Research paperDouble exothermic reaction of viscous dissipative Oldroyd 8-constant fluid and thermal ignition in a channel
Graphical abstract
Introduction
Non-Newtonian flow phenomena are encountered in thermoplastics and chemical processing, its also arises in mining industry in which muds and slurries are regularly used. The fluids with shear rate depending on the viscosity also find its application in biomedical and lubricant [1], [2]. The viscoelastic behaviour of the liquid is generally nonlinear, burdensome to simulate and predict for industrial operations. Though, not all non-Newtonian fluids depend on elastic properties, for example, a situation that arises in an internal passage flow where pressure is needed to propel the flow is not elastic in nature [3], [4]. Among the non-Newtonian fluids are the rate-type Oldroyd formulation initiated by Oldroyd [5]. The fluid measures retardation and relaxation times, and it is used to predict fluid shear and stress properties. A generalized form of Oldroyd fluids is the Oldroyd 8-constant fluid which can be used to predict the normal thickness or thinning of shear and stress fluid properties, and other fluid characteristics as mentioned by Baris [6]. In the absence of heat transfer, the authors [7], [8], [9] reported on the analytical solution of Oldroyd 8-constant fluid with detail report on the flow physical characteristics. Meanwhile, the flow of Oldroyd 8-constant fluid in the presence of chemical kinetics and activation energy that leads to exothermic heat reaction is very useful in biotechnology, pharmaceutical, heat exchangers, electromechanical system and thermal science industry.
A release of large amounts of heat from the exothermic reaction to the surroundings is very essential in industry and in nature, which depends on the combustion process. In a wide-ranging, combustion applications are imperative to the basic chemical reactive flow system and in pollution control, safety, fire prevention, rocket and jet propulsion, power production and much more, Kareem et al. [10]. Because of the importance of combustion, Hassan et al. [11] studied hydromagnetic heat radiation fluid flow with internal combustion past a porous channel. The solutions to the problem were obtained using Adomian decomposition techniques. In a single exothermic reaction, Chinyoka and Makinde [12] investigated reactive variable viscosity of the dynamical flow system in a permeable pipe. The Arrhenius generalized kinetics rate was adopted and it was reported that the fluid temperature decreases exponentially with rises in the fluid viscosity. Okoya [13] examined third grade reactive combustion in an annular axial flow with thermal influence and nonlinear viscosity. Computational analysis was done with the observation that inner maximum temperature is enhanced by increasing Frank-Kamenetskii and activation energy terms. Several idealized problems have been investigated for exothermic one-step combustible reaction model [14], [15], [16]. However, the single exothermic reaction assumption is not enough to explain ignition and flame propagation in a system, Salawu et al. [17]. For example, the automobile exhaust catalytic converter serves as a good platform for double exothermic reaction in which complete combustion of hydrocarbons occurs [18], [19]. This supports total reduction of the toxic emission from the engines to the surroundings.
No matter how little the starting temperature of a reactive exothermic combustion process, the system will reach a critical state. Evaluating the critical region, that is, the region separating the ignition and non-ignition paths of exothermic chemical reactions are the main challenge in combustion theory, Frank-Kamenetski [20]. Flame propagation is well linked to the succeeding explosion of reactive mixtures of combustible materials in a reactive process, Barenblatt et al. [21]. Therefore, it is important to determine the unsafe and safe conditions of reactive fluid for its effective usage in thermal science and other technological processes. As a result, Kobo and Makinde [22] studied Arrhenius kinetics and thermodynamic law of reactive heat relying viscosity in a Couette flow. It was reported that heat source terms should be controlled to prevent system ignition. Ajadi [23] Investigated the thermal explosion of critical parameters in a slab using an approximation techniques. The effect of various pre-exponential factors was reported in the study. Salawu et al. [24] considered the unsteady thermal stability of Powell-Eyring hydromagnetic reactive liquid in a channel. The authors gave insight into the effect of Frank-Kamenetski terms in a reactive combustible fluid. Okoya [25] analytically studied thermal explosion branched chain and ignition time with heat loss in a slab. However, of many studies carried out on Oldroyd 8-constant liquid, little or no study has been done on the exothermic reaction of the fluid. Considering the applicable areas of the fluid, it is worth study the combustible reaction of the liquid.
The present study was motivated by the work of Khan et al. [9] and that of Makinde et al. [18] which was extended by Salawu et al. [17]. This study considered theoretical analysis of double exothermic reaction of Oldroyd 8-constant fluid in order to reduce air pollution resulting from incomplete combustion in the engines. The working fluid is considered due to its applications in enhancing lubricant viscosity and other industrial and technological usefulness. To our best knowledge, no investigation has been carried out on two-step combustion processes in examining the safe and unsafe state of Oldroyd 8-constant liquid. The analysis is done using weighted residual integration collocation techniques and compared with numerical results. The obtained results are presented in tables and graphs for different emerging terms and chemical kinetics.
Two step combustion reaction mechanism within k-fluid can be expressed as Makinde et al. [18]
Section snippets
Mathematical exothermic reaction fluid flow model
The flow of exothermic double combustible reaction of Oldroyd 8-constant fluid material with temperature distribution in a horizontal infinite bounded channel is investigated. With molecular diffusion and pre-exponential kinetics, the viscous dissipative flow is propelled by the upper plate velocity slip U and pressure gradient G. The lower plate is fixed with non-isothermal wall temperature, and the flow direction is parallel to the applied pressure with negligible z-axis effect. The flow is
Method of solution
The flow momentum and temperature field solutions as well as the ignition branch bifurcation and explosion results are provided using collocation integration along with weighted residual method. The method main objective according to [29], [30], [31] is to find a polynomial approximate solution to the derivative of the formwhere is the derivative operator, g is a defined function with a known position, denotes the number of approximate boundary conditions
Discussion of results
The thermal ignition slice, energy and velocity fields results are obtained using weighted residual collocation integration techniques. Based on related studies, the adopted default values used are taking after [15], [17], [18]. The obtained results are presented in tables and figures for different values of parameters. Table 1 shows the comparison of computing results from weighted residual and numerical methods. As seen in the table, the
Conclusion
Two step viscous dissipation of combustible exothermic reaction for Oldroyd 8-constant fluid with thermal ignition and temperature distribution in a bounded medium is examined. A semi analytical weighted residual method coupled with collocation integration scheme is used to completely solve the formulated flow model. As obtained, the material viscosity is strengthened by increasing material dilatant term but discouraged by a rise in the material pseudoplastic term. Hence, the fluid viscosity
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (31)
- et al.
Entropy generation of a radiative hydromagnetic Powell-Eyring chemical reaction nanofluid with variable conductivity and electric field loading
Results Eng.
(2020) - et al.
Heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to a sudden moved plate
Commun. Nonlinear Sci. Numer. Simulat.
(2011) - et al.
Computational dynamics of unsteady flow of a variable viscosity reactive fluid in a porous pipe
Mech. Res. Commun.
(2010) - et al.
Radiative thermal criticality and entropy generation of hydromagnetic reactive Powell-Eyring fluid in saturated porous media with variable conductivity
Energy Reports
(2019) - et al.
Branch-chain criticality and thermal explosion of Oldroyd 6-constant fluid for a generalized Couette reactive flow
S. Afr. J. Chem. Eng.
(2020) - et al.
A reactive hydromagnetic heat generating fluid flow with thermal radiation within porous channel with symmetrical convective cooling
Int. J. Therm. Sci.
(2017) - et al.
Analysis of viscous dissipative Poiseuille fluid flow of two-step exothermic chemical reaction through a porous channel with convective cooling
Ain Shams Eng. J.
(2019) Approximate analytic solution for critical parameters in thermal explosion problem
Appl. Math. Comput.
(2011)- et al.
Thermal stability and entropy generation of unsteady reactive hydromagnetic Powell-Eyring fluid with variable electrical and thermal conductivities
Alexandria Eng. J.
(2019) - et al.
Pulsatile flow of a chemically-reacting non linear fluid
Comput. Math. Appl.
(2006)
Disappearance of criticality for reactive third-grade fluid with Reynold’s model viscosity in a flat channel
Int. J. Non-Linear Mech.
Thermal explosion and irreversibility of hydromagnetic reactive couple stress fluid with viscous dissipation and Navier slips
Theoret. Appl. Mech. Lett.
Analysis of third-grade heat absorption hydromagnetic exothermic chemical reactive flow in a Darcy-forchheimer porous medium with convective cooling
WSEAS Trans. Maths.
Dynamical analysis of hydromagnetic Brownian and thermophoresis effects of squeezing Eyring-Powell nanofluid flow with variable thermal conductivity and chemical reaction
Multidiscip. Model. Mater. Struct.
Cited by (32)
Thermodynamic study of radiative chemically reactive flow of induced MHD sutterby nanofluid over a nonlinear stretching cylinder
2023, Alexandria Engineering JournalThermal elaboration of ethylene glycol-based magnetized nanostructures via a convective permeable heated vertical surface employing modified Buongiorno model
2023, Journal of Magnetism and Magnetic MaterialsTwo-step exothermic reaction–diffusion of hydromagnetic Prandtl–Eyring viscous heating fluid in a channel
2023, International Journal of ThermofluidsReaction-diffusion of double exothermic couple stress fluid and thermal criticality with Reynold's viscosity and optical radiation
2022, Chemical PhysicsCitation Excerpt :The significant of combustible species in industries and to the thermal engineering sciences, along with the usefulness of exothermic reaction–diffusion to the chemical engineering for consistent prediction of their activities, has motivated the present investigation. Various reports on the significance of two-step exothermic reaction and suggested further investigation by [27,29,30] has also inspired the research. Therefore, this study will examine thermal criticality bifurcation and fluid temperature distribution of a couple stress generalized Arrhenius reaction in an horizontal device.
Nonlinear thermal radiation and activation energy significances in slip flow of bioconvection of Oldroyd-B nanofluid with Cattaneo-Christov theories
2021, Case Studies in Thermal EngineeringCitation Excerpt :Abbas et al. [27] explored the reaction process in applications in Oldroyd-B nanofluid flow confined by a rotating disk. Salawu et al. [28] directed the double exothermic applications in dissipative flow of Oldroyd 8-constant fluid with thermal ignition. Hashmi et al. [29] explained the contribution of viscous dissipation and Joule heating in the isothermal flow of Oldroyd-B fluid by using an analytical scheme.