1.1. Work Done in the Area of PIB
The concept of borrowing energy from a premixed flame to preheat the incoming reactants within the PM was first introduced by Weinberg . Following Weinberg’s idea, over the last four decades, a good amount of numerical [2-16], analytical  as well as experimental studies [3,8,19-24] pertaining to both gaseous and liquid fuels combustion in PM, and its various applications have been reported by many, and developments until 2010 have been summarized in review papers [25-30]. Combustion in the PM is characterized by lower NOx and CO emissions [31-33], extended limits for a stable flame , high flame speed [2, 3], and a high power density . Potential applications of devices employing porous media combustion (PMC) are, but not limited to IC engines [36-38], heat exchangers [39, 40], gas turbines and propulsion [20, 41], burners of cooking stoves , hydrogen and syngas production [22,24].
With advances in computing power and computational methods, numerical modeling has become a precursor to the design and development of any device. It helps in identifying the geometric and operating parameters to get the desired output. In the area of PMC, many researchers have done the analysis using different methods, and have outlined the influence of different parameters on gas and solid temperatures, heat flux, and CO emission. In the numerical analysis of the PMC, the work of Tong and Sathe  reported way back in 1991 bears significance. In a 1-D planar PM, to account for the non-local thermal equilibrium between the gas and the solid, they considered coupled energy equations for the gas and the solid phases. Heat generation due to combustion was assumed in the form of a centrally located uniform volumetric heat generation source, and volumetric radiation was accounted in the solid-phase energy equation. For a given rate
Introduction 3 of heat generation, large optical thickness and high heat transfer coefficient between the solid and the gas phases were found desirable for maximizing the radiant output.
Application of PM to study the heat transfer characteristics was extended by Talukdar et al. . With combustion modeled as a localized volumetric heat generation zone, they incorporated non-local thermal equilibrium between the gas and solid phases of the PM by using separate energy equations for them. Sathe et al.  modeled the methane-air oxidation using a one-step irreversible reaction and compared it to theoretical predictions.
It was found that the stable combustion could be maintained in two spatial domains, one in the upstream half of the porous segment and another at the downstream edge of the segment. The flame speed and radiative output were highest when the flame was located at the center of the segment.
In the analysis of combustion, estimation of emission products is an important aspect, and this cannot be accurately predicted with one-step irreversible reaction as reported in [2, 3, 16]. To address this issue, Hsu and Matthews  have justified the usage of multi-step kinetics model with detailed reaction mechanism. Diamantis et al.  and Mishra et al.
 have investigated methane-air combustion within PIB with detailed chemical kinetics. 164 chemical reactions with 20 species were considered. Separate energy equations for gas and solid phases were solved and the effects of the power density, equivalence ratio, extinction coefficient and volumetric heat transfer coefficient on temperature and concentration profiles were studied.
Stable burner operating range of PIBs has been studied by many researchers. Hanamura and Echigo  considered a 1-D model to analyze the flame stabilization mechanism in the PIB. Three critical limiting criteria for flame stabilization, i.e., blow off under the condition of higher mixture velocity than the burning velocity of the flame in free space, flame extinction under extremely low mixture velocity, and flashback into the PM were identified. The flame was stabilized only in the upstream half of the PM and was not sustained in the downstream half. Similar findings were reported by other researchers [2, 6] who had determined the stable operating limits by fixing the flame location inside the PIB. Bidi et al.  used entropy generation minimization method to study flame stabilization. It was found that the flame occurring upstream half of the PM was more
stable, more efficient, and produced less emission than those at the downstream half of the porous layer.
In PMC, volumetric thermal radiation plays an important role, and thus its consideration in the analysis is paramount. The volumetric radiation can be computed using any of the numerical radiative transfer methods like the discrete ordinates method , collapsed dimension method , Rosseland approximation , P3 approximation , and finite volume method (FVM) . The importance of thermal radiation and of the radiative properties, viz., extinction coefficient, scattering albedo, scattering phase function in the analysis of PIB was studied numerically by Malico and Pereira . They found that the temperature profiles were very sensitive to perturbation in the radiative coefficients, particularly when the scattering albedo was increased. When radiation was neglected, the predicted temperature profile was not in agreement with the available experimental values. Hendricks and Howell  found that scattering was far more important than absorption in PIB and that the scattering and absorption coefficients were relatively constant with wavelength and the phase function was mostly isotropic.
The input firing rate and equivalence ratio greatly influence the CO and NOx emissions and in this direction, numerous studies have been made in order to assess the effect of different operating conditions on various pollutant emissions of the PIB. At a given equivalence ratio, both Mital et al.  and Khanna et al.  reported an increase in CO concentration for the higher firing rate of the PIB, while NOx was measured to decrease with increase in thermal load input. A similar trend was observed by Xiong et al.  and Scribano et al.  where ultra-low emissions (<15 ppm) were achieved for CO and NOx pollutants under their respective operating conditions.
The combustion devices based on PIB exhibit better thermal performances than the conventional burners. In the recent past, several researchers [21, 51, 52] have extended the application of PMC to domestic burners to improve thermal efficiency and CO emission characteristics. Jugjai and Rungsimuntuchart  suggested mechanisms to extract heat from the burnt gases in the conventional liquefied petroleum gas (LPG) burner to achieve high thermal efficiency. They used PM to preheat the incoming LPG- air mixture. Dongbin et al.  investigated the effect on the combustion of porous ceramic stove doped with rare earth elements. They observed that the addition of rare
Introduction 5 earth elements to porous ceramic led to saving of the fuel consumption by 4.5%, and reduction in CO emission by 40.9%.