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Effect of Higher Order Chemical Reaction on Double Diffusive Mixed Convective Flow Over a Rotating Vertical Cone in a Darcy Porous Medium


Affiliations
1 Department of Mathematics, BMS College of Engineering, Bangalore, Karnataka, 560019, India
2 College of Engineering -Mechanical Engineering Department - Babylon University- Babylon City – Hilla, Iraq
     

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This paper examines numerically the combined effects of double diffusive mixed convective flow and higher order chemical reaction in Darcy porous medium over a rotating vertical cone. The governing equations for flow, energy and concentration are transformed into ordinary differential equation by using similarity transformation and are solved numerically by employing the fourth order Runge - Kutta method with shooting technique for different parametric values. The effects of mixed convection parameter, inverse Darcy number, and order of homogeneous chemical reaction, buoyancy ratio and chemical reaction parameter are investigated and reported graphically on velocity, temperature and concentration profiles together with the local Nusselt and Sherwood numbers. The numerical results are obtained for the mixed convection parameter varying as [0.5 ≤ gs ≤ 10] , inverse Darcy number varying as [0.5 ≤ Da-1 ≤ 3] , order of homogeneous chemical reaction varying as [1 ≤ n ≤ 4], chemical reaction parameter [-1.5 ≤ γ ≤ 3.5] and the buoyancy ratio [-0.5 ≤ N ≤ 1], while the Prandtl number is considered fixed at [Pr = 0.71].Comparison with previously published numerical work is performed and a good agreement between the results is observed. It is found that the increase in the chemical reaction parameter leads to reduce the tangential velocity and concentration profiles while, it increases the circumferential and normal velocity and temperature profiles. The results indicated that the skin-friction coefficients and the Nusselt and Sherwood numbers are strongly dependent on the buoyancy ratio. Moreover, both the local Nusselt and Sherwood numbers increase when the mixed convection parameter and the buoyancy ratio increase. Application of the present study includes rotating heat exchangers, spin stabilized missiles, packed-bed chemical reactors in geothermal and geophysics.

Keywords

Double Diffusive, Mixed Convection, Higher Order Chemical Reaction, Porous Medium, Rotating Cone.
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  • Effect of Higher Order Chemical Reaction on Double Diffusive Mixed Convective Flow Over a Rotating Vertical Cone in a Darcy Porous Medium

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Authors

B. Mallikarjuna
Department of Mathematics, BMS College of Engineering, Bangalore, Karnataka, 560019, India
Rangaswamy
Department of Mathematics, BMS College of Engineering, Bangalore, Karnataka, 560019, India
Ahmed Kadhim Hussein
College of Engineering -Mechanical Engineering Department - Babylon University- Babylon City – Hilla, Iraq

Abstract


This paper examines numerically the combined effects of double diffusive mixed convective flow and higher order chemical reaction in Darcy porous medium over a rotating vertical cone. The governing equations for flow, energy and concentration are transformed into ordinary differential equation by using similarity transformation and are solved numerically by employing the fourth order Runge - Kutta method with shooting technique for different parametric values. The effects of mixed convection parameter, inverse Darcy number, and order of homogeneous chemical reaction, buoyancy ratio and chemical reaction parameter are investigated and reported graphically on velocity, temperature and concentration profiles together with the local Nusselt and Sherwood numbers. The numerical results are obtained for the mixed convection parameter varying as [0.5 ≤ gs ≤ 10] , inverse Darcy number varying as [0.5 ≤ Da-1 ≤ 3] , order of homogeneous chemical reaction varying as [1 ≤ n ≤ 4], chemical reaction parameter [-1.5 ≤ γ ≤ 3.5] and the buoyancy ratio [-0.5 ≤ N ≤ 1], while the Prandtl number is considered fixed at [Pr = 0.71].Comparison with previously published numerical work is performed and a good agreement between the results is observed. It is found that the increase in the chemical reaction parameter leads to reduce the tangential velocity and concentration profiles while, it increases the circumferential and normal velocity and temperature profiles. The results indicated that the skin-friction coefficients and the Nusselt and Sherwood numbers are strongly dependent on the buoyancy ratio. Moreover, both the local Nusselt and Sherwood numbers increase when the mixed convection parameter and the buoyancy ratio increase. Application of the present study includes rotating heat exchangers, spin stabilized missiles, packed-bed chemical reactors in geothermal and geophysics.

Keywords


Double Diffusive, Mixed Convection, Higher Order Chemical Reaction, Porous Medium, Rotating Cone.

References