Mass conservation in a sphere to find radial velocity of a flame

[Andrew1235]

Homework Statement

Problem description: https://i.stack.imgur.com/7T2OM.png

Relevant Equations

Mass conservation for a spherical control volume

I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?

 

[PeterDonis]

Moderator's note: Moved thread to advanced physics homework forum.

 

[bob012345]

Homework Statement:: Problem description: https://i.stack.imgur.com/7T2OM.png
Relevant Equations:: Mass conservation for a spherical control volume

I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?

I would assume the mass of the combustion products, air and fuel, are present throughout the volume and the flame front propagates without mixing or changing the density of that mixture pre and post combustion. I would also assume the combustion rate is limited by the available surface area as the flame expands in a spherical shape. But those assumptions could be way off.