DSpace Repository :: Browsing by Author "Hristov J."

Browsing by Author "Hristov J."

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A Coupled PDE-ODE Model for Nonlinear Transient Heat Transfer with Convection Heating at the Boundary: Numerical Solution by Implicit Time Discretization and Sequential Decoupling
(2023-04-01) Filipov S.M.; Hristov J.; Avdzhieva A.; Faragó I.
This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower temperature leaves the tank through another pipe. We propose a one-dimensional mathematical model that consists of a nonlinear PDE for the temperature along the solid body, coupled to a linear ODE for the temperature in the tank, the boundary and the initial conditions. All equations are converted into a dimensionless form reducing the input parameters to three dimensionless numbers and a dimensionless function. A steady-state analysis is performed. To solve the transient problem, a nontrivial numerical approach is proposed whereby the differential equations are first discretized in time. This reduces the problem to a sequence of nonlinear two-point boundary value problems (TPBVP) and a sequence of linear algebraic equations coupled to it. We show that knowing the temperature in the system at time level n − 1 allows us to decouple the TPBVP and the corresponding algebraic equation at time level n. Thus, starting from the initial conditions, the equations are decoupled and solved sequentially. The TPBVPs are solved by FDM with the Newtonian method.
A generalized kinetic model of the advection-dispersion process in a sorbing medium
(2021-01-01) Baleanu D.; Kumar D.; Hristov J.; Vieru D.; Fetecau C.; Ahmed N.; Shah N.A.
A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu time-fractional derivative is defined along with the associated integral operator. Some properties of the new operators are proved. The new operator is suitable to generate by particularization the known Atangana-Baleanu, Caputo-Fabrizio and Caputo time-fractional derivatives. A generalized mathematical model of the advection-dispersion process with kinetic adsorption is formulated by considering the constitutive equation of the diffusive flux with the new generalized time-fractional derivative. Analytical solutions of the generalized advection-dispersion equation with kinetic adsorption are determined using the Laplace transform method. The solution corresponding to the ordinary model is compared with solutions corresponding to the four models with fractional derivatives.
A Note on the integral approach to non-linear heat conduction with jeffrey's fading memory
(2013-01-01) Hristov J.
Integral approach by using approximate profile is successfully applied to heat conduction equation with fading memory expressed by a Jeffrey's kernel. The solution is straightforward and the final form of the approximate temperature profile clearly delineates the ``viscous effects`` corresponding tothe classical Fourier law and the relaxation (fading memory). The optimal exponent of the approximatesolution is discussed in case of Dirichlet boundary condition.
A NOVEL VORTEX COMBUSTION DEVICE Experiments and Numerical Simulations with Emphasis on the Combustion Process and NOx Emissions
(2022-01-01) Dostiyarov A.; Hristov J.; Umyshev D.; Yamanbekova A.; Ozhikenova Z.
Experimental and numerical studies of combustion process in a vortex flow device have been developed. The modelling part of the study has been performed by means of ANSYS Fluent package. Fuel droplet trajectories and the flow pattern on their motions have been modeled by the function “injection”. The combustion process utilized the k-ε turbulence model. A special trend on the effect of the vortex gener-ator blade orientation on the gross process has been developed. It has been estab-lished that optimal process performance (high air excess ratio and low NOx emis-sions) could be attained with an angle of the vortex generator blade orientation, especially with respect to the minimization of NOx emissions.
A unified nonlinear fractional equation of the diffusion-controlled surfactant adsorption: Reappraisal and new solution of the Ward-Tordai problem
(2016-01-01) Hristov J.
The article addresses a reappraisal of the famous Ward-Tordai equation describing the equilibrium of surfactants at air/liquid interfaces under diffusion control. The new derivation is entirely developed in the light of fractional calculus. The unified approach demonstrates that this equation can be clearly reformulated as a nonlinear ordinary time-fractional equation of order 1/2. The work formulates versions with different isotherms. A simple solution of the case with the Henry's isotherm and a discussion of a Cauchy problem involving the Freundlich isotherm are provided.
Accidental burning of a fuel layer on a waterbed: A scale analysis of the models predicting the pre-boilover time and tests to published data
(2004-03-01) Hristov J.; Planas-Cuchi E.; Arnaldos J.; Casal J.
The paper concerns the heat transfer models of liquid fuel bed burning on water sublayer. The main efforts are stressed on the qualitative assessment of models available and their adequacy as well as on the prediction of the boilover onset. The analysis employed various data obtained by different research groups. The evaluation of the suitable functional relationships predicting the pre-boilover time was done based on dimensionless groups derived from two types of models published in the literature: Surface Absorption Models and In-Depth Absorption Models. © 2003 Elsevier SAS. All rights reserved.
Advances on integrodifferential equations and transforms
(2015-01-01) Srivastava H.M.; Yang X.J.; Baleanu D.; Nieto J.J.; Hristov J.
An approximate analytical (integral-balance) solution to a non-linear heat diffusion equation
(2015-01-01) Hristov J.
The paper presents a closed form approximate solution of the non-linear diffusion equation of a power-law non-linearity of the diffusivity developed by the heat-balance integral method. The main step in the initial transformation of the governing equation avoiding the Kirchhoff transformation is demonstrated. The consequent application of the integral method is exemplified by a solution of a Dirichlet problem with an approximate parabolic profile. Cases with predetermined positive integer and optimized non-integer exponents have been analyzed.
An inverse stefan problem relevant to boilover: Heat balance integral solutions and analysis
(2007-01-01) Hristov J.
Stefan problems relevant to burning oil-water systems are formulated. Two moving boundary sub-problems are defined. burning liquid surface and formation of a distillation (``hot zone``) layer beneath it. The basic model considers a heat transfer equation with internal neat generation due to radiation flux absorbed in the fuel depth. Inverse Stefan problem corresponding to the first case solved by the heat balance integral method and dimensionless scaling of semi-analytical solutions are at tissue.
Approximate solutions to fractional subdiffusion equations
(2011-03-01) Hristov J.
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations. © 2011 EDP Sciences and Springer.
BENEFITS FROM THE USE OF WIRE-COIL INSERTS IN WATER TRANSITIONAL AND LOW TURBULENT FLOW The Influence of the Wire-Coil Pitch
(2022-01-01) Zimparov V.; Bonev P.; Angelov M.; Hristov J.
Five wire-coil inserts with fixed wire diameter and different pitches, fitted inside a round tube have been experimentally studied in a transitional and low turbulent flow. Water was used as a working fluid at a wide range of flow conditions: 103 < Re < 104 and 3.9 < Pr < 10.0. The geometrical parameters of the inserts are: e/Di = 0.070, and p/e = 6.7, 9.0, 10.0, 12.5, and 15.0. The variation of the friction factor and heat transfer coefficients have been obtained and compared with those of the smooth pipe. Performance evaluation criteria for the cases FG-1a, FG-2a, and VG-2a have been used to evaluate the maximum and real benefit that can be obtained. The greatest benefit can be achieved with the pitch of the wire-coil insert p/e = 10.0.
Bio-Heat Models Revisited: Concepts, Derivations, Nondimensalization and Fractionalization Approaches
(2019-11-21) Hristov J.
The heat transfer in living tissues is an evergreen problem in mathematical modeling with great practical importance starting from the Pennes equation postulation. This study focuses on concept in model building, the correct scaling of the bio-heat equation (one-dimensional) by appropriate choice of time and length scales, and consequently order of magnitude analysis of effects, as well as fractionalization approaches. Fractionalization by different constitutive approaches, leading to application of different fractional differential operators, modeling the finite speed of the heat wave, is one of the principle problems discussed in the study. The correct choice of the damping (relaxation) function of the heat flux is of primarily importance in the formulation of the bio-heat equation with memory. Moreover, this affects the consequent scaling, order of magnitude analysis and solutions.
Diffusion models with weakly singular kernels in the fading memories how the integral-balance method can be applied?
(2015-01-01) Hristov J.
This work presents an attempt to apply the integral-balance approach to diffusion models with fading memories expressed by weakly singular kernels. It demonstrates how three integration techniques (heat-balance integral method, double-integration method, and frozen front approach) work with a general parabolic profile with unspecified exponent and result in closed-form solutions. The main steps are exemplified by solutions where the fading memory is represented by Volterra integrals and by a time-fractional Riemann-Liouville derivative.
Effects of different fuel supply types on combustion characteristics behind group of V-gutter flame holders: Experimental and numerical study
(2020-01-01) Umyshev D.R.; Dostiyarov A.M.; Duisenbek Z.S.; Tyutebayeva G.M.; Yamanbekova A.K.; Bakhtyar B.T.; Hristov J.
Experiments on fuel effects flame stabilization processes, NOx generation and tem-perature at combustion chamber outlet when using a group of three V-gutter flame holders have been reported. Fuel supply directly to the re-circulation zone on the inside of the V-gutter (type A fuel supply), and alternatively in the second type, fuel was supplied to the V-gutter symmetry axis on the outside (type B fuel supply have been carried out.
Energies of Mechanical Fractional-Order Elements: Causal Concept and Kernel Effects
(2024-01-01) Hristov J.
The energies of the classical Maxwell mechanical model of viscoelastic behavior have been studied as a template with a variety of relaxation kernels in light of a causal formulation of the force–displacement relationship. The starting point uses the Lorenzo–Hartley model with the time-fractional Riemann–Liouville derivative. This approach has been reformulated based on critical analysis, allowing for the application of a variety of relaxation (memory) functions mainly based on the Mittag-Leffler family, in order to meet the need for broader modeling of viscoelastic behavior. The examples provided include cases of the types of forces used by Lorenzo and Hartley as well as a new family of force approximations such as a general power-law ramp, polynomials, and the Prony series.
Fractional compound Poisson processes with multiple internal states
(2018-01-01) Atangana A.; Mophou G.; Hristov J.; Hammouch Z.; Xu P.; Deng W.
For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and functional distributions of the trajectories of particles; in particular, the equations governing the functional distribution of internal states are also obtained. The dynamics of the stochastic processes are analyzed and the applications, calculating the distribution of the first passage time and the distribution of the fraction of the occupation time, of the equations are given. For the further application of the newly built models, we make very detailed discussions on the none-immediately-repeated stochastic process, e.g., the random walk of smart animals.
Heat-balance integral to fractional (half-time) heat diffusion sub-model
(2010-01-01) Hristov J.
The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic profile with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the approximating profile as function of the thermal layer depth. This allows the exponent of the parabolic profile to be defined by a straightforward manner. The elegant solution performed by the fractional heat-balance integral method has been analyzed and the main efforts have been oriented towards the evaluation of fractional (half-time) derivatives by use of approximate profile across the penetration layer.
Influence of fiberglass mesh on flammability of EPS used as insulation of buildings
(2018-01-01) Xu Q.; Jin C.; Griffin G.J.; Hristov J.; Cvetinović D.B.; Jiang Y.
Different scale tests to explore the influence of fiberglass mesh on the fire behavior of expanded polystyrene (EPS) have been conducted. Micro scale combustion calorimeter to measure the heat release rate per unit mass, heat release capacity, and the total heat release of EPS and as well as the fiberglass for milligram specimen mass has been used. Cone colorimeter bench scale burning tests with the EPS specimens and EPS-fiberglass compound specimens have been carried out. The heat release rate per unit area, ignition times, and the derived minimum igniting heat fluxes were determined. Comparative burning tests on the fire spread tendency of EPS and EPS-fiberglass compound specimens have been carried out. It was established that the fiberglass mesh stabilizes the EPS fire as a wick fire due to the adherence of the melting polystyrene adheres to the fiberglass mesh and this causes an upwards fire spread.
Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations
(2021-01-01) Baleanu D.; Kumar D.; Hristov J.; Phuong N.D.; Tuan N.A.; Kumar D.; Tuan N.H.
Integral-Balance solution to the Stokes' first problem of a viscoelastic generalized second grade fluid
(2012-01-01) Hristov J.
Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes' first problem of a viscoelastic generalized second grade fluid has been developed. The solution has been performed by a parabolic profile with an unspecified exponent allowing optimization through minimization of the L2 norm over the domain of the penetration depth. The closedform solution explicitly defines two dimensionless similarity variables ξ = y/(vt)1/2 and Do = χ2 = = (p/vtβ)1/2, responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. The solution was developed with three forms of the governing equation through its 2-D forms (the main solution and example 1) and the dimensionless version showing various sides of the flow field and how the dimensionless groups control it: mainly the effect of the Deborah number. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed have been performed.

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