In most places 24 hours wouldn't be possible, because even if you were somewhere with 24 hour sunlight, for part of the day the shadow would not be cast on the earth. You need to angle the sundial so that it's perpendicular to the sun's path through the sky, so for at least a portion of the cycle the sun would be 'below' the sundial, casting a shadow upwards. I suppose if you were very close to a pole near the summer solstice it could work though.