**Author details**

**6. Conclusions**

**Table 7.**

**Nomenclature**

**174**

*Bi* Biot number, *hL*/*k Cp* specific heat

*h* heat transfer coefficient *K*(*θ*) thermal conductivity, *k*(*θ*)/*k0*

Analytical, transient numerical and two-node methods are used to compute temperature distribution in a finite slab. Numerical solution is carried out with temperature-dependent thermal conductivity. Implicit finite difference scheme with two-time level technique is implemented to solve nonlinear problem of heat conduction. Time delay is studied using finite element method with deforming grid strategy. A boundary shifting numerical scheme is used to solve transient heat conduction in radial coordinate. Evidence of temporal accuracy and dependence on time-step is demonstrated in the numerical solving of IHCP. Influence of thermocouple cavity and measurement errors in location and time are discussed. The IHCP is applied to predict the wall heat flux in a rocket nozzle of a solid motor. Wall heat flux is estimated in a free flight of a sounding rocket using the two-node method.

*Comparison between calculated and Van Driest's heat flux at location 29.*

*<sup>t</sup>***, s** *Tm***, K** *Tc***, K** *qw* **<sup>10</sup><sup>4</sup>**

*Inverse Heat Conduction and Heat Exchangers*

 313.0 320.0 2.756 8.246 341.3 349.4 16.695 14.82 408.0 412.3 19.387 22.647 469.7 469.3 8.657 18.876 495.2 495.8 8.145 10.117 504.1 513.3 9.302 4.569 502.4 521.2 2.757 1.176 495.2 506.8 7.695 0.977 487.4 487.6 0.040 2.320 477.4 477.0 0.037 3.134 467.4 467.0 0.028 3.578 457.4 457.5 0,034 3.769 445.8 447.2 0.905 3.789 438.6 437.5 0,005 1.628 444.1 445.9 5.173 4.135 469.1 467.5 13.518 11.524 533.0 521.2 20.618 19.732 556.3 558.4 9.180 13.122 567.1 573.5 6.514 8.581 584.1 587.2 8.592 5.467 596.9 602.2 7.018 3.314

**, W/m<sup>2</sup>** *q*van

*<sup>w</sup>* **<sup>10</sup><sup>4</sup>**

**, W/m<sup>2</sup>**

Rakhab C. Mehta Department of Aeronautical Engineering, Noorul Islam Centre for Higher Education, India

\*Address all correspondence to: drrakhab.mehta@gmail.com

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