TY - JOUR
TI - An integral transform solution for unsteady compressible heat transfer in fluids near their thermodynamic critical point
AU - Alves Leonardo S. De B.
JN - Thermal Science
PY - 2013
VL - 17
IS - 3
SP - 673
EP - 686
PT - Article
AB - The classical thermodynamic model for near critical heat transfer is an  integral-differential equation with constant coefficients. It is similar to  the heat equation, except for a source term containing the time derivative of  the bulk temperature. Despite its simple form, analytical methods required  the use of approximations to generate solutions for it, such as an  approximate Fourier transformation or a numerical Laplace inversion.  Recently, the Generalized Integral Transform Technique or GITT has been  successfully applied to this problem, providing a highly accurate analytical  solution for it and a new expression of its relaxation time. Nevertheless,  very small temperature differences, on the order of mK, have to be imposed so  that constant thermal properties can be assumed very close to the critical  point. The present paper generalizes this study by relaxing its restriction  and accounting for the strong dependence on temperature and pressure of  supercritical fluid properties, demonstrating that a) the GITT can be applied  to realistic nonlinear unsteady compressible heat transfer in fluids with  diverging thermal properties and b) temperature and pressure have opposite  effects on all properties, but their variation causes no additional  thermo-acoustic effect, increasing the validity range of the constant  property model.