Keller Box Technique Research Articles

Biconvection flow of Carreau fluid over an upper paraboloid surface: A computational study

Present article explored the physical characteristics of biconvection effects on the MHD flow of Carreau nanofluid over upper horizontal surface of paraboloid revolution along with chemical reaction. The concept of the Carreau nanofluid was introduced the new parameterization achieve the momentum governing equation. Using similarity transformed, the governing partial differential equations are converted into the ordinary differential equations. The obtained governing equations are solved computationally by using implicit finite difference method known as the Keller box technique. The numerical solutions are obtained for the velocity, temperature, concentration, friction factor, local heat and mass transfer coefficients by varying controlling parameters i.e. Biconvection parameter, fluid parameter, Weissenberg number, Hartmann number, Prandtl number, Brownian motion parameter, thermophoresis parameter, Lewis number and chemical reaction parameter. The obtained results are discussed via graphs and tables.

Numerical investigation of thermally stratified Williamson fluid flow over a cylindrical surface via Keller box method

Present study is addressed to express the implementation of Keller-Box technique on physical problem in the field of fluid rheology, for this purpose the Williamson fluid flow is considered along a cylindrical stretching surface manifested with temperature stratification. The flow model is translated mathematically in terms of differential equations. Numerical simulation is executed to trace out the solution structure of developed differential system. The graphical outcomes for the flow regime of two different geometries (i-e cylindrical and plane surface) are reported and examined towards involved physical parameters. Furthermore, the local skin friction coefficient and local Nusselt number are computed numerically. A remarkable agreement of present study is noticed with the previously published results, which confirms the implementation and validation of Keller-Box scheme and it will serve as a helping source for the future correspondence.

Magnetohydrodynamics Flow of Non-Newtonian Fluid from a Vertical Permeable Cone in the Presence of Thermal Radiation and Heat Generation/Absorption

The nonlinear, steady state magnetohydrodynamics natural convection boundary layer flow, heat and mass transfer of an viscoelastic incompressible Jeffrey’s fluid from a vertical permeable cone with thermal radiation and heat generation/absorption effects is investigated in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The Rosseland diffusion algebraic approximation is utilized to simulate thermal radiation effects. The surface of the cones is maintained at a constant temperature and concentration with mass flux present. Excellent correlation of the present results with previous studies is obtained to validate the numerical code. The influence of Deborah number (De), ratio of relaxation to retardation times ( $$\lambda $$ ), radiation parameter (F), heat generation/absorption parameter ( $$\Delta $$ ), suction/injection parameter ( $$f_{w}$$ ), magnetic parameter (M) and dimensionless tangential coordinate ( $$\xi $$ ) on velocity, temperature and concentration evolution in the boundary layer regime are examined in detail. Also, the effects of these parameters on local skin friction, heat transfer rate and mass transfer rate are investigated.

Computational study of Jeffrey’s non-Newtonian fluid past a semi-infinite vertical plate with thermal radiation and heat generation/absorption

Abstract The nonlinear, steady state boundary layer flow, heat and mass transfer of an incompressible non-Newtonian Jeffrey’s fluid past a semi-infinite vertical plate is examined in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The influence of a number of emerging non-dimensional parameters, namely Deborah number (De), ratio of relaxation to retardation times (λ), Buoyancy ratio parameter (N), suction/injection parameter (fw), Radiation parameter (F), Prandtl number (Pr), Schmidt number (Sc), heat generation/absorption parameter (Δ) and dimensionless tangential coordinate (ξ) on velocity, temperature and concentration evolution in the boundary layer regime is examined in detail. Also, the effects of these parameters on surface heat transfer rate, mass transfer rate and local skin friction are investigated. This model finds applications in metallurgical materials processing, chemical engineering flow control, etc.

Effects of Conduction Variation on MHD Natural Convection Flow along a Vertical Flat Plate with Thermal Conductivity

This paper reports the effect of conduction variation of free convection flow along a vertical flat plate on magnetohydrodynamic (MHD) with thermal conductivity. The governing equations with associated boundary conditions reduce to local non-similarity boundary layer equations for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method together with Keller-box technique. Numerical results of the velocity and temperature profiles, skin friction and surface temperature profiles for different values of the magnetic parameter, the thermal conductivity variation parameter, the Prandtl number and the conduction variation parameters are presented graphically. Detailed discussion is given for the effect of the aforementioned parameters. Opposite scenario is found in skin friction and surface temperature for the thermal conductivity variation parameter. Significant effect is found in skin friction and surface temperature for conduction variation parameter.

Joule heating and magnetohydrodynamic effects on ferrofluid(Fe3O4) flow in a semi-porous curved channel

Heat exchange investigation of a magnetohydrodynamic magnetic nanofluid flow in a semi porous curved channel is considered. The energy equation is modeled by incorporating the Joule heating effects. A curvilinear coordinate system that incorporates the effects of curvature is utilized to develop the mathematical model in the form of coupled nonlinear partial differential equations. Similar solution of the considered flow and heat exchange issue is attained numerically by the Keller-box technique. Analysis of the involved pertinent parameters on the velocity, skin-friction coefficient, pressure, temperature and local Nusselt number is presented through graphs and tables.

Magnetohydrodynamic free convection boundary layer flow of non-Newtonian tangent hyperbolic fluid from a vertical permeable cone with variable surface temperature

The nonlinear, non-isothermal steady-state boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian (viscoelastic) fluid from a vertical permeable cone with magnetic field are studied. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using the second-order accurate implicit finite difference Keller-box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely a Weissenberg number (We), rheological power law index (m), surface temperature exponent (n), Prandtl number (Pr), magnetic parameter (M) suction/injection parameter (fw) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime, is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is observed that velocity, surface heat transfer rate and local skin friction are reduced with increasing Weissenberg number, but temperature is increased. Increasing m enhances velocity and surface heat transfer rate but reduces temperature and local skin friction. An increase in non-isothermal power law index (n) is observed to decrease the velocity and temperature. Increasing magnetic parameter (M) is found to decrease the velocity and increase the temperature. Overall, the primary influence on free convection is sustained through the magnetic body force parameter, M, and also the surface mass flux (injection/suction) parameter, fw. The rheological effects, while still prominent, are not as dramatic. Boundary layers (both hydrodynamic and thermal) are, therefore, most strongly modified by the applied magnetic field and wall mass flux effect. The study is pertinent to smart coatings, e.g., durable paints, aerosol deposition processing and water-based solvent thermal treatment in chemical engineering.

Free Convection Flow and Heat Transfer of Tangent Hyperbolic past a Vertical Porous Plate with Partial Slip

This article presents the nonlinear free convection boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from a vertical porous plate with velocity slip and thermal jump effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Velocity slip (Sf), Thermal jump (ST), Prandtl number (Pr) and dimensionless tangential coordinate () on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that velocity, skin friction and heat transfer rate (Nusselt number) is increased with increasing Weissenberg number (We), whereas the temperature is decreased. Increasing power law index (n) enhances velocity and heat transfer rate but decreases temperature and skin friction. An increase in Thermal jump (ST) is observed to decrease velocity, temperature, local skin friction and Nusselt number. Increasing Velocity slip (Sf) is observed to increase velocity and heat transfer rate but decreases temperature and local skin friction. An increasing Prandtl number, (Pr), is found to decrease both velocity and temperature. The study is relevant to chemical materials processing applications.

Effects of Conduction Variation on MHD Natural Convection Flow Along a vertical Flat Plate

This paper reports free convection flow along a vertical flat plate with conduction variation on magneto hydrodynamic (MHD) effects. The governing equations with associated boundary conditions reduce to local non-similarity boundary layer equations for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method together with Keller-box technique. Numerical results of the velocity and temperature profiles, skin friction and surface temperature profiles for different values of the magnetic parameter, the Prandtl number and the conduction variation parameters are presented graphically. Detailed discussion is given for the effect of the aforementioned parameters.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 63-73

Magnetohydrodynamic Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from Horizontal Circular Cylinder with Biot Number Effects

This article presents the nonlinear, steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from a Horizontal Circular Cylinder in the presence of magnetic field and Biot number effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), power law index (n), Prandtl number (Pr), Biot number $$(\upgamma )$$ , the magnetic parameter (M) and dimensionless tangential coordinate ( $$\xi $$ ) on velocity and temperature evolution on the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that the velocity, skin friction and heat transfer rate reduce with increasing We. Whereas, there is slight increase in temperature. Increasing n is observed to increase the velocity and heat transfer rate but decreases temperature and skin friction. An increasing $$\upgamma $$ is seen to increase velocity, temperature, local skin friction and heat transfer rate. And an increasing M is found to decrease velocity, skin friction and heat transfer rate but increases the temperature. The study is relevant to chemical materials processing applications.

Boundary Layer Stagnation-Point Flow of Second Grade Fluid over an Exponentially Stretching Sheet

In this paper, the steady boundary layer stagnation point flow and heat transfer of a second grade fluid over an exponentially stretching sheet is investigated. The solutions are obtained through homotopy analysis method (HAM) and the Keller-box technique. Comparisons of both the solutions are given graphically as well as in tabular form. The effects of second grade parameter β Prandtl number Pr and other important physical parameters are presented through graphs and the salient features are discussed.

Mixed Convection Flow of Magnetic Viscoelastic Polymer from a Nonisothermal Wedge with Biot Number Effects

Magnetic polymers are finding increasing applications in diverse fields of chemical and mechanical engineering. In this paper, we investigate the nonlinear steady boundary layer flow and heat transfer of such fluids from a nonisothermal wedge. The incompressible Eyring-Powell non-Newtonian fluid model is employed and a magnetohydrodynamic body force is included in the simulation. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, the Eyring-Powell rheological fluid parameter (ε), local non-Newtonian parameter based on length scale (δ), Prandtl number (Pr), Biot number (γ), pressure gradient parameter (m), magnetic parameter (M), mixed convection parameter (λ), and dimensionless tangential coordinate (ξ), on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated.

Homogeneous-heterogeneous reactions in Williamson fluid model over a stretching cylinder by using Keller box method

This paper addresses the effect of homogeneous-heterogeneous reaction on Williamson fluid model over a stretching cylinder. The boundary layer partial differential equations are converted into ordinary differential equation by using suitable transformations. The non-linear ordinary differential equations are solved by using implicit finite difference Keller box technique. The effects of several pertinent parameters on velocity, temperature and concentration profiles are deliberated graphically. The behavior of skin friction coefficient and Nusselt number are examined through graphs.

Computational Analysis of Magnetohydrodynamic Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from a Horizontal Circular Cylinder with Partial Slip

An analysis is presented for the nonlinear steady boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian fluid from horizontal circular cylinder in the presence of thermal and hydrodynamic slip condition. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Weissenberg number $$(W_{e})$$ , power law index $$(n)$$ , velocity slip parameter $$(\hbox {S}_\mathrm{f})$$ , thermal jump parameter $$(\hbox {S}_\mathrm{T})$$ , Prandtl number (Pr), magnetic parameter $$(M)$$ and dimensionless tangential coordinate $$(\xi )$$ on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is observed that velocity, skin friction and heat transfer rate are reduced with increasing Weissenberg number ( $$W_{e}$$ ), whereas, temperature increases slightly. Increasing power law index ( $$n$$ ) increases velocity and heat transfer rate but decreases temperature and skin friction. An increase in $$S_{f}$$ , is observed to enhance velocity and heat transfer rate but decreases temperature and local skin friction. Whereas, increasing $$S_{T}$$ , is found to decrease velocity, temperature, skin friction and Nusselt number. The study is relevant to chemical materials processing applications.

EFFECTS OF THERMAL CONDUCTIVITY OF FLUID ON FREE CONVECTION FLOW ALONG A VERTICAL FLAT PLATE WITH TRANSVERSE CONDUCTION

This paper reports the effects of transverse conduction variation with thermal conductivity on freeconvection flow along a vertical flat plate. The governing equations with associated boundary conditions reduceto local non-similarity boundary layer equations for this phenomenon are converted to dimensionless forms usinga suitable transformation. The transformed non-linear equations are then solved using the implicit finitedifference method together with Keller-box technique. Numerical results of the velocity and temperature profiles,skin friction and surface temperature profiles for different values of the thermal conductivity parameter, thePrandtl number and the transverse conduction variation parameters are presented graphically. Detaileddiscussion is given for the effect of the aforementioned parameters. Mentionable effect is found in skin friction andsurface temperature for the transverse conduction variation parameter.

Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from an Isothermal Sphere with Partial Slip

An analysis is presented for the nonlinear steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from an isothermal sphere in the presence of thermal and hydrodynamic slip condition. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller-box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Velocity slip (Sf), thermal jump (ST), Prandtl number (Pr) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is observed that velocity, skin friction and the Nusselt number (heat transfer rate) are reduced with increasing (We), whereas the temperature is enhanced. Increasing power (n) enhances velocity and Nusselt number (heat transfer rate) but reduces temperature and skin friction. An increase in Sf, is observed to enhance velocity and Nusselt number but reduces temperature and local skin friction. Whereas increasing ST is found to decrease velocity, temperature, skin friction and Nusselt number. The study is relevant to chemical materials processing applications.

Solar Radiation Assisted Mixed Convection Flow Along a Vertical Plate

ABSTRACTSolar radiation assisted mixed convection boundary layer flow of Newtonian fluid along a non- reflecting, non-absorbing and ideally transparent semi-infinite vertical plate is studied here. Beer's law is used to express the solar radiation term. It is convenient to transform the non-linear dimensionless parabolic partial differential equations into (i) primitive variable formulation (PVF) and (ii) stream function formulation (SFF) before applying the numerical schemes. Coupled equations thus obtained from PVF are integrated numerically through implicit finite difference method together with the Gaussian elimination technique whereas block tridiagonal Keller-box technique is adopted to simulate the system of equations obtained from SFF. Numerical results from these two methods are also compared graphically in order to test the validation of the two schemes. However, due to less computation time and accuracy numeric results of shear stress, local Nusselt number coefficient, velocity and temperature profiles are obtained via SFF. It is found that velocity as well as temperature of the non-absorbing fluid enhances owing to the increase in solar radiation parameter.

Boundary Layer Flow past a Stretching Cylinder and Heat Transfer with Variable Thermal Conductivity

The boundary layer flow of viscous incompressible fluid over a stretching cylinder has been considered to study flow field and temperature field. Due to non-linearity, a numerical approach called Keller-box technique has been used to compute the values of velocity function f and temperature field at different points of dynamic region. The expressions for skin friction and Nusselt number have also been obtained. The dependence of velocity profile and temperature profile on the dimensionless parameter of practical interest has been analyzed in detail by graphs. The dependence of Skin friction and Nusselt number has been seen through tables.

Radiation effects on natural convection flow over an inclined flat plate with temperature-dependent viscosity

The effect of radiation on laminar natural convection flow of a viscous incompressible fluid over a semi-infinite flat plate inclined at a small angle to the horizontal with strong temperature-dependent viscosity has been investigated. The Rosseland approximation is considered while modelling the problem. The non-similar equations are obtained for upstream, downstream, and entire regimes, which are then solved numerically. For constant viscosity, the series solution technique has been employed in order to obtain solutions that are valid near the leading edge as well as in the downstream regime. Later, solutions of the governing equations have been obtained using the finite difference method along with the Keller box technique, taking into consideration variable viscosity. Effects of physical parameters like conduction—radiation para-meter Rd, surface temperature parameter θw, variable viscosity parameter λ, and Prandtl number Pr are shown on the local skin-friction coefficient Cf and the local Nusselt number, Nu. Effects of the parameters on the streamlines are also shown around the point of separation that occurs along the negatively inclined surface.

Numerical study of magnetohydrodynamic free convective heat transfer flow along a vertical flat plate with temperature dependent thermal conductivity

The present numerical work describes the effect of the magnetohydrodynamic (MHD) free convective heat transfer flow along a vertical flat plate with temperature dependent thermal conductivity and heat conduction. The governing equations reduce to local non-similarity boundary layer equations using suitable transformation have been integrated by employing an implicit finite difference method together with the Keller box technique. Comparison with previously published work is performed and excellent agreement is observed. Profiles of the dimensionless velocity and temperature distributions as well as the local skin friction coefficient and surface temperature distribution are shown graphically for various values of the magnetic parameter M, thermal conductivity variation parameter g and Prandtl number Pr.Keywords: Implicit finite difference method, free convection flow, vertical flow, vertical flat plate, temperature dependent thermal conductivityDOI: 10.3329/jname.v6i1.2654Journal of Naval Architecture and Marine Engineering Vol.6(1) 2009 16-29