# The Inverse Heat Transfer Problem

1662 Words 7 Pages
By utilizing heat transfer from the hot combustion gases we can determine temperature distribution in the nozzle. If the temperature distribution and heat flux which are time dependent are given on the surface of wall we can find internal temperature distribution. This problem can be classified as direct heat problem. However many heat transfer problems which occur in practical take transient measurements at more than one location to find heat flux and temperature distribution on the wall. This is the inverse heat transfer problem. Inverse heat conduction problem becomes non-linear in nature if thermal properties are the function of temperature. In the conventional problem by direct heat transfer we are given the data on the surface from which …show more content…
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^(). The mathematical formulation of this concept
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
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

• ## Double Diffusive Vargination Flows

Jin et al.  examined the double diffusive convection flow in a cavity with horizontal temperature and concentration gradients . They noticed the effect of operation in different buoyancy ratio regimes on the formation of fluid cells , heat and mass distribution within the cavity. Chen et al.  investigated the vortex formations in a 3 dimensional cavity model whose side walls are differentially heated and salted.…

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• ## Heat Release Rate Model

The gross heat release rate is synthesized with an equation (3) having two separate Wiebe efficiency factors ap and ad in the two Wiebe functions often referred to as double Wiebe function [25, 33]. The direct experimental measurement of heat release rate is difficult. Therefore, a net apparent heat release rate calculated from the experimentally measured pressure-time profile and computationally calculated piston displacement profile along with heat loss to the cylinder wall using equation (1) is applied for validation. The diesel and DME oxidation reaction equations assuming complete…

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• ## The Effect Of The Fluidized Bed Model: Model Equations

At : B.C.2: At the solid-air interface, the heat transferred from air to solid by convection is consumed in changing the solid temperature and evaporating the moisture at the solid surface. At : Equation (2) with its boundary conditions can be solved using finite difference method. Another method of solution is using the collocation method. Simply; this method assumes that the temperature profile within the solid particle can be expressed as a binomial of the second degree, function in two collocation points; the surface collocation point at and an interior collocation point at where their temperatures are nominated (Ti) and (T1) respectively. The collocation method is explained in details in appendix A.…

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• ## Thermal Mass Flow Meter Essay

Thermal dispersion mass flow meters, often called thermal mass flow meters, rely on the transmission of heat from a body to a gas flow. Inside the flow meter sensor head, a heated resistance thermometer (RTD) is electronically compared with an unheated RTD sensor. As a gas passes the heated RTD, heat is transferred from this sensor to the gas, and hence the RTD is cooled, thereby reducing the temperature difference between the two sensors. Heat transfer from the RTD to the process gas is based on the composition of the gas, therefore the temperature difference between the two RTDs is a function of the mass flow rate of the gas. The electronics of the meter can be an integral part of, the meter or mounted remotely (for instance for easy access…

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• ## Principle Components Of Rankine Cycle

Rankine cycle Figure 2: Rankine cycle As mentioned earlier, the Rankine cycle also includes the possibility of superheating the vapor, as cycle 1–2–3–4–1. If changes of kinetic and potential energy are neglected, heat transfer and work may be represented by various areas on the T–s diagram. The heat transferred to the working fluid is represented by area a–2–2–3–b–a and the heat transferred from the working fluid by area a–1–4–b–a. From the first law we conclude that the area representing the work is the difference between these two areas—area 1–2–2–3–4–1. The thermal efficiency is defined by the relation For analyzing the Rankine cycle, it is helpful to think of efficiency as depending on the average temperature at which heat is supplied and the average temperature at which heat is rejected.…

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• ## Gas Turbine Theory

Various components of the gas turbine were specifically designed to perform individual functions separately. These functions are known as Intake, Compression, Combustion, Expansion, and Exhaust. The Brayton cycle can also be better explained as air entering the inlet at atmospheric pressure and constant volume. As the air passes through the compressor, it increases in pressure and decreases in volume. Combustion occurs at constant pressure while the increased temperature causes a sharp increase in volume.…

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• ## Surface Tension Effect Essay

This experimental study deduced that the temperature gradient destabilizes the free surface. This means that when the temperature gradients occur the substance tends to evaporate easily. This provokes a higher instability at the interface (which means a decrease in the surface tension). Also, depending on the alcohol studying, in this article, turbulence begins at the interface at different temperature gradients. The instability starts near the interface and causes a sinuous movement to the interface.…

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• ## Heat Exchanger Analysis

The heat exchanger design is an optimization engineering problem, to approach the best solution for sizing and selection of a heat exchanger and also to analyze its thermal performance. A properly sized heat exchanger should incorporate excess capacity to account for fouling that will occur during operation but too much oversizing results in higher manufacturing and installation costs. The most appropriate metric to describe the performance of a heat exchanger is its thermal capacity, which is its ability to transfer heat between the hot and cold fluids at different temperatures. Thermal capacity depends on the design of the heat exchanger unit and the fluid properties that flow in the device. If the heat transfer surface is sufficient, the…

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• ## Difference Between Heat And Heat Flow

For value of for laminar flow and turbulent flow are usually equal to and , respectively (Cengel, Y.A. 2007). 3.2 Basic Heat Transfer Heat is normally absorbed or rejected by a working substance at a constant pressure. The heat transferred without a phase change results in a change of temperature is called sensible heat and can be measured by the…

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• ## Numerical And Computational Fluid Dynamics Analysis

The major heat transfer takes by two modes i.e. by conduction followed by convection. Heat transfer through the solid to the surface of the solid takes place through conduction where as from the surface to the surroundings takes place by convection. Further heat transfer may be by natural convectionor by forced convection. The rate of heat transfer from a surface at a temperature ‘Ts’ to the surrounding medium at ‘To’ is given by the Newton’s law of cooling…

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