  Thermal metamaterials provide rich control of heat transport which is
becoming the foundations of cutting-edge applications ranging from chip cooling
to biomedical. However, due to the fundamental laws of physics, the
manipulation of heat is much constrained in conventional thermal metamaterials
where effective heat conduction with Onsager reciprocity dominates. Here,
through the inclusion of thermal convection and breaking the Onsager
reciprocity, we unveil a regime in thermal metamaterials and transformation
thermotics that goes beyond effective heat conduction. By designing a
liquid-solid hybrid thermal metamaterial, we demonstrate a continuous switch
from thermal cloaking to thermal concentration in one device with external
tuning. Underlying such a switch is a topology transition in the virtual space
of the thermotic transformation which is achieved by tuning the liquid flow via
external control. These discoveries illustrate the extraordinary heat transport
in complex multi-component thermal metamaterials and pave the way toward an
unprecedented regime of heat manipulation.
