Transient-heat-conduction temperature profiles

Figure 4. Temperature profiles in transient heat conduction.

Temperature profiles can be determined from the transient heat conduction equation or, in integral models, by assuming some functional form of the temperature profile a priori. With the former, numerical solution of partial differential equations is required. With the latter, the problem is reduced to a set of coupled ordinary differential equations, but numerical solution is still required. The following equations embody a simple heat transfer limited pyrolysis model for a noncharring polymer that is opaque to thermal radiation and has a density that does not depend on temperature. For simplicity, surface regression (which gives rise to convective terms) is not explicitly included. 

In the previous examples, the initial condition was a constant and independent of X. The same technique can be applied for the case where there is an initial temperature profile. Consider the transient heat conduction problem in a slab... 

In this technique, the transient heat flux to a relatively large uncooled body is determined indirectly. The temperature profiles in the target are measured by an array of imbedded thermocouples, usually at or near the impingement surface. The flux is then calculated from the measured temperature responses, using inverse conduction heat transfer computational techniques... 

Rigorous modelling must take the selected geometry into consideration and this usually requires CFD. It must, in addition to heat transfer across the wall and film mass and heat transfer between the gases and catalysts, also include axial heat conduction in the metals due to steep temperature profiles. In addition transient behaviour and interaction between the steep temperature profiles must be understood for a proper design, especially when a reasonable catalyst deactivation is... 

Figure 13.6 Transient temperature profiles of an 80nm gold nanosphere irradiated with 250fs laser pulse ofSOmJcm" average fluence (energy per area) and 780 nm wavelength as calculated utilizing the thermodynamic model and the heat transfer model and with (w/) and without (w/o) interface conductance.

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