in which state of matter does convection not happen
Convection Convection cannot take place in most solids because neither bulk current flows nor significant diffusion of matter can take place. Diffusion of heat takes place in rigid solids, but that is called heat conduction. Convection, however, can take place in soft solids or mixtures where solid particles can move past each other.
Absolute zero At temperatures near 0 K (−273.15 °C; −459.67 °F), nearly all molecular motion ceases and ΔS = 0 for any adiabatic process, where S is the entropy. In such a circumstance, pure substances can (ideally) form perfect crystals as T → 0. Max Planck's strong form of the third law of thermodynamics states the entropy of a perfect crystal vanishes at absolute zero. The original Nernst heat theorem makes the weaker and less controversial claim that the entropy change for any isothermal process approaches zero as T → 0: