What will happen if we boil water in the absence of gravity? We know that, Convection is the mode of heat transfer due to the motion of individual molecules of a fluid (liquid or gas). The motion of the constituent particles arises due to difference in densities.
In the absence of gravity, water takes a spherical shape in order to minimize the energy due to surface tension, simply it wants to minimize its surface area for greater stability. Let us assume, we are able to manage to heat the centre of the water sphere by some kind of mechanism, how will the heat be transferred from the centre of the water sphere to its surface? Do convection currents, which are the major modes of heat transfer in the presence of gravity, take place in the absence of gravity? I think it will not take place. Is the heat transfer is due to conduction? 
Further, it would be great if you could explain what will happen as time progress? Will the bubbles of dissolved gases formed inside stay where they are formed or move to the surface or they move towards the centre? How will the water boil (or it just explodes)?
For reference, this is how water looks in the absence of gravity (in the International Space Station):

Please note: Water is coloured to enhance visibility 
 A: If you heat a sphere of water from the center in the absence of gravity, I see no reason for convective instability (in the usual sense of buoyancy of hot fluid).  The heat transport should purely conductive, and the idealized heat conduction equation could be solved by the familiar Green function method.  Hot liquid expands, so the sphere will inevitably grow.  But there are many complications.   


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*A steam bubble will form around the heat source, and vaporization will use up 540 cal/g.   

*A steam bubble might start to form on an impurity off-center, breaking the spherical symmetry. 

*As the fluid and/or steam bubble at the center begins to expand, there will be a transient outward acceleration of fluid further out.  This is the precondition for a Rayleigh-Taylor instability that could further break the spherical symmetry.  (The classic example of R-T instability is water on top of oil in the presence of gravity.  In the problem at hand, the outward acceleration mimics the effect of gravity.)
A: The heat flow will be radial.  A bubble will form at the center of the sphere and increase in volume with time.  Because of the much greater specific volume of the vapor compared to the liquid, the vapor will push the surrounding fluid outward radially, just as if a non-condensible gas were being released at the center of the sphere.  So, within the surrounding fluid region, there will be radial convection of heat, with radial conduction superimposed on the radial convection.  Is this good enough, or do you need to see the equations also?
A: In absence of gravity water start to evaporate due to kinetic motion of water molecules.The making of water vapor absorbing latent heat from either near heat source or from water itself .So in this way water become solid ice which was locate far from heat source and other part become water vapor.
