In what direction does heat flow? Why do particles of matter transfer thermal energy in this direction?

Heat flows towards colder objects.

heat goes downward, cold goes upward.

Nuts to that answer. Heat is energy of vibration, rotation, or translational movement of molecules and atoms. The more heat, the more movement. Temperature is a measure of the average kinetic energy of these molecules.

Now a hot object, with all this molecular motion, when it comes into contact with other molecules, they collide, and energy is transfered to the "slower" "colder" molecules making them move faster. thus, heat "flows" from hotter to colder. Heat flow is really energy flow, from the more vigrous movers to the slower or stationary movers, regardless which one is upward, or downward.

Heat flows from an object or substance at a higher temperature to an object or substance at a lower temperature. This process is known as thermal energy transfer. The direction of heat flow is governed by the fundamental principle of thermodynamics called the Second Law of Thermodynamics, specifically the concept of entropy.

The Second Law of Thermodynamics states that the entropy of an isolated system tends to increase over time. Entropy can be understood as a measure of the disorder or randomness in a system. In the context of heat transfer, it means that heat tends to spread out and distribute itself evenly within a system.

When two objects or substances at different temperatures come into contact, heat is transferred from the hotter object to the colder one. This occurs because the atoms or molecules in the hotter object have more kinetic energy (or thermal energy) and therefore move and collide at a higher rate. These collisions transfer energy from the faster-moving particles to the slower-moving particles, thus equalizing the energy distribution within the system.

In simpler terms, particles of matter transfer thermal energy by colliding with each other. Hotter particles collide more frequently and with greater force, causing them to transfer their energy to colder particles. This process continues until thermal equilibrium is reached, meaning both objects or substances reach a balanced temperature where there is no net transfer of heat.

To determine the direction of heat flow in a specific situation, you can consider the temperature difference between objects or substances. Heat always flows spontaneously from a higher temperature region to a lower temperature region until equilibrium is achieved.