South East Asian J. of Mathematics and Mathematical Sciences
Cubic set is a structure with two components which has been applied in the conditions of β idea... more Cubic set is a structure with two components which has been applied in the conditions of β ideals. This paper presents the notion of cubic fuzzy β ideal of a β algebra. In addition that, the notion of cubic (a, b)-translation, cubic µ- multiplication were presented. Further, some engrossing results of cubic β ideals with the combination of multiplication and translation were investigated.
A steady incompressible nanofluid flow past an inclined permeable plate is numerically studied, i... more A steady incompressible nanofluid flow past an inclined permeable plate is numerically studied, including radiation, viscous dissipation, and Soret and Dufour effects. A coupled non-linear simultaneous differential similarity equation is created by non-dimensionalizing the ruling partial differential equations. Then, nonlinear coupled equations with transformed boundary conditions are resolved by the shooting method based on the Runge-Kutta fourth-order method. The Prandtl number, Grashof number, Schmidt number, magnetic parameter, and Soret and Dufour effects are just a few of the controlling flow parameters for which computations are done. Graphs are used to illustrate how various flow factors affect momentum, energy, and concentration equations. The impacts of these variables on skin friction coefficients, Nusselt number, and Sherwood number are given in tabular form. The concentration profile increases with the Soret number and the reverse trend is observed with the Dufour numbe...
Recently, Nanoparticles have supplied diverse challenges to several scientific issues. Nanopartic... more Recently, Nanoparticles have supplied diverse challenges to several scientific issues. Nanoparticles dispersed in a variety of conventional fluids can change the flow and heat transmission properties of the fluids. The mathematical technique is used in this work to investigate the MHD water-based nanofluid flow via an upright cone. The heat and mass flux pattern is used in this mathematical model to examine MHD, viscous dissipation, radiation, chemical reactions and suction/injection processes. The finite difference approach was used to find the solution to the basic governing equations. A combination of nanofluids comprising nanoparticles including aluminum oxide (Al$$_{2}$$ 2 O$$_{3}$$ 3 ), silver (Ag), copper (Cu) and titanium dioxide (TiO$$_{2}$$ 2 ) with a volume fraction of nanoparticles (0, 0.01, 0.02, 0.03, 0.04), viscous dissipation ($$\epsilon = 0.4, 0.8$$ ϵ = 0.4 , 0.8 ), MHD (M = 0.5, 1.0), radiation (Rd = 0.4, 1.0, 2.0), chemical reaction ($$\lambda = 0.2, 2.0$$ λ = 0.2...
A numerical analysis was carried out on convective flow past a vertical oscillating cylinder with... more A numerical analysis was carried out on convective flow past a vertical oscillating cylinder with non-constant viscosity under the influence of magnetic field effects. The governing equations related to the flow problem are unsteady, nonlinear coupled partial differential equations. The same was transformed into a dimensionless form and the final form of equations was solved numerically. The approximate values of velocity, temperature, skin friction and Nusselt number are obtained. The viscosity considered as a function of temperature.
Natural convective heat and mass transfer over an isothermal vertical cone due to the simultaneou... more Natural convective heat and mass transfer over an isothermal vertical cone due to the simultaneous action of buoyancy, chemical reaction, and transverse magnetic field is studied. The governing boundary-layer equations are transformed into a dimensionless form, and then the resulting unsteady nonlinear coupled partial differential equations are solved by using an efficient, more accurate, and unconditionally stable implicit finite difference scheme of the Crank–Nicolson type. A parametric study is performed to illustrate the effect of the buoyancy ratio parameter, Prandtl number, Schmidt number, chemical reaction parameter, and the magnetic field parameter on the velocity, temperature, and concentration profiles. The local and average characteristics: shear stresses, heat transfer coefficients, and mass transfer coefficients, are obtained numerically. The numerical results reveal that the velocity decreases in the case of a destructive reaction, whereas it increases for a generative reaction.
Heat transfer effects on dusty gas flow past a semi-infinite isothermal inclined plate are consid... more Heat transfer effects on dusty gas flow past a semi-infinite isothermal inclined plate are considered here-with. The governing boundary layer equations for the above problem are set up and non-dimensionalised. The non-dimensional governing equations are solved by an implicit finite difference scheme of Crank–Nicolson method, which is fast convergent and unconditionally stable. Gas-velocity, dust particle-velocity, temperature, skin friction and Nusselt numbers
ABSTRACT The present numerical analysis addresses free convection flow of a viscous incompressibl... more ABSTRACT The present numerical analysis addresses free convection flow of a viscous incompressible fluid along an inclined semi-infinite flat plate considering the variation of viscosity and thermal diffusivity with temperature. The governing equations are developed with the corresponding boundary conditions are transformed to non-dimensional form using the appropriate dimensionless quantities. Due to complexity in the transformed governing equations, analytical solution will fail to produce a solution. Hence, most efficient and unconditionally stable implicit finite difference method of Crank-Nicolson scheme has been used to solve the governing equations. Numerical results are obtained for different values of the viscosity, thermal conductivity, inclination angle, Grashof number, and Prandtl number. The overall investigation of the variation of velocity, temperature, shearing stress and Nusselt number are presented graphically. To examine the accuracy of the present approximate results, the present results are compared with the available results.
An analysis is performed to study the free convective flow over a moving vertical porous plate wi... more An analysis is performed to study the free convective flow over a moving vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation. The fluid considered here is a gray, absorbing-emitting radiation, but a nonscattering medium. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature, skin friction and Nusselt number are studied for different parameters like the radiation parameter, Grashof number, Prandtl number, magnetic field parameter, permeability parameter, and time. It is observed that the velocity decreases with increasing radiation parameter.
ABSTRACT A numerical investigation is performed to study the MHD free convection flow past a semi... more ABSTRACT A numerical investigation is performed to study the MHD free convection flow past a semi-infinite inclined plate subjected to a variable surface temperature. The Joule heating and viscous dissipation effects are taken into account in the energy equation. The governing equations of the flow are transformed into a nondimensional form using suitable dimensionless quantities. A fully developed implicit finite-difference scheme of Crank-Nicolson type is engaged to solve the dimensionless governing equations, which is more accurate, fast convergent, and unconditionally stable. The effects of the MHD, inclination angle, power law, Grashof number, Prandtl number, Joule heating, and viscous dissipation effects are studied on the velocity, temperature, shear stress, and heat transfer coefficients during transient periods. It is observed that the MHD has retarding effects on velocity.
ABSTRACT Numerical modeling of two-dimensional, unsteady, laminar, isothermal heat and mass trans... more ABSTRACT Numerical modeling of two-dimensional, unsteady, laminar, isothermal heat and mass transfer by MHD free convection flow past an impulsively started vertical cylinder in the presence of Dufour and Soret effects is considered. The governing equations of the flow problems, valid in the free convection regime, are transformed into a nondimensional form using appropriate nondimensional parameters. These equations are solved numerically by an efficient, implicit, iterative, finite-difference scheme of Crank-Nicolson type. A parametric study illustrating the influence of the magnetic field, Grashof number, and the Dufour and Soret numbers on the fluid velocity, temperature, and concentration, as well as the local and average skin friction, Nusselt and Sherwood numbers is conducted. The obtained results are shown graphically and the physical aspects of the problem are discussed.
Journal of Applied Mechanics and Technical Physics, 2012
ABSTRACT An analysis is performed to study the heat transfer characteristics of natural convectio... more ABSTRACT An analysis is performed to study the heat transfer characteristics of natural convection over a vertical cone under the combined effects of a magnetic field and thermal radiation. The cone surface is subjected to a variable surface temperature. The fluid considered is a gray absorbing/emitting, but non-scattering medium. The boundary layer equations governing the flow are reduced to non-dimensional equations using non-dimensional quantities valid in the free-convection regime. The resulting non-dimensional governing equations are solved by an implicit finite-difference method of the Crank-Nicolson type, which is rapidly convergent and unconditionally stable. Numerical results are obtained for velocity, temperature, local and average skin friction, and local and average Nusselt numbers for various values of parameters occurring in the problem and are presented in the graphical form. Excellent agreement of the results obtained with available data is demonstrated.
South East Asian J. of Mathematics and Mathematical Sciences
Cubic set is a structure with two components which has been applied in the conditions of β idea... more Cubic set is a structure with two components which has been applied in the conditions of β ideals. This paper presents the notion of cubic fuzzy β ideal of a β algebra. In addition that, the notion of cubic (a, b)-translation, cubic µ- multiplication were presented. Further, some engrossing results of cubic β ideals with the combination of multiplication and translation were investigated.
A steady incompressible nanofluid flow past an inclined permeable plate is numerically studied, i... more A steady incompressible nanofluid flow past an inclined permeable plate is numerically studied, including radiation, viscous dissipation, and Soret and Dufour effects. A coupled non-linear simultaneous differential similarity equation is created by non-dimensionalizing the ruling partial differential equations. Then, nonlinear coupled equations with transformed boundary conditions are resolved by the shooting method based on the Runge-Kutta fourth-order method. The Prandtl number, Grashof number, Schmidt number, magnetic parameter, and Soret and Dufour effects are just a few of the controlling flow parameters for which computations are done. Graphs are used to illustrate how various flow factors affect momentum, energy, and concentration equations. The impacts of these variables on skin friction coefficients, Nusselt number, and Sherwood number are given in tabular form. The concentration profile increases with the Soret number and the reverse trend is observed with the Dufour numbe...
Recently, Nanoparticles have supplied diverse challenges to several scientific issues. Nanopartic... more Recently, Nanoparticles have supplied diverse challenges to several scientific issues. Nanoparticles dispersed in a variety of conventional fluids can change the flow and heat transmission properties of the fluids. The mathematical technique is used in this work to investigate the MHD water-based nanofluid flow via an upright cone. The heat and mass flux pattern is used in this mathematical model to examine MHD, viscous dissipation, radiation, chemical reactions and suction/injection processes. The finite difference approach was used to find the solution to the basic governing equations. A combination of nanofluids comprising nanoparticles including aluminum oxide (Al$$_{2}$$ 2 O$$_{3}$$ 3 ), silver (Ag), copper (Cu) and titanium dioxide (TiO$$_{2}$$ 2 ) with a volume fraction of nanoparticles (0, 0.01, 0.02, 0.03, 0.04), viscous dissipation ($$\epsilon = 0.4, 0.8$$ ϵ = 0.4 , 0.8 ), MHD (M = 0.5, 1.0), radiation (Rd = 0.4, 1.0, 2.0), chemical reaction ($$\lambda = 0.2, 2.0$$ λ = 0.2...
A numerical analysis was carried out on convective flow past a vertical oscillating cylinder with... more A numerical analysis was carried out on convective flow past a vertical oscillating cylinder with non-constant viscosity under the influence of magnetic field effects. The governing equations related to the flow problem are unsteady, nonlinear coupled partial differential equations. The same was transformed into a dimensionless form and the final form of equations was solved numerically. The approximate values of velocity, temperature, skin friction and Nusselt number are obtained. The viscosity considered as a function of temperature.
Natural convective heat and mass transfer over an isothermal vertical cone due to the simultaneou... more Natural convective heat and mass transfer over an isothermal vertical cone due to the simultaneous action of buoyancy, chemical reaction, and transverse magnetic field is studied. The governing boundary-layer equations are transformed into a dimensionless form, and then the resulting unsteady nonlinear coupled partial differential equations are solved by using an efficient, more accurate, and unconditionally stable implicit finite difference scheme of the Crank–Nicolson type. A parametric study is performed to illustrate the effect of the buoyancy ratio parameter, Prandtl number, Schmidt number, chemical reaction parameter, and the magnetic field parameter on the velocity, temperature, and concentration profiles. The local and average characteristics: shear stresses, heat transfer coefficients, and mass transfer coefficients, are obtained numerically. The numerical results reveal that the velocity decreases in the case of a destructive reaction, whereas it increases for a generative reaction.
Heat transfer effects on dusty gas flow past a semi-infinite isothermal inclined plate are consid... more Heat transfer effects on dusty gas flow past a semi-infinite isothermal inclined plate are considered here-with. The governing boundary layer equations for the above problem are set up and non-dimensionalised. The non-dimensional governing equations are solved by an implicit finite difference scheme of Crank–Nicolson method, which is fast convergent and unconditionally stable. Gas-velocity, dust particle-velocity, temperature, skin friction and Nusselt numbers
ABSTRACT The present numerical analysis addresses free convection flow of a viscous incompressibl... more ABSTRACT The present numerical analysis addresses free convection flow of a viscous incompressible fluid along an inclined semi-infinite flat plate considering the variation of viscosity and thermal diffusivity with temperature. The governing equations are developed with the corresponding boundary conditions are transformed to non-dimensional form using the appropriate dimensionless quantities. Due to complexity in the transformed governing equations, analytical solution will fail to produce a solution. Hence, most efficient and unconditionally stable implicit finite difference method of Crank-Nicolson scheme has been used to solve the governing equations. Numerical results are obtained for different values of the viscosity, thermal conductivity, inclination angle, Grashof number, and Prandtl number. The overall investigation of the variation of velocity, temperature, shearing stress and Nusselt number are presented graphically. To examine the accuracy of the present approximate results, the present results are compared with the available results.
An analysis is performed to study the free convective flow over a moving vertical porous plate wi... more An analysis is performed to study the free convective flow over a moving vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation. The fluid considered here is a gray, absorbing-emitting radiation, but a nonscattering medium. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature, skin friction and Nusselt number are studied for different parameters like the radiation parameter, Grashof number, Prandtl number, magnetic field parameter, permeability parameter, and time. It is observed that the velocity decreases with increasing radiation parameter.
ABSTRACT A numerical investigation is performed to study the MHD free convection flow past a semi... more ABSTRACT A numerical investigation is performed to study the MHD free convection flow past a semi-infinite inclined plate subjected to a variable surface temperature. The Joule heating and viscous dissipation effects are taken into account in the energy equation. The governing equations of the flow are transformed into a nondimensional form using suitable dimensionless quantities. A fully developed implicit finite-difference scheme of Crank-Nicolson type is engaged to solve the dimensionless governing equations, which is more accurate, fast convergent, and unconditionally stable. The effects of the MHD, inclination angle, power law, Grashof number, Prandtl number, Joule heating, and viscous dissipation effects are studied on the velocity, temperature, shear stress, and heat transfer coefficients during transient periods. It is observed that the MHD has retarding effects on velocity.
ABSTRACT Numerical modeling of two-dimensional, unsteady, laminar, isothermal heat and mass trans... more ABSTRACT Numerical modeling of two-dimensional, unsteady, laminar, isothermal heat and mass transfer by MHD free convection flow past an impulsively started vertical cylinder in the presence of Dufour and Soret effects is considered. The governing equations of the flow problems, valid in the free convection regime, are transformed into a nondimensional form using appropriate nondimensional parameters. These equations are solved numerically by an efficient, implicit, iterative, finite-difference scheme of Crank-Nicolson type. A parametric study illustrating the influence of the magnetic field, Grashof number, and the Dufour and Soret numbers on the fluid velocity, temperature, and concentration, as well as the local and average skin friction, Nusselt and Sherwood numbers is conducted. The obtained results are shown graphically and the physical aspects of the problem are discussed.
Journal of Applied Mechanics and Technical Physics, 2012
ABSTRACT An analysis is performed to study the heat transfer characteristics of natural convectio... more ABSTRACT An analysis is performed to study the heat transfer characteristics of natural convection over a vertical cone under the combined effects of a magnetic field and thermal radiation. The cone surface is subjected to a variable surface temperature. The fluid considered is a gray absorbing/emitting, but non-scattering medium. The boundary layer equations governing the flow are reduced to non-dimensional equations using non-dimensional quantities valid in the free-convection regime. The resulting non-dimensional governing equations are solved by an implicit finite-difference method of the Crank-Nicolson type, which is rapidly convergent and unconditionally stable. Numerical results are obtained for velocity, temperature, local and average skin friction, and local and average Nusselt numbers for various values of parameters occurring in the problem and are presented in the graphical form. Excellent agreement of the results obtained with available data is demonstrated.
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Papers by G Palani