[mps]

in heat transfer from high to low temperature objects, is the rate of heat transfer (dq/dt) a function of their temperature difference, dT; or just the absolute quantity, q?  from the formula  q=mcdT, dT only indicates the final quantity, q, transferred.  (says nothing about rate of transfer.)  does another eqtn (or principle) relate the rate of heat transfer to dT?  would ice

intuitively, it's clear that an ice cube placed on a grill melts faster than on a tabletop, but by what eqtn is this known?

thanks a lot...

[Yggdrasil]

In general, transport problems involve solving the Boltzmann Transport equation, which is a fairly nasty partial differential equation.  However, in the case of a steady-state temperature gradient along the z-axis, the flux of heat through a material, J, follows this equation:

J = -κ(dT/dz)

where κ is the thermal conductivity of the material.  So basically, the rate of heat transfer is linearly proportional to the magnitude of the temperature gradient and the thermal conductivity of the material transporting the heat.