Stellar convection is customarily described by the mixing-length theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to claim that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in literature are hampered by this basic uncertainty. I present a new theory of stellar convection that does not require the mixing-length parameter. This analytical formulation determines all the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and the surrounding medium. I obtain an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory are compared with those from the standard mixing-length paradigm for the solar model with very satisfactory results.
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