What drives heat transfer?

What drives heat transfer?

There are two aspects in heat transfer, [1] quantum of heat Q or heating and heat flux Q flux.

The heat flux is the rate of heat transfer. ?Heat flux is proportional to the thermal gradient. Q flux = - K dt/dx, where K is thermal conductivity.

Heating equation Q = m Cp dt, where m is mass, Cp is specific heat and dt is the temperature gradient. Heating is a bit of a complex phenomenon as you have two variables, mass, and Cp in addition to dt.

The point to note here is that both thermal conductivity and specific heat are temperature-dependent. Thermal conductivity reduces with temperature as there is more scattering of phonons while the specific heat increases with temperature due to larger atomic vibrations.

At a constant mass and constant dt the heating can still be different if the specific heats are different. So, the heat transfer process is a combined effect of thermal conductivity and specific heat and maybe more.

Thermal conductivity refers to the material's ability to conduct heat, while specific heat is a measure of the material's capacity to store heat. Both heat transfer rate and heating depend on the interplay of specific heat and thermal conductivity. Of course, the temperature has a role or a compulsion Now let’s get into the specifics

Detail

Imagine two metal pieces, one copper and the other iron of the same surface area and same mass kept under the sun next to each other with equal dt.

You will observe. Copper with a thermal conductivity 400 Watts per meter Kelvin gets heated faster than iron with a thermal conductivity 79.5 Watts per meter Kelvin. This is purely an effect of the larger thermal conductivity of copper.

?You will further observe, that copper piece will still be at a lower temperature than iron after infinite time. This is the effect of specific heat. The specific heat of iron is 450 J/kg-K and the specific heat of copper is 389 J/kg-K. Therefore, iron can store more heat than copper and that explains why despite of same mass and same dt the piece of iron feels hotter than copper.

Now let’s go to the main point and see how we can explain this.

To cut short, it is the entropy change that works behind the scenes for heat transfer.

Explanation

How and why?

With everything being the same the entropy [change] ?of iron is 27.28 J/K/mole. The entropy of copper is 9.58 J/K/mole

Both at standard temperature and pressure.

The molecular weight of copper is 63.54 while the molecular weight of iron is 55.84. Therefore, on a weight basis, 1 gram of iron has more atoms than copper, and therefore, their entropies are different with iron having more entropy than copper.

Since entropy always increases, copper is at a lower entropy level, copper receives under identical conditions preferentially more heat than iron. This explains why copper has a larger thermal conductivity and heat transfer rate. Thermal conductivity is an offshoot of entropy change and direction.

Coming to heating, copper can never reach the heat content of iron since iron has larger specific heat and a large heat storage capacity.

Finally, if you critically look into ‘what drives heat transfer ‘it is the molar mass or the molecular structure that drives heat transfer. This single factor connects thermal conductivity, specific heat, molar mass, entropy, and temperature.

Therefore, in summary, the driving force for heat transfer is an interplay between so many complex factors as mentioned above

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