# The Inverse Heat Transfer Problem

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Inverse problem reformulation generally involved as approximate well posed problems for a successful solutions. By adding smoothing terms in the least square method approach unstable effects of measurements error can be reduced by Tikhonovs regularization procedure. Sequential improvement of the solution takes place in iterative regularization procedure. To stabilize the error of the input data for the final solution stopping criteria for iterative process are chosen.

Inverse heat transfer problem concept

By considering standard one dimensional, transient heat conduction problem in a slab of thickness L the physical significance of inverse heat conduction problem can be better understood. Initially measurements distribution in slab is F(x). For time t>0 a transient heat flux f(t) is applied on the boundary conditions at x=0 and x=L^([1]). The mathematical formulation of this concept

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The injection hole pattern on the face of injector provide propellant distribution form the injector inlet to all of the injector holes. High passage velocities will cause uneven flow through the injection holes and will also disturb the distribution and the composition. When talking about engine performance injector has main impact on the engine than any other component. While designing injector an important factor which is kept in mind is the combustion stability. The injector will have only secondary performance if it triggers to destructive instability.

4.1 Types of injector

There are different types of injector

Impinging injectors

Shower head injectors

Coaxial hollow post injector

Fan former injector

Slots and sbeets injector

Pintle Injector

4.2 Impinging Injector

These injectors are normally used for oxygen-hydrocarbons and storable propellants. In the unlike doublet pattern fuel and oxidizer are injected through small holes in such a manner that the stream of fuel and oxidizer impinge on each other. Impingement will thin the liquid and atomization of the liquid in to the droplets will occur. Impinging may be Like on like impinging Unlike impinging Triplet impinging

Fig. 4.1 Impinging injector Fig. 4.2