1) When modeling heat flow one usually postulates a model thermal energy flux field ϕ​:U×[0,T)→Rn directly with [ϕ​]=Ln−1⋅T[ energy ]​ In addition, one can introduce a model quantity u:U×[0,T)→R taken to have fundamental units [u]=[ temperature ]= Temp . Fourier's law of heat conduction states the following: The thermal energy flux is (instantaneously and pointwise) proportional to, and in the opposite direction of, the spatial gradient of the temperature. (i) Express [energy] in terms of fundamental units. Hint: [ energy ]=[ force ]⋅L and [ force ]=M⋅[ acceleration] (ii) Express Fourier's law of heat conduction as a model relation among (the) functions (ϕ​ and u ) with a constant of proportionality K>0 called the thermal conductivity. (iii) Find the physical units of K.