Research Article | Open Access
M. Shanmugapriya, R. Sundareswaran, P. Senthil Kumar, "Heat and Mass Transfer Enhancement of MHD Hybrid Nanofluid Flow in the Presence of Activation Energy", International Journal of Chemical Engineering, vol. 2021, Article ID 9473226, 12 pages, 2021. https://doi.org/10.1155/2021/9473226
Heat and Mass Transfer Enhancement of MHD Hybrid Nanofluid Flow in the Presence of Activation Energy
In this study, water is apprehended as conventional fluid with the suspension of two types of hybrid nanoparticles, namely, single-walled CNTs (SWCNTs) and multiwalled CNTs (MWCNTs). The influence of a magnetic field, thermal radiation, and activation energy with binary chemical reaction has been added to better examine the fine point of hybrid nanofluid flow. The mathematical structure regarding the physical model for hybrid nanofluid is established and then the similarity variables are induced to transmute the leading PDEs into nonlinear ODEs. These equations were solved using the shooting technique together with RKF 4-5th order for various values of the governing parameters numerically. The results of prominent parameters were manifested through graphs and tables. The results indicate that the hybrid nanofluid is fully adequate in cooling and heating compared to other hybrid nanofluids. In addition, the rise in the value of activation energy upsurges the nanoparticle transfer rate of hybrid nanofluid.
Hybrid nanofluids are a new kind of working fluid that is made by suspension of two different types of nanoparticles with sizes (under 100 nm) into the conventional fluid (water, oils, ethylene glycol, biological fluids, etc.). This new form of nanofiluid is having higher thermal conductivity and thermo-physical properties than conventional fluids. In recent years, these hybrid nanofluids were used in various heat transfer applications such as heat pipe, solar energy, refrigeration as well as heating, heat exchanger, ventilation, air conditioning system, coolant in machining and manufacturing, biomedical, space, ships, defense, etc. A comprehensive review on hybrid nanofluids in heat transfer applications is given in Sarkar et al. ; Sidik et al. ; Sundar et al. ; and Sajid and Ali . Khashi’ie et al.  presented analytical and numerical solutions of MHD flow of hybrid nanofluid towards a shrinking cylinder. The effect of velocity and thermal slips and chemical and thermal radiation on -water-based hybrid nanoliquid over a stretching sheet in both steady and unsteady was examined by Santhi et al. . Khan et al.  discussed the impact of two different nanoparticles and with two different base fluids and along a stretched surface under the impact of nonlinear thermal radiation, inclined magnetic field, and mass suction. Their results showed that the hybrid nanofluid is more effective in cooling and heating compared to hybrid nanofluid, and a simple nanofluid . Saeed et al.  established the analytical solution of Darcy-Forchheimer MHD hybrid nanofluid flow and heat transfer using HAM. They found that increasing values of Brownian motion increases the temperature profile of the hybrid nanofluid. Sheikholeslami et al.  investigated the entropy generation and free convection of MHD hybrid nanofluid flow within a porous tank. They observed that the growth of permeability reduces the exergy loss while augments with rise of .
Carbon nanotubes (CNTs) are the cylindrical structures of carbons atoms (graphene). CNTs are classified into three groups depending on the number of graphene layers: single-walled CNTs (SWCNT) consisting of one graphene layer with a diameter of 0.5–1.5 nm, double-walled carbon nanotube (DWCNT), and multiwalled CNTs (MWCNTs) dwelling of many graphene layers interlinked nanotubes, with diameters of ranges between 10 and 100 nm. Due to the unique properties such as high mechanical strength, rigidity, hardness, adhesion, high dimensional ratio, chemical stability and high thermal and electrical conductivity, they provide many applications in nanotechnology, chemical and biochemical sensors, catalytic, conductive plastics, structural composite materials, etc. Prabhavathi et al.  analyzed the slip effects of SWCNTs and MWCNTs based Maxwell nanofluid flow and identified that the temperature of both nanofluids intensifies as the values of Maxwell parameter rises. Sreedevi and Sudarsana Reddy  deliberated the impact of radiation on MWCNT-kerosene-dependent nanofluid over a wedge. Recently, several authors (Tassaddiq et al. ; Esfe et al. ; Al-Hanaya et al. ; Upreti et al. [15, 16]) studied heat and mass transfer analysis of CNT-based hybrid nanofluid over different geometries.
Activation energy is a term introduced in 1889 by Svante Arrhenius that is defined the minimum energy attained through the atoms or molecules required to start a chemical reaction. Activation energy along with binary chemical reaction existing in mass transfer has numerous applications in chemical and geothermal engineering, oil reservoirs, water and oil emulsions, food processing, etc. Initially, this concept was introduced by Bestman . Some researchers reported the impact of activation energy in binary chemically reactive flow of hybrid nanofluids under numerous features (Ijaz Khan et al. ; Ahmad and Nadeem ; Zaib et al. ; Khan et al. ).
The research regarding the boundary layer flow with heat and mass transfer, involving hybrid nanofluid, has revealed to be realistically significant in engineering processes. However, a cautious review of the current literature reveals that the flow over a moving wedge embedded in the hybrid nanofluid was not taken into account. Due to broad fascinating in energy sector, the present work investigate the impact of activation energy with binary chemical reaction on mass and heat transport characteristics of magnetohydrodynamic (MHD) flow of a hybrid nanofluid induced by moving wedge. The resultant equations were solved using shooting technique along with RKF 4-5th order. Results for velocity, temperature, concentration profiles, skin friction coefficient, heat transfer rate, and nanoparticle transfer rate are graphically displayed and debated briefly.
2. Mathematical Formulation
2.1. Physical Description
The steady two-dimensional MHD boundary layer flow of a hybrid nanofluid induced by moving wedge was investigated. It is assumed that the wedge is moving with the velocity and the free stream velocity . Here, is the Hartree pressure gradient in which is the wedge angle parameter which can be symbolized as (see Figure 1). Temperature and concentration hybrid nanofluids at the wall are and , respectively, while and are ambient temperature and concentration.
2.2. Flow Analysis
The modeled equations based on the above assumptions are stated as follows :with
In (4), exemplify the modifies Arrhenius equation in which is the rate of chemical reaction rate, is fitted rate constant, and is the modified Arrhenius function.
In order to transform the modeled equations, the following transformations are established :with the components of velocity and stream function as
2.4. Thermophysical Properties of -Based Hybrid Nanofluid
The dynamic viscosity , the effective dynamic density , the specific heat or heat capacitance, and the thermal conductivity of the hybrid nanofluid are specified aswhere .
and are used for the solid volume fraction of and respectively, and are the respective densities, specific heat, and thermal conductivity of the conventional fluid. The thermophysical properties of the present flow modeled are listed in Table 1.
2.5. Transformed Problems
Plugging the above-mentioned transformation and thermophysical properties, -based hybrid nanofluid, the momentum, and thermal and concentration boundary layers becamesubject towhere
Equations (9)–(12) include the nondimensional magnetic parameter , radiation parameter , Prandtl number , Brownian movement parameter , thermophoresis parameter , Lewis number , moving wedge parameter , temperature relative parameter , chemical reaction parameter , and activation energy parameter which are defined as follows:
2.6. Physical Quantities
The dimensionless forms of skin friction coefficient , heat transfer rate , and nanoparticle transfer rate are defined aswhere is the Reynolds number.
3. Computational Scheme
A shooting technique together with RKF 4-5th order integration scheme is adopted to establish the computational results of nonlinear differential equations (9)–(11) with the boundary restrictions represented in equation (12). Following the basic methodology of shooting technique, we reduce this dimensionless boundary value flow system into first-order system by using the pursuing procedure:with
4. Outcomes and Discussions
We graphically analyze the behavior of various sundry parameters on fluid velocity, temperature, and concentration dissemination in Figures 2–21. The ranges of constraints in this research are considered as Figures 2–7, given the impact of and on . The intensification of and reduces the thickness of the boundary layer flow, which arises in an increase of fluid velocity. We boost the quantity of both in , the heat absorbing capacity of the fluid intensifies. As a result, the temperature profile is enhanced. Additionally, the higher values of and decay the mass transfer rate. Figures 8 and 9 demonstrate the effects of (Hartree pressure gradient parameter) on . The augmented values of augmented the surface drag force and increases. A reverse configuration is grasped for growing values of .
The variation of on (magnetic parameter) is shown in Figures 10 and 11. An increment in magnetic strength strengthens the velocity and weakens the temperature. This is due to the fact that with growing values of , the Lorentz forces enhances, which raises the resistive force to the hybrid nanofluid motion. The response of to the variation of (moving wedge parameter) are illustrated in Figures 12 and 13. Rising of increases the velocity distribution and diminishes the temperature distribution. Furthermore, the thickness of the hydrodynamic boundary layer depreciation and thermal boundary layer are upgraded.
Figure 14 demonstrates the effect of on . It explains that, due to the increment of , depreciate (the mean absorption coefficient), consequently increases (heat flux radiation) and the radiative heat transfer rate into the hybrid nanofluid that caused an increase in . Figures 15 and 16 show the disparities of and on up surging values of is the proportion of the molecular diffusivity over thermal diffusivity, increase in in the hybrid nanofluid has reduce the thermal diffusivity. Therefore, the temperature of -based hybrid nanofluid worsens as intensifies, while the reverse phenomena occurs in . The variation of via (thermophoresis parameter) and (Brownian motion) is displayed in Figures 17 and 18. With increase in the value of , thickening the concentration boundary layer, increases. portrays a declining performance of . Figure 19 reveals that an elevation in (Lewis number) diminishes the mass diffusion and ; this is because that inversely related to the mass diffusion.
Figure 20 illustrates the profiles decline due to the intensification of (dimensionless reaction rate) in the entire flow region. Physically, growing values of causes an increment in the term , it helps to calamitous (chemical reaction rate) that decreases . Figure 21 shows the abating phenomena of hybrid nanoparticle concentration due to the fluctuation of . The portrayal of (activation energy) in distribution of is shown in Figure 22. It is found that attained a maximum level when is assigned the maximum value. Physically, due to involvement of afford some extra energy to system, which enhances the chemical reaction rate and hence increases with higher values of .
The current results of the present problem are compared with the available literature and divulged in Table 2. Tables 3–5 show the computational results of skin friction, heat transfer rate, and nanoparticle transfer rate against certain physical parameters. These tables shows that enhances for larger values of and , while it decays for . upsurges for increasing values of , and , while decreases for and also the larger values of and intensifies . Thus, hybrid nanofluid evinced an eminent performance in , , and compared to other nanofluid.
Effect of thermal radiation and activation energy with binary chemical reaction of hybrid nanofluid is studied. The key findings were as follows: Widening of caused skin friction increases and heat transfer and mass transfer rates to be decreased Heat transfer is intensified subject to large radiation Upsurge of leads to enhance and decline upgrades via and it degrades enhances by larger activation energy and it decays through An increase in and diminish and and enhances From the above analysis, we can conclude that the impact of heat transfer in -based hybrid nanofluid is more powerful compared to the common fluid
|:||Velocity components of x and y direction|
|:||Temperature and concentration of the hybrid nanofluids at the wall|
|:||Temperature and concentration far away from the surface|
|:||Velocities near and far away from the surface|
|:||Skin friction coefficient|
|:||Heat transfer rate|
|:||Nanoparticle transfer rate|
|:||Hartree pressure gradient|
|:||Wedge angle parameter|
|:||Brownian motion parameter|
|:||Moving wedge parameter|
|:||Dimensionless reaction rate|
|:||Fitted rate constant|
|:||Chemical reaction rate|
|:||Solid volume fraction of MWCNT and SWCNT|
|:||Kinematic viscosity of the fluid|
|:||Effective dynamic density of the hybrid nanofluid|
|:||Mean absorption coefficient|
|:||Magnetic induction parameter|
|:||Specific heat of hybrid nanofluid|
|:||Dynamic viscosity of the hybrid nanofluid|
|:||Thermal conductivity of the hybrid nanofluid|
|:||Effective heat capacity of the nanoparticle|
|:||Density of the fluid|
|:||Specific heat of the fluid|
|:||Thermal conductivity of the fluid|
|:||Quantities at wall|
|:||Quantities at free stream.|
No data were associated with this submission.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
- J. Sarkar, P. Ghosh, and A. Adil, “A review on hybrid nanofluids: recent research, development and applications,” Renewable and Sustainable Energy Reviews, vol. 43, pp. 164–177, 2015.
- N. A. C. Sidik, I. M. Adamu, M. M. Jamil, G. H. R. Kefayati, R. Mamat, and G. Najafi, “Recent progress on hybrid nanofluids in heat transfer applications: a comprehensive review,” International Communications in Heat and Mass Transfer, vol. 78, pp. 68–79, 2016.
- L. S. Sundar, K. V. Sharma, M. K. Singh, and A. C. M. Sousa, “Hybrid nanofluids preparation, thermal properties, heat transfer and friction factor-a review,” Renewable and Sustainable Energy Reviews, vol. 68, pp. 185–198, 2017.
- M. U. Sajid and H. M. Ali, “Thermal conductivity of hybrid nanofluids: a critical review,” International Journal of Heat and Mass Transfer, vol. 126, pp. 211–234, 2018.
- N. S. Khashi’ie, N. M. Arifin, I. Pop, R. Nazar, and N. Wahi, “Flow and heat transfer of hybrid nanofluid over a permeable shrinking cylinder with Joule heating: a comparative analysis,” Alexandria Engineering Journal, vol. 59, pp. 1787–1798, 2020.
- M. Santhi, K. V. Suryanarayana Rao, P. Sudarsana Reddy, and P. Sreedevi, “Heat and mass transfer characteristics of radiative hybrid nanofluid flow over a stretching sheet with chemical reaction,” Heat Transfer, pp. 1–21, 2020.
- M. R. Khan, M. Li, S. Mao, R. Ali, and S. Khan, “Comparative study on heat transfer and friction drag in the flow of various hybrid nanofluids effected by aligned magnetic field and nonlinear radiation,” Scientific Reports, vol. 11, no. 1, p. 3691, 2021.
- A. Saeed, A. Tassaddiq, A. Khan et al., “Darcy-Forchheimer MHD hybrid nanofluid flow and heat transfer analysis over a porous stretching cylinder,” Coatings, vol. 10, no. 4, p. 391, 2020.
- M. Sheikholeslami, Z. Shah, A. Shafee, P. Kumam, and H. Babazadeh, “Lorentz force impact on hybrid nanofluid within a porous tank including entropy generation,” International Communications in Heat and Mass Transfer, vol. 116, Article ID 104635, 2020.
- B. Prabhavathi, P. Sudarsana Reddy, and R. Bhuvana Vijaya, “Heat and mass transfer enhancement of SWCNTs and MWCNTs based Maxwell nanofluid flow over a vertical cone with slip effects,” Powder Technology, vol. 340, pp. 253–263, 2018.
- P. Sreedevi and P. Sudarsana Reddy, “Heat and mass transfer analysis of MWCNT‐kerosene nanofluid flow over a wedge with thermal radiation,” Heat Transfer, vol. 50, no. 1, pp. 10–33, 2021.
- A. Tassaddiq, S. Khan, M. Bilal et al., “Heat and mass transfer together with hybrid nanofluid flow over a rotating disk,” AIP Advances, vol. 10, no. 5, Article ID 055317, 2020.
- M. H. Esfe, M. Rejvani, R. Karimpour, and A. A. Abbasian Arani, “Estimation of thermal conductivity of ethylene glycol-based nanofluid with hybrid suspensions of SWCNT-Al2O3 nanoparticles by correlation and ANN methods using experimental data,” Journal of Thermal Analysis and Calorimetry, vol. 128, no. 3, pp. 1359–1371, 2017.
- A. M. Al-Hanaya, F. Sajid, N. Abbas, and S. Nadeem, “Effect of SWCNT and MWCNT on the flow of micropolar hybrid nanofluid over a curved stretching surface with induced magnetic field,” Scientific Reports, vol. 10, no. 1, Article ID 8488, 2020.
- H. Upreti, A. K. Pandey, M. Kumar, and O. D. Makinde, “Ohmic heating and non-uniform heat source/sink roles on 3D Darcy-Forchheimer flow of CNTs nanofluids over a stretching surface,” Arabian Journal for Science and Engineering, vol. 45, no. 9, pp. 7705–7717, 2020.
- H. Upreti, A. K. Pandey, and M. Kumar, “Unsteady squeezing flow of magnetic hybrid nanofluids within parallel plates and entropy generation,” Heat Transfer, vol. 50, no. 1, pp. 105–125, 2021.
- A. R. Bestman, “Natural convection boundary layer with suction and mass transfer in a porous medium,” International Journal of Energy Research, vol. 14, no. 4, pp. 389–396, 1990.
- M. Ijaz Khan, S. A. Khan, T. Hayat, M. Imran Khan, and A. Alsaedi, “Arrhenius activation energy impact in binary chemically reactive flow of TiO2-Cu-H2O hybrid nanomaterial,” International Journal of Chemical Reactor Engineering, vol. 17, no. 3, Article ID 20180183, 2019.
- S. Ahmad and S. Nadeem, “Analysis of activation energy and its impact on hybrid nanofluid in the presence of Hall and ion slip currents,” Applied Nanoscience, vol. 10, no. 12, pp. 5315–5330, 2020.
- A. Zaib, M. M. Rashidi, A. J. Chamkha, and K. Bhattacharyya, “Numerical solution of second law analysis for MHD Casson nanofluid past a wedge with activation energy and binary chemical reaction,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 27, no. 12, pp. 2816–2834, 2017.
- N. S. Khan, P. Kumam, and P. Thounthong, “Second law analysis with effects of Arrhenius activation energy and binary chemical reaction on nanofluid flow,” Scientific Reports, vol. 10, p. 1226, 2020.
- S. Gopi Krishna and M. Shanmugapriya, “Inquiry of MHD bioconvective non-Newtonian nanofluid flow over a moving wedge using HPM,” Materials Today: Proceedings, vol. 38, no. 5, pp. 3297–3305, 2021.
- I. Ullah, I. Khan, and S. Shafie, “Heat and mass transfer in unsteady MHD slip flow of Casson fluid over a moving wedge embedded in a porous medium in the presence of chemical reaction,” Numerical Methods for Partial Differential Equations, vol. 34, no. 5, pp. 1–25, 2017.
Copyright © 2021 M. Shanmugapriya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.