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Conformal Ricci and conformal matter collineations for the combination of two perfect fluids in General Relativity are investigated. We study the existence of timelike and spacelike conformal Ricci and matter collineations by introducing the kinematical and dynamical properties of such fluids and using the Einstein field equations. Some recent studies on conformal collineations are extended and new results are found. It is worth mentioning that we recover all the previous results a special cases., Comment: 15 pages, accepted for publication Chinse J. Physics

We study the consequences of timelike and spaccelike conformal Ricci and conformal matter collineations for anisotropic fluid in the context of General Relativity. Necessary and sufficient conditions are derived for a spacetime with anisotropic fluid to admit conformal Ricci and conformal matter collineations parallel to u^a and x^a. These conditions for timelike and spacelike conformal Ricci and conformal matter collineations for anisotropic fluid reduce to the conditions of perfect fluid when the heat flux and the traceless anisotropic stress tensor vanish. Further, for $\alpha=0$ (the conformal factor), we recover the earlier results of Ricci collineations and matter collineations in each case of timelike and spacelike conformal Ricci collineations and conformal matter collineations for the perfect fluid. Thus our results give the generalization of the results already available in the literature. It is worth noticing that the conditions of conformal matter collineations can be derived from the conditions of conformal Ricci collineations or vice versa under certain constraints., Comment: 16 pages, accepted for publication in Chinese J. Physics