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.Â
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.
An analysis of the effects of MHD on a two-dimensional free-convective flow of a viscous incompre... more An analysis of the effects of MHD on a two-dimensional free-convective flow of a viscous incompressible fluid past a semi-infinite isothermal inclined plate is carried out. The effects of viscous dissipation and the induced magnetic field are assumed to be negligible. A more accurate, unconditionally stable, and fast converging implicit finite difference scheme is used to solve the dimensionless governing equations. The effects of MHD on velocity, temperature, local and average skin friction, and local and average Nusselt number are studied. It is observed that the magnetic field parameter has a retarding effect on the velocity. The study of flow problems involving heat transfer is of primary importance in the fields of modern engineering design and operation of various kinds of machinery. Buoyancy-driven flows are of common occurrence in technological, atmospheric, and oceanic phenomena, with the buoyancy stratification being achieved often by the temperature field. Due to its numerous applications, the study of the natural convection heat transfer from the differently-inclined surfaces has received much attention in recent years, both theoretically and experimentally. A lot of detailed studies have been made on the problem of natural convection on a vertical plate. At the same time, very little attention has been given to the problem of natural convection over inclined and horizontal plates or the plates slightly inclined to the horizontal. However, free-convection heat transfer from an inclined surface is very frequently encountered in engineering devices and natural environment. The unsteady natural convection flow past a semi-infinite vertical plate was first considered by Hellums and Churchill with the use of an explicit finite difference scheme. This scheme suffers from some deficiencies, and hence a more efficient implicit finite difference scheme was used by Soundalgekar and Ganesan . During last few years, attention was given to natural convection flows past inclined plates. Kierkus [3] presented a perturbation analysis for a two-dimensional laminar free-convection flow about an inclined isothermal plate in air and studied the problem experimentally for different angles of inclination. Pera and Gebhart [4] studied the laminar natural convection boundary-layer flow above horizontal and inclined surfaces with uniform temperatures and heat fluxes. Chen et al. [5] obtained a numerical solution for the problem of natural convection over an inclined plate with a variable surface temperature. Ganesan and Ekambavannan [6] solved the problem of transient free-convective flow of an incompressible viscous fluid past a semi-infinite isothermal plate by an implicit finite difference method which is unconditionally stable. Callahan and Marner [7] gave a numerical solution for free convection with mass transfer on an isothermal vertical flat plate by employing an explicit finite difference scheme. The problem of free convection of an electrically conducting fluid past a plate under the influence of a magnetic field is important for gaining an understanding of such flows and for possible application in geophysics, astrophysics, and aerodynamics. An exact analysis of the MHD Stokes problem for the flow of an electrically conducting, incompressible viscous fluid past an impulsively started vertical plate under the action of transversely applied magnetic field was carried out by Soundalgekar et al. [8]. Sacheti et al. [9] obtained an exact solution for unsteady magnetohydrodynamic free-convection flow on an impulsively started vertical plate with a constant heat flux. Elbashbeshy [10] studied heat and mass transfer along a vertical plate under combined buoyancy effects of thermal and species diffusion in the presence of magnetic field. Ganesan and Palani [11] considered the effects of MHD on a two-dimensional freeconvective flow of a viscous incompressible fluid past a semi-infinite isothermal vertical plate using an efficient im-
In the present analysis, a numerical study is performed to examine the heat transfer characterist... more In the present analysis, a numerical study is performed to examine the heat transfer characteristics of a convective flow over a vertical plate under the combined effects of magnetic field and thermal radiation in the presence of heat source/sink. The surface of the plate is subjected to a variable surface temperature. The boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime using the suitable non-dimensional parameters. The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent, more accurate and unconditionally stable. Numerical results are obtained and presented for velocity, temperature, local and average wall shear stress, local and average Nusselt number in air. The present results are compared with the results available in the literature and are found to be in an excellent agreement.
MHD(Magneto Hydro Dynamic) natural convective flow over a vertical cone under the influence of co... more MHD(Magneto Hydro Dynamic) natural convective flow over a vertical cone under the influence of combined effects of viscous dissipation and joule heating is considered herewith. The principal equations of the flow problems are converted into a dimensionless form by means of the appropriate non-dimensional quantities. The transformed dimensionless equations are solved approximately using an well-known method. The current approximate values are match up with the previous work available in the journal and are found as an excellent match with each other. It is observed from these investigations,that transverse applied magnetic field diminished the velocity. The temperature is maximum near the cone surface and then tends to zero asymptotically. The effects of MHD, exponent, Prandtl number, Joule heating and viscous dissipation are analysed on the flow field, temperature, shearing stress and rate of heat transfer.
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.
Free convection flow over an isothermal vertical cone immersed in a fluid with variable viscosity... more Free convection flow over an isothermal vertical cone immersed in a fluid with variable viscosity and MHD is studied in this paper. Using appropriate variables, the basic equations are transformed into the nondimensional boundary-layer equations. These equations are then solved numerically using a very efficient implicit finite-difference method known as Crankl-Nicolson scheme. Detailed results for the velocity, temperature, skin friction, and heat transfer rates for a selection of parameter sets consisting of the viscosity parameter, magnetic field parameter, and Prandtl number are discussed. In order to validate our numerical results, the present results are compared with the available work in the literature and are found to be in an excellent agreement.
Journal of Mechanical Science and Technology, 2009
A study of the velocity and thermal boundary layers on a semi-infinite inclined plate with temper... more A study of the velocity and thermal boundary layers on a semi-infinite inclined plate with temperature oscillations is presented in this work. The non-linear, coupled parabolic integro-partial differential equations governing flow and heat transfer have been solved numerically using an implicit finite difference scheme of Crank-Nicolson type. The numerical values for the flow field, temperature, shearing stress, and heat transfer coefficients are presented in a graphical form. It is observed that the velocity and temperature profiles decrease as the frequency parameter increases.
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, 2010
The effects of viscous dissipation are considered for natural convection flow past a semi-infinit... more The effects of viscous dissipation are considered for natural convection flow past a semi-infinite inclined plate with variable surface temperature. Velocity and temperature profiles, skin friction, and rate of heat transfer are obtained. The effects of Grashof and Prandtl numbers, inclination angle, exponent in the wall temperature variation law, and viscous dissipation parameter on the flow are discussed. It is shown that the time required to reach steady states increases with increasing Prandtl number of the fluid. In addition, an increase in the plate temperature due to viscous dissipation was found to lead to a rise in the average skin friction and a decrease in the average Nusselt number.
Journal of Applied Mechanics and Technical Physics, 2011
A numerical solution of the first-order homogeneous chemical reaction in an unsteady free convect... more A numerical solution of the first-order homogeneous chemical reaction in an unsteady free convective flow past a semi-infinite vertical plate is studied. The dimensionless governing equations are solved by an efficient, more accurate, unconditionally stable, and rapidly converging implicit finite-difference scheme. The effect of various parameters, such as the Prandtl number, Schmidt number, buoyancy ratio parameter, and chemical reaction parameter on flow velocity and temperature is determined. The velocity profiles are in excellent agreement with available results in the literature. The local and average values of skin friction and Nusselt and Sherwood numbers are calculated. The effects of the chemical reaction parameters on these values are discussed for both generative and destructive reactions. Owing to the presence of the first-order chemical reaction, the velocity is found to increase in the generative reaction and to decrease in the destructive reaction.
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.Â
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.
An analysis of the effects of MHD on a two-dimensional free-convective flow of a viscous incompre... more An analysis of the effects of MHD on a two-dimensional free-convective flow of a viscous incompressible fluid past a semi-infinite isothermal inclined plate is carried out. The effects of viscous dissipation and the induced magnetic field are assumed to be negligible. A more accurate, unconditionally stable, and fast converging implicit finite difference scheme is used to solve the dimensionless governing equations. The effects of MHD on velocity, temperature, local and average skin friction, and local and average Nusselt number are studied. It is observed that the magnetic field parameter has a retarding effect on the velocity. The study of flow problems involving heat transfer is of primary importance in the fields of modern engineering design and operation of various kinds of machinery. Buoyancy-driven flows are of common occurrence in technological, atmospheric, and oceanic phenomena, with the buoyancy stratification being achieved often by the temperature field. Due to its numerous applications, the study of the natural convection heat transfer from the differently-inclined surfaces has received much attention in recent years, both theoretically and experimentally. A lot of detailed studies have been made on the problem of natural convection on a vertical plate. At the same time, very little attention has been given to the problem of natural convection over inclined and horizontal plates or the plates slightly inclined to the horizontal. However, free-convection heat transfer from an inclined surface is very frequently encountered in engineering devices and natural environment. The unsteady natural convection flow past a semi-infinite vertical plate was first considered by Hellums and Churchill with the use of an explicit finite difference scheme. This scheme suffers from some deficiencies, and hence a more efficient implicit finite difference scheme was used by Soundalgekar and Ganesan . During last few years, attention was given to natural convection flows past inclined plates. Kierkus [3] presented a perturbation analysis for a two-dimensional laminar free-convection flow about an inclined isothermal plate in air and studied the problem experimentally for different angles of inclination. Pera and Gebhart [4] studied the laminar natural convection boundary-layer flow above horizontal and inclined surfaces with uniform temperatures and heat fluxes. Chen et al. [5] obtained a numerical solution for the problem of natural convection over an inclined plate with a variable surface temperature. Ganesan and Ekambavannan [6] solved the problem of transient free-convective flow of an incompressible viscous fluid past a semi-infinite isothermal plate by an implicit finite difference method which is unconditionally stable. Callahan and Marner [7] gave a numerical solution for free convection with mass transfer on an isothermal vertical flat plate by employing an explicit finite difference scheme. The problem of free convection of an electrically conducting fluid past a plate under the influence of a magnetic field is important for gaining an understanding of such flows and for possible application in geophysics, astrophysics, and aerodynamics. An exact analysis of the MHD Stokes problem for the flow of an electrically conducting, incompressible viscous fluid past an impulsively started vertical plate under the action of transversely applied magnetic field was carried out by Soundalgekar et al. [8]. Sacheti et al. [9] obtained an exact solution for unsteady magnetohydrodynamic free-convection flow on an impulsively started vertical plate with a constant heat flux. Elbashbeshy [10] studied heat and mass transfer along a vertical plate under combined buoyancy effects of thermal and species diffusion in the presence of magnetic field. Ganesan and Palani [11] considered the effects of MHD on a two-dimensional freeconvective flow of a viscous incompressible fluid past a semi-infinite isothermal vertical plate using an efficient im-
In the present analysis, a numerical study is performed to examine the heat transfer characterist... more In the present analysis, a numerical study is performed to examine the heat transfer characteristics of a convective flow over a vertical plate under the combined effects of magnetic field and thermal radiation in the presence of heat source/sink. The surface of the plate is subjected to a variable surface temperature. The boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime using the suitable non-dimensional parameters. The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent, more accurate and unconditionally stable. Numerical results are obtained and presented for velocity, temperature, local and average wall shear stress, local and average Nusselt number in air. The present results are compared with the results available in the literature and are found to be in an excellent agreement.
MHD(Magneto Hydro Dynamic) natural convective flow over a vertical cone under the influence of co... more MHD(Magneto Hydro Dynamic) natural convective flow over a vertical cone under the influence of combined effects of viscous dissipation and joule heating is considered herewith. The principal equations of the flow problems are converted into a dimensionless form by means of the appropriate non-dimensional quantities. The transformed dimensionless equations are solved approximately using an well-known method. The current approximate values are match up with the previous work available in the journal and are found as an excellent match with each other. It is observed from these investigations,that transverse applied magnetic field diminished the velocity. The temperature is maximum near the cone surface and then tends to zero asymptotically. The effects of MHD, exponent, Prandtl number, Joule heating and viscous dissipation are analysed on the flow field, temperature, shearing stress and rate of heat transfer.
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.
Free convection flow over an isothermal vertical cone immersed in a fluid with variable viscosity... more Free convection flow over an isothermal vertical cone immersed in a fluid with variable viscosity and MHD is studied in this paper. Using appropriate variables, the basic equations are transformed into the nondimensional boundary-layer equations. These equations are then solved numerically using a very efficient implicit finite-difference method known as Crankl-Nicolson scheme. Detailed results for the velocity, temperature, skin friction, and heat transfer rates for a selection of parameter sets consisting of the viscosity parameter, magnetic field parameter, and Prandtl number are discussed. In order to validate our numerical results, the present results are compared with the available work in the literature and are found to be in an excellent agreement.
Journal of Mechanical Science and Technology, 2009
A study of the velocity and thermal boundary layers on a semi-infinite inclined plate with temper... more A study of the velocity and thermal boundary layers on a semi-infinite inclined plate with temperature oscillations is presented in this work. The non-linear, coupled parabolic integro-partial differential equations governing flow and heat transfer have been solved numerically using an implicit finite difference scheme of Crank-Nicolson type. The numerical values for the flow field, temperature, shearing stress, and heat transfer coefficients are presented in a graphical form. It is observed that the velocity and temperature profiles decrease as the frequency parameter increases.
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, 2010
The effects of viscous dissipation are considered for natural convection flow past a semi-infinit... more The effects of viscous dissipation are considered for natural convection flow past a semi-infinite inclined plate with variable surface temperature. Velocity and temperature profiles, skin friction, and rate of heat transfer are obtained. The effects of Grashof and Prandtl numbers, inclination angle, exponent in the wall temperature variation law, and viscous dissipation parameter on the flow are discussed. It is shown that the time required to reach steady states increases with increasing Prandtl number of the fluid. In addition, an increase in the plate temperature due to viscous dissipation was found to lead to a rise in the average skin friction and a decrease in the average Nusselt number.
Journal of Applied Mechanics and Technical Physics, 2011
A numerical solution of the first-order homogeneous chemical reaction in an unsteady free convect... more A numerical solution of the first-order homogeneous chemical reaction in an unsteady free convective flow past a semi-infinite vertical plate is studied. The dimensionless governing equations are solved by an efficient, more accurate, unconditionally stable, and rapidly converging implicit finite-difference scheme. The effect of various parameters, such as the Prandtl number, Schmidt number, buoyancy ratio parameter, and chemical reaction parameter on flow velocity and temperature is determined. The velocity profiles are in excellent agreement with available results in the literature. The local and average values of skin friction and Nusselt and Sherwood numbers are calculated. The effects of the chemical reaction parameters on these values are discussed for both generative and destructive reactions. Owing to the presence of the first-order chemical reaction, the velocity is found to increase in the generative reaction and to decrease in the destructive reaction.
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