What is thermal conductivity write its formula?
Answers
Thermal conduction is defined as the transport of energy due to random molecular motion across a temperature gradient. It is distinguished from energy transport by convection and molecular work in that it does not involve macroscopic flows or work-performing internal stresses.
Energy flow due to thermal conduction is classified as heat and is quantified by the vector {\displaystyle \mathbf {q} (\mathbf {r} ,t)}{\displaystyle \mathbf {q} (\mathbf {r} ,t)}, which gives the heat flux at position {\displaystyle \mathbf {r} }\mathbf {r} and time {\displaystyle t}t. According to the second law of thermodynamics, heat flows from high to low temperature. Hence, it is reasonable to postulate that {\displaystyle \mathbf {q} (\mathbf {r} ,t)}{\displaystyle \mathbf {q} (\mathbf {r} ,t)} is proportional to the gradient of the temperature field {\displaystyle T(\mathbf {r} ,t)}{\displaystyle T(\mathbf {r} ,t)}, i.e.
{\displaystyle \mathbf {q} (\mathbf {r} ,t)=-k\nabla T(\mathbf {r} ,t),}{\displaystyle \mathbf {q} (\mathbf {r} ,t)=-k\nabla T(\mathbf {r} ,t),}