Single hot solid particle hits the outer surface of the tube. Heat is transfered from the particle to the tube's wall. The equation should include porosity, shape, diameter of the particle. Which formula fits best?
Please provide more details: how big is this particle? do you want to consider temperature distribution inside particle? What kind of impact it is? (particle is stick to the wall?) What kind of contact is between particle and wall?
Intention of the question may be to get formulation on the optimum size, nature, temperature , velocity of impact and material of a particle which may become detrimental to the heat exchanger tube surface resulting in initiation of crack causing its failure.
@Abdul aziz Jaafar: Dimensional analysis is in progress. I can not perform the experiment (yet). I have to rely on theories.
@Maciej Jaskulski: Particles are sferical d=6 mm (later on will change to non sferical coarse). For now do not consider distributions inside the particle. Elastic collisions are taken into account.
@SOHAIL AHMAD KHAN: Yes, overall intention is correct with exception of the crack and exchanger failure. I need to recover heat from the hot slug.