Is there any other possible way to transmit heat apart from conduction convection and radiation? How and Why?

Yes, Advection.

Thanks. I did learn something new. It seems like I can argue with my school teacher now.

Isn't advection a subset of convection? Or is it that convection requires both advection and diffusion? (which would make diffusion another possible heat transport method)?

My understanding was that advection was the conveyance of stuff (heat, material, etc.) due solely due to a forced fluid flow. This is meant to differentiate between a natural convection situation wherein fluid flow carries heat, the flow occurs due to density differences, and that density difference is due to the heating source.

 

In math terms, I've always heard the [math]\mathbf{u} \cdot \nabla \phi[/math] part called the advection part of the conservation equation.

Isn't advection a subset of convection? Or is it that convection requires both advection and diffusion? (which would make diffusion another possible heat transport method)?

No, but convection (in the conventional use of the word- hot air rises, moves round the room + cools + falls again) might be thought of as a subset of advection.

Mr. Bignose, you mean the flows occur due to fluid flow carries heat due to density differences that is due to the heating source is advection or convection? Sorry, my English is bad.