Is there any equation (or equations) to describe cooling and radiation of white dwarfs? How can cooling period of white dwarf be calculated? I'll be very happy to hear from you and extremely thankful for your answer.
Thanks for contacting Ask An Astronomer! Your question is extremely interesting; the cooling of white dwarfs can be extremely complicated depending on the amount of detail that is to be studied. I refer you, as a primer, to the following links:
and many other websites of classes of introductory astronomy. Another good reference that is also an excellent book for advanced students and amateurs that uses very simple freshman-level math is An Introduction to Modern Astrophysics, Carrol & Ostlie, which can be easily bough on any online bookstore such as Amazon.
As for the details of your question, an indicative measure of the timescale of cooling of a white dwarf is given by
t = E / L
where L is the luminosity of the white dwarf (energy emitted per unit time) and E is the energy content of the white dwarf, which is given by N k T (N = number of atoms, k = Boltzmann's constant, T = temperature of the white dwarf). With this formula, you can try to work out yourself the cooling timescale for some typical white dwarf (M = 0.6 solar masses, T = 10000 K).