Since heat flows from hotter to cooler body, heat will flow from the right hand side to the left hand side.
The term temperature gradient refers to the difference in temperature between two substances. Note that heat flows from the hotter to the cooler body when a temperature gradient exists between two bodies.
Hence, the direction of heat flow is that heat will flow from the molecules from the right collide and transfer heat to the barrier, which transfers heat to the left side.
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