# Heat Conduction Theory

1748 Words 7 Pages
Heat conduction mechanism represents the energy loss at the particle surface due to the collisions with the surrounding gas molecules. There is no simple theory to explain the cooling mechanism of the particles. During the laser pulse, the particle achieves the peak temperature and emit thermal signal. After the laser pulse duration, the particle starts to cool down. The cooling of the particles is characterized by a decay function. The decay of LII signal provides information about the primary particle size and size distribution \cite{Dankers:04, DankersSchraml,rousselle,Will:98}. The decay time of LII signal can be described by heat conduction models. A heat-conduction model for soot particle conduction cooling is known as McCoy and Cha …show more content…
The Knudsen number, $K_n$, correlates the ratio of the mean free path ($\lambda_{mfp}$) of the molecular gas and a characteristic particle size dimension ($L_c$), for instance the particle radius. This dimensionless number serves as an evaluation criterion and defines three distinct gas regimes: free molecular regime $Kn > 10$, continuum regime $Kn << 1$ and transition regime.
The Knudsen number is defined
The Planck's radiation law is written as a function of the temperature and wavelength

According to Kirchhoff's law, a black body in thermal equilibrium has an emissivity of $\epsilon = 1.0$ and the energy is radiated isotropically, independent of radiation direction. In other words, the absorption is equal to the emissivity \cite{Huffman}. Soot has a lower emissivity independent of the frequency and often it is referred to as a gray body. The emissivity used in this work is defined as the Rayleigh limit according to

The integration of Eq. \ref{planck_eq} does not have an analytical solution, but has only numerical solution. In this work, $\gamma$ and $\zeta$ functions were used to solve the radiation equation \cite{arfken, erwin}. Bladh solves the radiation equation by applying $\gamma$ and $\zeta$ function according to \cite{Bladh}

and from numerical evaluation $\zeta (5)= 1.0369$ and $\Gamma (5) = 24$. Reimann \cite{reimann} chose the same way to solve the radiation equation using the Rayleigh condition. This elegant solution can be seen in more detail in \cite{Liu2005301}. The Reimann simplification is presented

• ## Explain The Adiabatic Reaction Temperature Of Pyro-Oxidation Zone

The kinetics model is able to predict the rate of each of the reactions and the temperature variations along the length of the gasifier. (Wang and Kinoshita) modelled the biomass gasification considering kinetics of the surface reactions and assumed the initial concentrations of before char reduction to be equal to zero. The gasifier was divided into Flaming Pyrolysis, Char Reduction and inert char zones. In the Char reduction zone the reaction rate is much greater than in the flaming pyrolysis zone. The temperature of the reduction zone is around and hence no equilibrium is achieved in the reduction zone.…

Words: 905 - Pages: 4
• ## Theories Of Thermoelasticity

In this model, in comparison to the classical theory, the free energy and the heat flux both depend on the temperature and the strain tensor, and also on the elastic heat flow that satisfies a non-linear evolution equation. Chandrasekharaiah (1998) and Tzou, (1995) formulated a dual phase lag thermoelasticity. They replaced Fourier’s law by an approximation to a modification of Fourier’s law in which two different translation times for the heat flux and the temperature gradient are used. Each of these five models have been developed to eliminate the short comings of the classical dynamical thermo elasticity such as (1) infinite velocities of thermo elastic disturbances, (2) unsatisfactory thermo elastic response of a solid to short heat pulses,(3) poor description of thermo elastic behavior at low temperature (Francis, 1972; Ignaczak, 1981). Out of these five different models of a thermo elastic solid, in which disturbances are transmitted in a wave like manner, only H-I model is strongly non-linear and the rest of the models are…

Words: 1245 - Pages: 5
• ## Crystal Chemistry Lab

Compare and contrast the crystal structures and crystal chemistry of quartz, α-FePO4 and β-FePO4. The structural evolution of FePO4 arises due to the deviation in temperatures from 294K to 1073K via a process known as the neutron powder diffraction. This happens when the temperature of 980K is reached to result in the α to β transition. There are however certain observations of discontinuities in structural parameters during this transition. The stark contrast is that during the α phase, there are huge thermal expansions or contractions that present a non-linear angular variation.…

Words: 984 - Pages: 4
• ## The COSMO Solvation Model

The default density value is 0.0004. occurred only by single point calculations. Self-Consistent Isodensity model (SCIPCM):in which iterations are folded in SCF issues regarding scaling of charges still remain[9]. Onsager Model: Spherical cavity dipolar reaction field, no constructing of the cavity surface elements, because the Poisson equation is solved analytically. Solute shape is close to spherical and polar (>> 0).[10,11]. The molecular free energy of solvation is computed as the sum of three terms: Gsol = Ges + Gdr + Gcav Ges =…

Words: 1469 - Pages: 6
• ## 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.…

Words: 1160 - Pages: 5
• ## Ellingham Diagram Lab Report

2.2) Construction of Gibbs Free Energy Diagram of Binary Solutions A binary solution is a system that consists of two components. Consider the Gibbs free energy of one mole of atoms, some of which are atoms A and some of which are atoms B. For research purpose, a partition separates both types of atoms and the relative amounts of A and B are changed as shown in Figure 2.2. Figure 2.2.1 Therefore, it is deduced that g (pure, combined) = gA•XA + gB•XB Where gA is the gibbs free energy of A, gB is the gibbs free energy of B, XA is molar fraction of A and XB is molar fraction of B. When plotted against composition, the gibbs free energy for the combination of pure A and pure B is a straight line connecting gA and gB as shown in Figure 2.2.2 Figure 2.2.2 Now, consider removing the imaginary partition in Figure 2.2.1.…

Words: 2188 - Pages: 9
• ## Lab Report: Moolar Volume Of A Gas At STP

Formal Lab Report: Molar Volume of a Gas at STP Abstract: The purpose of this experiment is to find out how to experimentally determine what the volume of a mole of H₂(g) is at STP by using gas laws. The hypothesis for the experiment is that if H₂(g) is produced at RT and STP, Avogadro’s law can be used to experimentally determine the amount of H₂(g) because equal gases at the same pressure and temperature have the same amount of particles. In order to find the molar volume, hydrogen gas was produced in a eudiometer tube by reacting magnesium and hydrogen chloride. The results showed that the molar volume of H₂(g) was 27.5L per mole of H₂(g). It was concluded that the molar volume of a gas can be experimentally determined by using gas…

Words: 1765 - Pages: 8
• ## 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…

Words: 836 - Pages: 4
• ## Experiment 5: Anions And Redox Reactions

From a titration the concentration of a given sample, in this case Fe(II) can be found by using a standard compound of whose concentration is known, in this example: 0.02M of KMnO4. A redox titration involves an oxidation-reduction reaction, hence the name redox. Redox reactions involve the transfer of electrons, i.e. the loss and gain of electrons. KMnO4 is an oxidising agent which means it brings about oxidation and therefore it is being reduced.…

Words: 2461 - Pages: 10
• ## Oxidation And Reduction In Chemistry

Oxidation numbers are values assigned to an atom in a compound which measures the electron control or the possession it has relative to the atom in its pure element. In a redox equation, equations are assigned for separate reactions for oxidation and reduction. These equations are called half-equations. (Brown and Ford, 2008). For…

Words: 795 - Pages: 4