  Motivated by the experimental report of unusual low temperature magnetism in
quasi one-dimensional magnet CuInVO$_5$, we present results of a cluster
mean-field study on a spin-$1/2$ Heisenberg model with alternating
ferromagnetic and antiferromagnetic nearest-neighbor coupling. We map out the
ground state phase diagrams with varying model parameters, including the effect
of an external magnetic field. An unexpected competition between different
spin-spin correlations is uncovered. Multiple spin-flop transitions are
identified with the help of component resolved correlation functions. For the
material-specific choice of model parameters we discuss the temperature
dependence of specific heat and magnetic susceptibility, and compare our
results with the available experimental data. A detailed account of spin-spin
correlations allows us to present a microscopic understanding of the
low-temperature magnetic ordering in CuInVO$_5$. Most notably, we identify the
origin of an extra peak in the low temperature specific heat data of CuInVO$_5$
reported by Hase {\it et al.}
