Analysis of arrhenius activation energy and chemical reaction in nanofluid flow and heat transfer Over a thin moving needle

2021 ◽  
Vol 17 ◽  
Author(s):  
I Sadham Hussain ◽  
D Prakash ◽  
Bahaaeldin Abdalla ◽  
M Muthtamilselvan
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Volume Fraction ◽  
Chemical Species ◽  
Transform Method ◽  
Analytical Technique ◽  
Flow And Heat Transfer ◽  
Differential Transform ◽  
Concentration Layer

Objective: A numerical and theoretical study is developed to analyze the combined effect of activation energy and chemical reaction in the flow of nanofluids due to the thin moving needle using the mathematical nanofluid model offered by Buongiorno. A passively controlled nanoparticle volume fraction boundary is assumed rather than actively controlled. Methods: A similarity transformation is utilized to convert the governing partial differential equations to a set of ordinary differential equations which are then solved numerically by Runge-Kutta Shooting Method (RKSM). The physical characteristics of flow, heat and mass transfer are illustrated via graphs and tables for some set of values of governing parameters. Results: In addition, the basic non-linear governing equations are solved analytically using semi-analytical technique called Differential transform method (DTM) and the comparison has been made with the numerical and the published results. Conclusion: The present study reveals that the ratio between the needle velocity and the composite velocity brings out to increase the velocity distribution with λ<0. Moreover, the activation energy influences the chemical species to react from the thickness of the concentration layer η=0.6 and the fraction of nanoparticles to the fluid is significantly more away from the needle surface.

Flow and heat transfer over a permeable moving wedge in a hybrid nanofluid with activation energy and binary chemical reaction

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Activation Energy ◽  
Mass Transfer ◽  
Chemical Reaction ◽  
Volume Fraction ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Transfer Rates ◽  
Flow And Heat Transfer ◽  
Moving Wedge

Purpose The analysis of boundary layers is needed to reflect the behaviour of fluid flows in current industrial processes and to improve the efficacy of products. Hence, this study aims to analyse the flow and heat transfer performance of hybrid alumina-copper/water (Al2O3-Cu/H2O) nanofluid with the inclusion of activation energy and binary chemical reaction effect towards a moving wedge. Design/methodology/approach The multivariable differential equations with partial derivatives are converted into a specific type of ordinary differential equations by using valid similarity transformations. The reduced mathematical model is elucidated in the MATLAB system by using the bvp4c procedure. This solution method is competent in delivering multiple solutions once appropriate assumptions are supplied. Findings The results of multiple control parameters have been studied, and the findings are verified to provide more than one solution. The coefficient of skin friction was discovered to be increased by adding nanoparticles volume fraction from 0% to 0.5% and 1%, by almost 1.6% and 3.2%. Besides, increasing the nanoparticles volume fraction improves heat transfer efficiency gradually. The inclusion of the activation energy factor displays a downward trend in the mass transfer rates, consequently reducing the concentration profile. In contrast, the increment of the binary reaction rate greatly facilitates the augmentation of mass transfer rates. There is a significant enhancement in the heat transfer rate, approximately 13.2%, when the suction effect dominates about 10% in the boundary layer flow. Additionally, the results revealed that as the activation energy rises, the temperature and concentration profiles rise as well. It is proved that the activation energy parameter boosts the concentration of chemical species in the boundary layer. A similar pattern emerges as the wedge angle parameter increases. The current effort aims to improve the thermal analysis process, particularly in real-world applications such as geothermal reservoirs, chemical engineering and food processing, which often encountered mass transfer phenomenon followed by chemical reactions with activation energy. Originality/value The present results are original and new for the study of flow and heat transfer over a permeable moving wedge in a hybrid nanofluid with activation energy and binary chemical reaction.

Bioconvection of nanofluid flow in a thin moving needle in the presence of activation energy with surface temperature boundary conditions

2021 ◽  
pp. 095440892110539
Author(s):  
I Sadham Hussain ◽  
D Prakash ◽  
S Kumar ◽  
M Muthtamilselvan
Keyword(s):  
Heat Transfer ◽  
Activation Energy ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Heating Process ◽  
Newtonian Heating ◽  
Transform Method ◽  
Flow Equations ◽  
Flow And Heat Transfer ◽  
Differential Transform

A comparative analysis is formed to analyze the combined effects of a binary chemical reaction and activation energy in the flow of bio-nanofluid due to the thin moving needle using the mathematical nanofluid model offered by Buongiorno with different boundary conditions namely, Newtonian heating and prescribed surface temperature. The governing partial differential equations converted into a set of final controlled governing physical flow equations by using similarity variables and then solved numerically by Runge–Kutta–Fehlberg method along with shooting technique and analytically by differential transform method. The results gained for the dimensionless velocity, temperature, concentration, motile diffusivity number, Nusselt number and Sherwood number are presented through graphs and tables. The present study reveals that an enhancement in the pertinent parameters has considerably altered the physical characteristics of the flow and heat transfer, which applies in biosensors and biomedical instrumentation. Also, the rate of heat transfer from the needle to the fluid is controlled by applying Newtonian heating than by applying prescribed surface temperature against all the parameters. In addition, we carried out the statistical analysis to determine the dependence of the physical parameter on the rate of heat transfer for both cases of heating process.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

scholarly journals A fuzzy solution of nonlinear partial differential equations

2021 ◽  
Vol 5 (1) ◽  
pp. 51-63
Author(s):  
Mawia Osman ◽  
◽  
Zengtai Gong ◽  
Altyeb Mohammed Mustafa ◽  
◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Infinite Series ◽  
Nonlinear Partial Differential Equations ◽  
Differential Transform Method ◽  
Series Expansions ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Fuzzy Solution

In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

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