- Problem 3 The Two Temperature Model Proposed By Chen And Gurtin Uses Conductive Temperature Y And Thermodynamic Temp 1 (40.33 KiB) Viewed 43 times
Problem 3. The two-temperature model proposed by Chen and Gurtin' uses conductive temperature, y, and thermodynamic temperature, 7, in describing the nonequilibrium transition of thermodynamic states. Mathematically, the CV-wave model is applied to the conductive temperature, q(r.) + (r.t)=-kVw(r.) (1) which is to be coupled with the energy equation applied to the thermodynamic temperature, -V-q(r,1)=COT (r.1). (2) Equations (1) and (2) provide two equations for three unknowns, q (the heat flux vector), y (the conductive temperature), and T (the thermodynamic temperature). An additional equation is established to relate to 7: y(r,t)-T(r,t)=aV²y(r.1) (3) with a being the temperature discrepancy factor. (a) What is the physical meaning and significance of the temperature discrepancy factor, a. used in Eq. (3)? Assess it from the nonlocal behavior, y(r+L, 1) = T(r. 1). (b) What's the difference between y and T, in steady state? (c) Develop a correlation between the two-temperature model described by Eqs. (1) to (3) to the dual-phase-lag model. Derive the two phase lags, and, in terms of the thermodynamic properties involved in Eqs. (1) to (3). Chen, P. J. and Gurtin, M. E., 1968, "On a Theory of Heat Conduction Involving Two Temperatures," Z. Angew Math. Phys. 19, 614-627.