Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer
One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in...
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MDPI AG
2023-06-01
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| author | Pervinder Singh Vinod K. Gupta Isaac Lare Animasaun Taseer Muhammad Qasem M. Al-Mdallal |
| author_facet | Pervinder Singh Vinod K. Gupta Isaac Lare Animasaun Taseer Muhammad Qasem M. Al-Mdallal |
| author_sort | Pervinder Singh |
| collection | DOAJ |
| description | One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the <i>x</i>-direction and between two concurrent plates at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mi>d</mi></mrow></semantics></math></inline-formula> was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>u</mi></mrow></semantics></math></inline-formula>), Sherwood number proportional to mass transfer of solute 1 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>h</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) and Sherwood number proportional to mass transfer of solute 2 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>h</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection. |
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| spelling | doaj.art-70ce9557915e4b44b6d304fa7dd01ac02023-11-18T17:03:03ZengMDPI AGMathematics2227-73902023-06-011113290710.3390/math11132907Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass TransferPervinder Singh0Vinod K. Gupta1Isaac Lare Animasaun2Taseer Muhammad3Qasem M. Al-Mdallal4Department of Mathematics, School of Physical Sciences, DIT University, Dehradun 248009, IndiaDepartment of Mathematics, School of Physical Sciences, DIT University, Dehradun 248009, IndiaFluid Dynamics and Survey Research Group, Department of Mathematical Sciences, Federal University of Technology, Akure PMB 704, NigeriaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematical Sciences, United Arab Emirates University, Al Ain PMB 15551, United Arab EmiratesOne of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the <i>x</i>-direction and between two concurrent plates at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mi>d</mi></mrow></semantics></math></inline-formula> was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>u</mi></mrow></semantics></math></inline-formula>), Sherwood number proportional to mass transfer of solute 1 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>h</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) and Sherwood number proportional to mass transfer of solute 2 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>h</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection.https://www.mdpi.com/2227-7390/11/13/2907triple-diffusive convectiongravitational modulationthermal Rayleigh numberLewis numbersolute Rayleigh number |
| spellingShingle | Pervinder Singh Vinod K. Gupta Isaac Lare Animasaun Taseer Muhammad Qasem M. Al-Mdallal Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer Mathematics triple-diffusive convection gravitational modulation thermal Rayleigh number Lewis number solute Rayleigh number |
| title | Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer |
| title_full | Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer |
| title_fullStr | Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer |
| title_full_unstemmed | Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer |
| title_short | Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer |
| title_sort | dynamics of newtonian liquids with distinct concentrations due to time varying gravitational acceleration and triple diffusive convection weakly non linear stability of heat and mass transfer |
| topic | triple-diffusive convection gravitational modulation thermal Rayleigh number Lewis number solute Rayleigh number |
| url | https://www.mdpi.com/2227-7390/11/13/2907 |
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