Dear Nikopla,  after learning of the meaning of nucleate boiling condition, and the mechanism behind that enhancement, Now I could answer your question without any hesitation.  YES YOU CAN USE IF ONLY IF  THE HEAT TRANSFER COEFFICİENT DOESN'T DEPENDENT ON THE TEMPERATURE  OR  DURING THE TRANSIENT REGIME TEMPERATURE FLUCTUATIONS ARE TOO GREAT.

I think you can get the same results without introducing the foreign objects as nucleation sites but just having sustainable rough surfaces, which can be generated by the applied bi-axial surface compressive stresses that enhance the process.

 Best Best Regards

Nucleate boiling is characterized by the formation of bubbles at the nucleation sites and resulting liquid agitation. The bulk agitation induces considerable mixing and that promotes substantial increase in heat flux and the boiling coefficeint.

The transient nucleate boiling process takes place during quenching of steels and alloys . During last decades the new characteristics of the transient nucleate boiling process were discovered which can be formulated as follows. The duration of the transient nucleate boiling process is directly proportional to squared size of a component and inversely proportional to thermal diffusivity of a given material, depends on configuration of component, initial temperature and thermal properties of liquid. The surface temperature of a component during the nucleate boiling process is maintained at the level of boiling point of liquid until heat flux densities during nucleate boiling and convection become equal.  

Ref;Discovered Characteristics of the Transient Nucleate Boiling Process to Be

Widely Used for Testing of Materials and New Technologies Development by NIKOLAI KOBASKO

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

www.wseas.us/e-library/conferences/2012/.../FLUHMABE-01.pdf

Dear Dr. Krishna,  I thank you for comments. BUT I put my constrained which tells us under what conditions my statement is warrant.

There is a misuse  of terminology here, what you are describing a process, which is fully dynamic even you can not talk about the existence of  a stationary boundary layer  that one can put that even in the category of  heat transfer coefficient.  As you said the duration of that event depends on size and thermal conductivity of the bulk!!

Transient implies  the initial stage of the  nonlinear process where the  external constrains the on the system stay invariant but the behavior is control by the maximum entropy production criteria before switching  to the second stage where the system approaches non-equilibrium  stationary state in the sense of  Prigogine' minimum entropy production criteria.

 As we have observed in our simulations on the  grain boundary crack initiation and propagation under the uniaxial  tension, very recently. 

Best Regards

Dear Prof.  Krishna,

Thanks for your comments. Yes, the duration of the transient nucleate boiling process is very important and it is directly proportional to squared size of a component and inversely proportional to thermal diffusivity of a given component material, depends on configuration of component, initial temperature and thermal properties of liquid. Knowing this time we can switch form third type of boundary condition to the first type of boundary condition. Transient nucleate boiling processes are not investigated deeply and widely yet. Such transition simplifies calculations and increases their accuracy.

Dear  Prof. Ogurtani,

Thanks for your interesting comments. I'm not sure that I understood completely your comments.

1. During transient nucleate boiling process, the real heat transfer coefficient  (HTC) is a function of the overheat  T - Ts, where T is surface temperature, Ts is saturation temperature. So, HTC during boiling process depends on surface temperature and changes significantly during quenching. In heat treating industry during quenching is widely used Grossmann factor H which is connected with the effective HTC. It doesn't depend on surface temperature and is characteristic of a quenchant. We came to conclusion that effective HTC can be used only for steel parts core cooling time calculations and cannot be used for temperature fields calulations. We discussed these issues when considering real and effective HTCs.

2. During nucleate boiling proces at the surface of steel parts can be compressive or tensile stresses depending on intensity of cooling. How compressive stresses can affect the boiling process?  We have experimental data that compressive stresses can eliminate cavities and sims at the surface of steel parts. Maybe that can affect boiling processes. 

There are some differences between transient and steady - state nucleate boiling processes. At the beginning of transient process, shock boiling is observed. Nobody observed shock boiling when investigating steady - state boiling processes. During shock boiling thousands of tiny bubbles act producing specific noise which can be depicted by noise control system. During shock boiling heat flux densities and heat transfer coefficients (HTCs) are extremely high. Duration of shock boiling is very short. We used  HTCs, received for steady -state nucleate boiling to calculate transient nucleate boiling. Error was within + (-) 5% due to shock boiling.

Also, during transient nucleate boiling process, so called self - regulated thermal process is observed.  During this process surface temperature maintains at the level of boiling point of liquid and never cannot be below it until heat flux densities at the end of transient nucleate boiling (qnb) and at the beginning of convection  (qconv ) become equal.  Unfortunately, transient nucleate boiling processes are not investigated enough deeply and widely by thermal scientists,  although they are very important for the practice and are used in many industries..  

Dear Nikolai,  I am ın general agree with you as far as the context of the process and its interpretation is concerned. Only the terminologies  you guys  are using in engineering don't fit the mathematical counter parts  of these terms  in the classifications of various regimes in the treatment of the nonlinear problems.  For example strictly nonlinear dynamics systems can't have any steady.state since this implies that there is no connection exist between the final state of the system and the  initial state,  no  'history effect'. But one may talk about the stationary state or non-equilibrium stationary state etc. 

Transient state can be only observable if you uses the logarithmic time scale. Some times  I had to go down to  10-12-15 compared to unity where maximum entropy criteria switches to minimum entropy production (second derivative becomes zero on S-type transition curve in semilog scale).   Best Regards

Note: If the boundary surface layer heat transfer coefficient  depends on  T-Ts, that means some problem exist in the definition of transfer coefficient.,

By definition  the Heat flux intensity at the hypothetical surface =  HTC x  (T-Ts ), where T  is temperature of the geometric surface, and Ts  is the temperature of the environment just at the interface between media and boundary layer, which is assumed to be stagnant. Otherwise there is no use by  making  over simplification by  introducing boundary layer model. Where boundary layer is composed of liquid bobbles, where the coming and out going bobbles  into the ensemble  is constantly  changing   but keeping the size distribution fct invariant (static).  Here one can apply the solution of Fokker_Planck   as it was done by Russians 1943 (SEE Landau& Lifshitz, Statistical Physics I-II).

Thanks for useful comments.

Dear Tarik,

Some misunderstanding was in our discussion. For investigating transient nucleate boiling processes, at the beginning.  we used parabolic heat conductivity equation with the initial condition and the non- linear boundary condition responsible for boiling process. Later we noticed that Fourier law doesn't work during shock transient nucleate boiling process and we switched from parabolic heat conductivity equation to hyperbolic heat conductivity equation. As you know, the last is generated by modified Fourier law. I was saying that we used HTCs which were received by thermal scientists in steady state condition for modeling  transient boiling process. So, with the history of the process  and boundary condition everything is OK.

As for depending heat transfer coefficient during boiling process on T-Ts, it is well known fact. Kutateladze, Tolubinskii and other well - known thermal scientists established correlation between HTC and T - Ts. By the way, HTC during nucleate boiling depends on T-Ts as squared  value. Your comments are true for Newton's law.

Transient nucleate boiling processes are so interesting and I don't understand why they are not enough investigated by thermal scientists and physicians. 

Dear Krishna & Nikolai, both of you have done excellent job by putting this rather complicated quasi-boundary layer heat transfer problem on top of their four feet by giving their concise and transparent description even pointing out the short comings of the present and past approach to the homogeneous nucleation theory. 

The conceptual structure of  the classical nucleation theories were  always bothering me since I was a graduate student taking advanced phase transformation course delivered by Late Professor John Shyne at Stanford early 1962. Till I  have met the fluctuation theory as advocated by  Ya. B. Zel'dovich (1942), which was briefly but concisely presented in Kinetics of Phase Transitions chapter of Landau& Lifshitz' book entitled as 'Physical Kinetics' . Similarly the classical theory  nucleation for  the formation of liquid droplet in supercooled vapour, or of vapour bubbles in the superheated liquid is presented in first part of 'Statistical Physic' pp533-537, with problems. But this classical  theory is some how mixed with the growth theory since it doesn't make any reference to the statistical nature of the problem. 

Actually very sophisticated growth theory is recently formulated by Ogurtani using the irreversible thermodynamics of surfaces and interfaces,  which includes not only the capillary forces but also electrostatic and elastostatic forces without assuming any restriction of the shape of growing particles, which adjusts itself spontaneously because of the positive definite internal   entropy production criteria. This criteria for the  isochoric and isobaric processes under the isothermal conditions are replaced by the variation minimal problems having Helmholtz and Gibbs free energies as functionals, respectively. Best Regards

Dear Nikolai, In the lattice treatment of the  diffusion jumps of interstitial in the fluctuating stress field, I have used discrete Fourier transform for the space  variables and the Laplace transform for the time variable, and solve the very complicated problem moving kinks in the atmosphere of paraelastic point defects where got relaxation band structure for BCC lattice using the octahedral or  tetrahedral sites as the potential  positions for the occupation. I applied this theory on internal friction in BCC lattice. Some of those publications are cited in RG. Tetrahedral sitesin BCC lattice have five optical and one acoustic relaxation bands, which was also calculated by Fulde et. al. at Max Planck,   later  for AgI xtal  in connection with superionic conduction. I was rely amused because of that  coincidence, which gave exactly the same band picture. Best REgards

Dear Tarik, First  of all thanks a lot for your two papers published in Physical Review and Journal of Applied Physics you kindly provided. Especially is very interesting to me the second one. I'll use it to explain our experimental results connected with the healing defects by surface compressive residual stresses. As for investigation of phase transformation, your powerful mathematical tool can make a big difference in improving metallurgical processes. We will continue our discussion.