Question

Which process transfers heat from inside earth to its surface

Answer 1

Answer is b
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Answer 2

Answer is: thermal conduction.
Thermal conduction is the transfer of heat through physical contact. Thermal conduction is the transfer of heat by microscopic collisions of particles. Heat spontaneously flows from a hotter to a colder body.
The thermal energy of that core is transferred to the surface of the Earth and lower levels of the oceans by conduction. Water in lakes and oceans transfers heat to the surface by convection.