
Jordan HristovUniversity of Chemical Technology and Metallurgy | UCTM · Department of Chemical Engineering
Jordan Hristov
Professor (Full), PhD, DSc
About
229
Publications
69,262
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
4,161
Citations
Introduction
Jordan Hristov currently works at the Department of Chemical Engineering, University of Chemical Technology and Metallurgy. Jordan does research in Chemical Engineering. His current projects are 'The Craft of Fractional Modelling in Science and Engineering 2020 in Fractal and Fractional (MDPI)
and
Special Issue: MODELLING PROBLEMS ARISING IN SCIENCE AND ENGINEERING WITH FRACTIONAL DIFFERENTIAL OPERATORS: Beyond the power-law limit (2019) in Mathematics (MDPI)
Additional affiliations
September 2007 - January 2008
June 2002 - December 2002
February 2014 - present
Publications
Publications (229)
This note aims for a non-local extension of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetic equation, describing solid phase transformation through the implementation of the time-fractional Caputo derivative and Mittag-Leffler function instead of the exponential Avrami kinetics. These are preliminary results that include tests on some published d...
Approximate analytical solutions to doubly degenerate reaction-diffusion models pertinent to population dynamics and chemical kinetics have been developed. The double integral-balance method applied to preliminary transformed models and by a direct integration approach has provided physically reasonable results. The model equation scaling has revea...
Employing a modified version of the cardinal $Sinc_{\pi} \left(\pi x^{n} \right)$ function as the assumed profile, the work presents approximate solutions of a non-linear (degenerate) diffusion equation with a power-law-type concentration-dependent diffusivity in a semi-infinite domain by the integral-balance method (double integration technique)....
Approximate analytical solutions to a degenerate reaction-diffusion model with power-law absorption (source) and production (sink) terms have been developed. The integral-balance method applied to a preliminary transformed model and by a direct integration approach has provided physically reasonable results. The model equation scaling has revealed...
An experimental study has been carried out investigating the fluidization behavior of a bubble column with a bottom magnetic particle bed controlled by an external transverse magnetic field. The magnetization-first/gas-scanning mode was applied, at up to 45 kA m-1 field intensity, with liquid superficial velocities of up to 20 mm s-1 and with a gas...
Integrals pertinent to fractional operators with non-singular kernels (Caputo-Fabrizio and Atanagana-Baleanu) have been considered and analyzed. Special attention has been paid to the definitions of associate and constitutive integrals, clearly defining the principal differences between them. A conceptual application of the constitutive integrals t...
Following the two successful events, ICAME'21 and ICAME'18, we are pleased to announce that The 3rd International Conference on Applied Mathematics in Engineering (ICAME'24) will be held between June 26-28, 2024 in a hybrid format where both physical and remote participation will be allowed. The aim of this conference is to bring together leading r...
The experimental methods for the determination of sorption consider contacts of dry samples contacting with water at the interface without sample immersion (see Fig. 10.1, left panel). Records of the weight change in time are used to establish the relationship between the mass of moisture accumulated, M(t), and time [1,2]. Typically, the capillary...
Discriminated dimensional analysis combined with the scale analysis has been implemented to obtain new correlations describing the dimensionless pressure drop as Hagen number and Nusselt number for laminar and turbulent swirl flow in a circular tube with a classical twisted-tape insert. The new insight into the phenomenon revealed that the swirl pa...
This chapter does not provide a straightforward explanation of the rules of mathematical modeling but demonstrates some basic steps toward the correct implementation of fractional operators in non-local models of transport phenomena. Knowledge of physics, mechanics , and thermodynamics is essential for comprehension, along with in-depth expertise i...
This book addresses different applied problems in order to demonstrate the feasibility of fractional calculus’ use, irrespective of the type of memory kernels used, to model varieties of natural phenomena and new processes emerging in advanced technologies. In this context, the book’s focus is on modelling, adequate results, and interpretations, ra...
The chapter addresses a fractional approach to modelling non-integer kinetics of sorption/ release from polymers, swelling substances, and various materials capable to absorb liquids or gases. For the clarity of the following exposition, we consider the processes of capillary sorption in inorganic and organic solids, and anomalous transport of liqu...
Systematic studies of a double-tier (double-stage) combustion device allowing an effective combustion process due to controlled fuel excess independently in the tiers have been reported. The investigations reported stress the attention on the relationship of the NOx and CO emissions to the air excess and demonstrate that there is an optimal range o...
The double integral-balance approach and Barenblatt?s assumed profile have been used to create approximate solutions to the Zeldovich equation, both linear and degenerate. The evaluation of the controlling dimensionless groups and proper dimensional scaling have been the main focus of the solution developments and analyses.
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...
The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton's law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the stability of the solution on the half-axis have been an...
The talk addresses the approximate analytical solutions to transient heat conduction problems developed by the integral-balance method and semi-derivatives and semi-integrals upon various boundary conditions.
This talk addresses a systematic systematic application to the fading memory formalism with different Mittag-Leffler-type memory kernels towards generation of non-local operators based on various Mittag-Leffler kernels.
The chapter addresses constitutive fractional modeling based on
basic thermodynamic principles with emphasis on applications of fractional
operators with singular and non-singular memory kernels. The Boltzmann superposition
and the fading memory principles form the fundament of the developed
models and refer to the formulation of diffusion and line...
Fractional calculus has played an important role in the fields of mathematics, physics, electronics, mechanics, and engineering in recent years [...]
Citation: Filipov, S.M.; Hristov, J.; Avdzhieva, A.; Faragó, I. A Coupled PDE-ODE Model for Nonlinear Transient Heat Transfer with Abstract: 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 t...
In this chapter, Koeller's original idea on polynomial fractional operators with singular (Riesz) kernels and solutions to a few viscoelasticity relaxation issues is highlighted. Now, we show how this concept can be directly related to how relaxation relationships are presented using fractional operators with non-singular kernels. Additionally, it...
Transient heat conduction in semi-infinite medium with a power-law
temperature-dependent thermophysical properties has been solved by Double
integral-balance method. Correct formulation of the energy equation with
temperature-dependent heat capacity is discussed and analyzed.
Non-local kinetic problems spanning a wide area of problems where fractional calculus is applicable have been analyzed. Classical fractional kinetics based on the Continuum Time Random Walk diffusion model with the absence of stationary states, real-world problems from pharmacokinetics, and modern material processing have been reviewed. Fractional...
Transient heat conduction problems are systematically applied to the fading memory
formalism with different Mittag-Leffler-type memory kernels. With such an approach, using various
memories naturally results in definitions of various fractional operators. Six examples are given
and interpreted from a common perspective, covering the most well-liked...
Analytical derivations of the Richardson-Zaki power-law in the case of aereatable fine particle beds where the interparticle forces allow the creation of expanded beds, known also as meta-states, with fixed structures, but not yet fluidized, have been developed. The analysis is based on the concept that the fluid flow through such beds is governed...
The models of fourth-order fractional diffusion analyzed in this chapter allow us to see the
multifaceted nature of the problem and what follows when different approaches and memory
kernels are used. The principle question of what is correct and what is not depends on the
physical process mechanism underlying the model build-up. However, it is very...
Analysis and approximate integral-balance solutions of a non-linear diffusion model of wood impregnation by methacrylate have been developed in two cases: (i) Dirichlet boundary condition assuming instantaneous saturation of the wood surface contacting the liquid bath and (ii) Relaxing Dirichlet boundary conditions accounting for the fact that inst...
This chapter presents an attempt to demonstrate that the Duhamel theorem applicable for time-dependent boundary conditions (or time-dependent source terms) of heat conduction in a finite domain and the use of the Fourier method of separation of variable (superposition version) naturally lead to appearance of the Caputo-Fabrizio operators in the sol...
The talk addresses exponential series (Prony’s series) applied in the time and frequency domains with respect to the complex relaxation process. The main goal of this task is the creation of links to time-dependent fractional operators with non-singular (exponential involved in time-fractional equations. The principle problems of the decomposition...
A new approach in the formulation of assumed profiles for integral-balance solutions has been formulated. The main idea is based on the linear transmutation of basic parabolic profile with stipulated exponents commonly used in integral-balance solutions. Solution with quadratic and cubic transmuted profiles have been developed by applying single an...
The chapter addresses Prony's series approximation of monotonically responses in material viscoelastic rheology and possibilities to implement on this basis modern fractional operators with non-singular kernels, precisely the Caputo-Fabrizio operator. The origins of the Prony's series in time and frequency domains are outlined together with relevan...
A new concept in the transmutation of distribution applying variable transmuting function has been conceived. Test examples with power function by quadratic and cubic transmutations have been demonstrated by the applications of the error-function and standard logistic function variable transmuting functions. The efficiency and properties of the new...
Constitutive non-singular functional relationship of time-dependent diffusivities pertinent to chlorides diffusion in concrete, in particular, have been conceived. Approximated integral-balance solutions (Dirichlet problems) with singular and non-singular diffusivities have been developed. The approximate solutions developed allow minimization of t...
Metal plate heating by new microflare burner has been studied experimentally and by CFD simulations, additionally, concentrations of NOx were measured to compare conventional and microflare burners. In addition, the article provides a numerical simulation of the combustion of a microflame burner. It has been demonstrated that microflare burners are...
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-? turbulence m...
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 =...
A constitutive heat flux equation with a Mittag-Leffler function as a memory kernel is proposed for transient heat conduction. With this new constitutive equation, the energy balance naturally leads to transient heat conduction equation with a damping term represented by the Atangana-Baleanu derivative of Caputo sense (ABC).
A comprehensive understanding of fractional systems plays a pivotal role in practical applications [...]
Original scientific paper https://doi.org/10.2298/TSCI Transient heat conduction in semi-infinite medium with a time dependent heat flux as boundary condition has been solved by a semi-derivative integral-balance method. Two versions boundary fluxes have been considered: power-law and exponential.
A non-Arrhenius model based on the Mittag-Leffler function has been conceived as a basic concept. This approach allows modelling both sub-Arrhenius and super-Arrhenius behaviours and giving rise to modified temperature integrals. Introduction The temperature integral is a main tool for data treatment in thermal analysis of reaction kinetics involvi...
The names of five researchers for the second consecutive year are included in the list of top 2% of the best scientists in the world in the ranking of Stanford University (2021). The ranking covers more than 9 million scientists from around the world who have published in reputable international journals stored in the SCOPUS database. The Stanford...
This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presen...
The paper addresses diffusion approximations of magnetic field penetration of ferromagnetic materials with emphasis on fractional calculus applications and relevant approximate solutions. Examples with applications of time-fractional semi-derivatives and singular kernel models (Caputo time fractional operator) in cases of field independent and fiel...
Transient heat conduction in semi-infinite medium with a power-law time-dependent boundary conditions has been solved by an integral-balance integral method applying to a semi-derivative approach. Two versions of the integral-balance method have been applied: Goodman?s method with a generalized parabolic profile and Zien?s method with exponential (...
The lecture stresses the attention on an old idea developed by Koeller regarding polynomial fractional operators with singular (Riesz) kernels and solutions of some relaxation problems in the viscoelasticity.
Now, we demonstrate that this idea has a direct relation to presentation of relaxation relationships through fractional operators with non-s...
Nonlocal effects in materials and memory formalism in modelling physical properties and heat-mass transfer
The lecture presents addresses non-local effect in modelling material properties time and space causality in material , their physical basis and the memory formalism applied in mathematical modelling. Precisely, problems concerning the princi...
The present paper is a response to “Comments on “New insight into the definitions of the Bejan number”” [1] and aims at to increase the acquaintance of the readers of the International Communications of Heat and Mass Transfer, with the unique Bejan number and its scope of implementation. It has been stressed again that the unique Bejan number is de...
This paper is an extension of our recently published paper (Zimparov et al., 2020 [1]), proving that the unique form of the Bejan number (Be) is derived from the classic fluid mechanics and that the other forms, derived from the first law of thermodynamics (related to the convection heat or mass transfer), are combination of unique Bejan number wit...
The talk addresses the Prony decomposition methods applied in the time domain with respect to complex relaxation processes. The main goal of this task is the creation of links to time-dependent fractional operators with non-singular (exponential) involved in time-fractional equations. The principle problems of decomposition process and relevant cal...
In the past few years, fractional differential equations have emerged as a strong and well-organized mathematical tool in the study of many occurrences in science and engineering. Research in fractional differential equations is multidisciplinary and is used in diverse fields such as control systems, elasticity, electric drives, circuits systems, c...
Non-linear heat conduction with a power-law thermal diffusivity and ramped
surface temperature has been solved by the double-integration technique of
the integral-balance integral method. The case of a semi-infinite medium
and infinite ramp of surface temperature has been considered as example
demonstrating the versatility of the solution approach....
Diffusion is a principle transport mechanism emerging widely at different scale, from nano to micro and macro levels. This is a contributed book of seventh chapters encompassing local and no-local diffusion phenomena modelled with integer-order (local) and non-local operators. This book collates research results developed by scientists from differe...
The chapter address analysis and approximate solutions of a diffusion equation with concentration dependent diffusivity of exponential type frequently encountered in polymers and soils. This is a well-known problem solved by various approximate methods. The present chapter applies the integral-balance approach in two versions: Heat-balance integral...
Scope: This special issue addresses a wide range of fractional operators, and their implementations in mathematical modeling of problems arising in engineering, finance and social sciences. In this special issue, we invite and welcome reviews, expository and original research articles dealing with the recent advances on the topics in fractional cal...
The lecture stress the attention on the correct application of fractional operators with non-singular kernels (Caputo-Fabrizio Atangana-Baleanu) with exponential or Mittag-Leffler kernels in applied rheology of materials starting from constitutive equations. We especially address the fact that these memory kernels naturally appear from approximatio...
This paper presents new insight concerning the formulation and definition of one of the two Bejan numbers (Be) derived from the first and second law analysis, namely this one derived from the first law of thermodynamics. The systematic analysis performed reveals the role and physical meaning of the Bejan number (Be) as criterion of similarity or di...
Non-linear heat conduction with a power-law thermal diffusivity and ramped surface temperature has been solved by the double-integration technique of the integral-balance integral method. The case of a semi-infinite medium and infinite ramp of surface temperature has been considered as example demonstrating the versatility of the solution approach....
The heat transfer in living tissues is an evergreen problem in mathematical modelling 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 o...
Abstract. The article investigates implementation of fractional operators with non-singular memories (Caputo-Fabrizio) and Atangana-Baleanu (ABC) derivatives in response to functions and constitutive equations of linear viscoelastic models. The analysis focuses on the adequate selection of fractional operators with the strong requirement that stres...
This work addresses the stress-strain relaxation functions of solid polymers in the framework of the linear viscoelasticity with aim to establish the adequate fractional operators emerging from the hereditary integrals. The analysis encompasses power-law and non power-law materials thus allowing to see the origins of application of the tools of the...
Phone (631) 231-7269 Fax (631) 231-8175 Email: nova.main@novapublishers.com www.novapublishers.com science publishers nova H C: M, AA R H ISBN: 978-1-53614-673-8 B ISBN: 978-1-53614-674-5 R P: $160 S P: $128 B D: Heat conduction plays an important role in energy transfer at the macro, micro and nano scales. is book collates research results develop...
The constructions of physically adequate forms of the diffusion equation with implementation of the Atangana–Baleanu derivative with Mittag-Leffler exponential kernel have been discussed. The specific form of the corresponding Atangana–Baleanu integral relates it directly to the fading memory concept, following the Boltzmann linear superposition pr...
The constructions of physically adequate forms of the diffusion equation with implementation of the Atangana-Baleanu derivative with Mittag-Leffler exponential kernel have been discussed. The specific form of the corresponding Atangana-Baleanu integral relates it directly to the fading memory concept, following the Boltzmann linear superposition pr...
A new approximate solution relevant to case of rectangular (Langmuirian) adsorption isotherms has been developed on the basis of the integral-balance method with double integration technique. The solution is based on the model developed by Ruthven for slab and spherical adsorption pellets where the adsorption is controlled by the diffusion in macro...
A constitutive approach to modelling of heat shock waves described by the diffusion approximation in radiation heat transfer in terms of time fractional derivatives has been developed. Approximate closed-form analytical solutions by a double integration method concerning a step change of the surface temperature and two classical problems with time-...
Experiments on fuel effects flame stabilization processes, NOx generation and temperature 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 t...
A multiple integration technique of the integral-balance method allowing solving high-order subdiffusion diffusion equations is presented in this article. The new method termed multiple-integral balance method (MIM) is based on multiple integration procedures with respect to the space coordinate and is generalization of the widely applied Heat-bala...
The study addresses the physical background and modeling of linear viscoelastic response functions and their reasonable relationships to the Caputo-Fabrizio fractional operator via the Prony (Dirichlet series) series decomposition. The problem of interconversion with power-law and exponential (single and multi-term functions) has been discussed. Sp...
This chapter summarizes the recent results on approximate analytical integral-balance solutions of initial-boundary value problems of spatial-fractional partial differential diffusion equation with Riemann–Liouville fractional derivative in space. The approximate method is based on two principal steps: the integral-balance method and a series expan...
The integral-balance method to the nonlinear Mullins model of thermal grooving has been applied. The successful integral-balance solution utilizing the double-integration techniques has been able after application of the nonlinear Broadbridge transform. The Broadbridge transform converts the Mullins equation into a Dirichlet problem of a nonlinear...
NONLINEAR AND ANOMALOUS APPLIED DIFFUSION MODELS: Approximate solutions, analysis, synthesis, and examples NONLINEAR AND ANOMALOUS APPLIED DIFFUSION MODELS: Approximate solutions, analysis, synthesis, and examples
This edition is a reprint of the Special Issue published online in the open access journal Fractal
Fract (ISSN 2504-3110) from 2017–2018 (available at: http://www.mdpi.com/journal/fractalfract/
special issues/Fractional Modelling).
the book page is http://www.mdpi.com/books/pdfview/book/649
The integral-balance method to the non-linear Mullins model of ther-mal grooving has been applied. The successful integral-balance solution utilizingthe double-integration techniques has been able after application of the nonlinearBroadbridge transform. The Broadbridge transform converts the Mullins equationinto a Dirichlet problem of a nonlinear d...
The chapter is an attempt to collate the basics of fractional electric circuits involving fractional time derivatives in the sense of Riemann–Liouville, Caputo and Caputo–Fabrizio. The examples analysed use mainly Caputo time-fractional derivative but comparative analyses with derivative based on different relation kernels are provided, too. Abstra...
Approximate explicit analytical solutions of the heat radiation diffusion equation by applying the double integration technique of the integral-balance method have been developed. The method allows approximate closed form solutions to be developed. A problem with a step change of the surface temperature and two problems with time-dependent boundary...
Transient flow of second grade fluid, modelled by mixed time-space derivative, due to sudden change of the boundary condition (Stokes first problem) has been solved by an improved integral-balance method utilizing double integration technique. Two versions of mixed time-space derivative, integer-order and fractional in time (Riemann-Liouville) have...
Starting from the Cattaneo constitutive relation with exponential kernel applied to mass diffusion the derivation of a new
form the diffusion equation with a relaxation term expressed through the Caputo-Fabrizio time fractional derivative has been
developed. The developed equation reduces to the fractional Dodson equation for large relaxation times...
Casson fluids are non-Newtonian fluid exhibiting yield stresses. Concentrated cement suspensions and human blood can be treated as Casson fluids due to chain formation by the particles suspended in the continuous phase. The Stokes first problem has been investigated in case of integer-order and different time-fractional derivatives. The approximate...
The Dodson mass diffusion equation with exponentially diffusivity is analyzed through approximate integral solutions.
Integral-balance solutions were developed to integer-order versions as well as to formally fractionalized models. The formal fractionalization considers replacement of the time derivative with a fractional version with either singul...
A multiple integration technique of the integral-balance method allowing solving high-order diffusion equations is conceived in this note. The new method termed multiple-integral balance method (MIM) is based on multiple integration procedures with respect to the space coordinate and is generalization of the widely applied Heat-balance integral met...
Starting from the Cattaneo constitutive relation with a Jeffrey's kernel the derivation of a transient heat diffusion equation with relaxation term expressed through the Caputo-Fabrizio time fractional derivative has been developed. This approach allows seeing the physical background of the newly defined Caputo-Fabrizio time fractional derivative a...
The paper presents the procedure for solving the
inverse problem for the binary alloy solidification in a twodimensional
space. This is a continuation of some previous
works of the authors investigating a similar problem but in
the one-dimensional domain. Goal of the problem consists
in identification of the heat transfer coefficient on boundary
of...
This paper focuses on an approximate analytical solution of an initial-boundary value
problem of spatial-fractional partial differential diffusion equation with RiemannLiouville fractional
derivative in space. The spatial correlation of the superdiffusion coefficient as a power-law
has been discussed in cases of fast and slow spatial superdiffusion...
This paper presents approximate analytical solutions of an initial-boundary
value problem of fractional partial differential diffusion equation with
spatial Riemann-Liouville fractional derivative. The proposed approximate
solutions are based on the concept of a finite penetration depth with the
integral-balance method and series expansions of the...
Closed form approximate solutions to nonlinear transient heat conduction with linearly temperature-dependent thermal diffusivity have been developed by the integral-balance integral method under transient conditions. The solutions uses improved direct approaches of the integral method and avoid the commonly used linearization by the Kirchhoff trans...
The paper addresses approximate integral-balance approach to a time-fractional diffusion equation of order with a time-dependent diffusion coefficient of power-law type where .The form of the solution spreading in a semi-infinite medium through an analysis of the second moment of the approximate solution reveals that depending on the sum the soluti...
An approximate analytical solution of transient diffusion equation with space-fractional Riemann–Liouville fractional derivative has been developed. The integral-balance method and an assumed parabolic profile with undefined exponent have been used. The spatial correlation the superdiffusion coefficient in potential power-law form has been discusse...
This chapter presents an attempt to collate existing data about fractional derivatives with
non–singular kernels conceived by Caputo and Fabrizio in 2015. The idea attracted immedi-
ately the interest of the researcher and the text encompasses the consequent developments of
the idea with new derivatives of Riemann–Liouville type and the generalizat...