For the record, I’m with Frankenstein Monster on this. The sort of “ball of fire” or “ongoing/cycling explosion” the OP demands is not something that can be currently engineered or even conceived of as being engineered. What is basically being asked for is a miniature sun, brought into being without destroying what created it, and persisting or repeating.
Because as I said, we could engineer a device, perhaps even a man-portable device, that emits deadly radiation over a room-sized area or better for either a prolonged period of time or at set intervals, but that is apparently a non-starter for the OP. Wells hypothesized a device based on a flawed understanding of just what exactly radiation does, what it is, where it comes from, and a whole host of other things that, not surprisingly, makes it unrealistic now that our understanding has evolved. You want a ball of fire? Fill a pop bottle with gasoline. You want to lay waste to cities? Take a melon-sized sphere of plutonium, surround it with precision-timed explosives, and make it implode to a super-critical mass in a fraction of a second. Wells didn’t know what he was talking about.
If I understood the Wiki page correctly, a 1cm radius sphere (surface area of 12.6 cm^2) emitting 48MW of heat equals 38.4 GW/m^2 which corresponds to a temperature of 29,000 degC.
How far do you have to throw it not to be burned to a crisp yourself?
For calculations like that for your "grenade, " why not consider some sort of gaseous core rather than a fuel rod? Then you don’t have to worry about the core melting since it’s already vaporized, you just need to work out the desired core composition, containment materials to last however many minutes, whether there should be any cooling (as in a nuclear rocket), etc 
Grenade for a giant mecha robot.
Wells describes these nuclear handgrenades as exploding for days, while performing a random-walk that knocks down buildings. It seems obvious that the hand grenade itself would fragment into multiple smaller pieces, unless it were fantastically robust.
How about a sphere made of diamond, with multiple miniature gaseous-core nuclear rockets poking out at odd angles? An engineering challenge for the ordnance expert. Or something like a nuclear-powered jumping jack firework?
https://para-phenalia.com/cart/images/cache/GROUP__JUMP_JACKS_489.800.jpg
Can you have something that ablates away over a prolonged period, maybe in bursts? Like layers of fissile material and some combustable control material. Some control material burns away, the next onion skin layer of fissile material goes critical and blows outwards, the next layer starts burning, etc. etc.
It wouldn’t be a hand grenade, and would be more like a series of dirty fizzle bombs. Dunno if you could shield the stuff inside from the chain reaction of the outer layers; my notion is that the layers are relatively thin and blow off quickly, while the shielding layers are thicker.
Not quite an atomic grenade, but a very small black hole could produce a continuous stream of very strong hawking radiation as it evaporated.
I like that idea. An evaporating black hole would radiate a lot of energy in the last few seconds of its life. Unfortunately the hole would be so small and so dense that it would probably fall straight down towards the centre of the Earth, and explode somewhere beneath the Earth’s crust.
You’d get enough energy to make a decent “grenade” for a lot longer than the last few seconds. But you’re right that it would just fall through the Earth.
A 1 kg black hole (approximately grenade sized) will evaporate in something like 10[sup]-16[/sup] seconds.
If, by magic, you could somehow stabilize the black hole while inside the grenade device, once the containment is released there will be nowhere close to enough time for it to sink to the center of the Earth. It’ll just release all of its energy immediately. A 1 kg black hole won’t fall any faster than any other 1 kg object.
If it weren’t for the evaporation, containment would be fairly easy. You just charge up the black hole (one of the few things you can do to a black hole besides adding mass), and then just suspend it electromagnetically.
A lot of the energy will go into neutrinos and the like, but it should still make a pretty big boom.
Simple process.
[ol]
[li] Take any small-ish fission bomb. [/li][li] Launch it with a humongous booster.[/li][li] When it hits a desired fraction of c, trigger it.[/li][li] Watch the time-contracted explosion last quite awhile.[/li][/ol]
For our purposes, launch it from Tau Ceti IV, timed to detonate in our solar system. We’ll watch it whiz by.
I was thinking of starting with a black hole that’s at the appropriate power level, not with one that’s the appropriate mass. If anyone can give me a ballpark figure for what power level would be needed for a “continual explosion”, I could run the numbers.
Going with 1 TW as the xkcd scale for a continuous explosion, you end up with a mass of 19 billion kg for your black hole. And it’ll take about 18 million years to burn out.
It does increase power as the mass goes down: four times the power at half the mass, and so on. But I guess there won’t be many people around to witness the final boom.
It might be kinda hard to throw. And would definitely sink to the center of the Earth if you let it. But while 19 billion kg is a lot, it’s basically the same scale of mass as a large dam. So it might be possible to suspend it electromagnetically as well, with some kind of large, charged base to support it. Not exactly trivial, but probably easier than making the black hole in the first place.
And actually, charging a black hole up to the point where you can suspend it electromagnetically is decidedly nontrivial. The problem is that you get to a point where shoving more electrons in takes so much energy that the mass is increasing just as fast as the charge.