Search results

This paper aims to investigate the unsteady mixed convection along an exponentially stretching surface in presence of transverse magnetic field applied at the wall and the opposing buoyancy flow.

The dimensional partial differential equations governing the flow field are transformed to non-dimensional coupled partial differential equations with the aid of suitable non-similar transformations. The resulting equations are then solved by the coalition of quasilinearization technique and the finite difference method.

Effects of volumetric heat source/sink, suction/blowing and other dimensionless parameters on velocity and temperature profiles are examined numerically. This investigation reveals that in presence of opposing buoyancy flow, the suction and volumetric heat source enhances the skin-friction coefficient, while the rise in the MHD increases the momentum boundary layer.

To the best of the authors’ knowledge, no such investigation has been carried out in the literature.

The purpose of this paper is to consider the influence of slip flow and thermal jump and to investigate its effects on unsteady mixed convection along an exponentially stretching surface. It is also intended to explore the influence of suction/injection and volumetric heat source/sink on the fluid flow.

The assumed problem is modelled into governing equations which are dimensional non-linear partial differential equations in nature. To obtain solutions, initially the governing equations were made non-dimensional by the suitable non-similar transformations. Then, the dimensionless non-linear partial differential equations are linearized with the aid of Quasilinearization technique. The so obtained equations are discretized by the implicit finite difference method.

The detailed analysis of the considered problem displays that the non-similarity variable reduces the velocity and temperature profiles. For higher values of mixed convection parameter, the magnitude of velocity profile as well as the Nusselt number increase. The unsteady variable diminishes the fluid flow. The higher values of velocity ratio parameter reduce the skin-friction coefficient. Further, the magnitude of skin-friction coefficient and heat transfer rate are to minimize for increasing values of partial slip and thermal jump parameters, respectively. Volumetric heat source and injection parameters are to rise the flow behavior within the momentum and thermal boundary layers significantly.

To the best of authors’ knowledge, no such investigation has been found in the literature.

The purpose of this paper is to study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the flow.

In this case, the numerical difficulties to obtain the non‐similar solution are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique.

Numerical results are reported here to display the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different stream‐wise locations on velocity and temperature profiles, and on skin friction and heat transfer coefficients.

Thermo‐physical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate the density changes to temperature changes and to couple in this way the temperature field to the flow field.

Convective heat transfer over a stationary cone is important for the thermal design of various types of industrial equipments such as heat exchangers, conisters for nuclear waste disposal, nuclear reactor cooling systems and geothermal reservoirs, etc.

The combined effects of thermal diffusion and surface mass transfer on a vertical cone has been studied.

The purpose of this paper is to present the surface roughness effects on mixed convection nanofluid flow with liquid hydrogen/liquid nitrogen diffusion.

The small parameter (α) is considered along with the frequency parameter n to study the surface roughness. The non-similar transformations are used to reduce the dimensional non-linear partial differential equations into dimensionless form, and then, the resulting equations are solved with the help of Newton’s Quasilinearization technique and the finite difference scheme.

The impacts of several dimensionless parameters such as Brownian diffusion parameter (Nb), thermophoresis parameter (Nt), small parameter (α), etc., are analyzed over various profiles as well as gradients. Also, the investigation is carried out for in presence and absence of nanoparticles. The influence of surface roughness is sinusoidal in nature and is more significant near the origin in case of skin-friction coefficient. The addition of nanoparticles enhances the skin-friction coefficient and reduces the Nusselt number, while its effects are not noticeable in case of mass transfer rates. The presence of suction/blowing, respectively, enhances/decreases the Sherwood number pertaining to the liquid hydrogen.

The results of the present analysis are expected to be useful for the design engineers of polymer industries in manufacturing good quality polymer sheets.

To the best of the author’s knowledge, no such investigation has been carried out in the literature.

The purpose of this study is to analyze the impacts of aqueous solutions such as NaCl-water and Sucrose-water on unsteady triple diffusive mixed convection flow along an exponentially decreasing external flow velocity in presence of suction/injection.

The proposed problem is modelled into dimensional partial differential equations which are nonlinear and coupled in nature. Non-similar transformations are used to transform these equations into non-dimensional form. To linearize the equations, quasilinearization technique has been used and then implicit finite difference scheme is used to discretise the linear partial differential equations.

The variations of various dimensionless parameters have been depicted on velocity, temperature and species concentration profiles for NaCl and Sucrose aqueous solutions through graphical representations. In addition, several results have been expressed through graphs pertaining to skin-friction coefficient, heat and mass transfer rates. The results indicate that the increase in Schmidt number raises the mass transfer rate for the case of NaCl-water and Sucrose-water solutions.

As per the authors’ best of knowledge, no investigations have been carried out in the literature on unsteady triple diffusive mixed convection flow along an exponentially decreasing mainstream velocity.

This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave.

First, the authors discritize the time-dependent term using Crank–Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method.

Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers’ equation and yields results better than other methods and compatible with the exact solutions.

The numerical results for non-planar Burgers’ equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers’' equation.

The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field.

The non-similar solutions have been obtained from the origin of the streamwise co-ordinate to the point of zero skin friction using quasilinearization technique with an implicit finite-difference scheme.

The effect of M is not notable on the temperature and heat transfer coefficient when λ is large. The skin friction coefficient and velocity profile are enhance with the increase of MHD parameter M when λ is small. Viscous dissipation has no significant on the skin friction coefficient under MHD effect. For M=1, the movement of the slot or slot suction or slot injection do not cause any effect on flow separation. The slot suction and the movement of the slot in downstream direction delay the point of zero skin friction for M=0.

The present results are original and new for water boundary-layer flow over sphere in mixed convection flow with MHD effect and non-uniform mass transfer. So this study would be useful in analysing the skin friction and heat transfer coefficient on sphere of mixed convection flow of water boundary layer with MHD effect.

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear Hadamard-type fractional differential equations.

The aim of this paper is to develop a numerical scheme for numerical solutions of Hadamard-type fractional differential equations. The classical Haar wavelets are modified to align them with Hadamard-type operators. Operational matrices are derived and used to convert differential equations to systems of algebraic equations.

The upper bound for error is estimated. With the help of quasilinearization, nonlinear problems are converted to sequences of linear problems and operational matrices for modified Haar wavelets are used to get their numerical solution. Several numerical examples are presented to demonstrate the applicability and validity of the proposed method.

The numerical method is purposed for solving Hadamard-type fractional differential equations.

The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration.

An implicit finite difference scheme in combination with the quasilinearisation technique is employed to obtain non‐similar solutions of the governing boundary layer equations for momentum, temperature and concentration fields.

The numerical results are reported here to display the effects of mixed convection parameter, ratio of buoyancy forces, surface mass transfer (suction and injection), the ratio of free stream velocity to the composite reference velocity, Prandtl number and Schmidt number on velocity, temperature and concentration profiles as well as on skin friction, Nusselt number and Sherwood number.

Thermophysical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate density changes, and to couple in this way the temperature and concentration fields to the flow field. The concentration of diffusing species is assumed to be very small in comparison with other chemical species far away from the surface. Hence the Soret and Dufour effects are neglected. The stretching sheet is assumed to be subject to a power‐law wall temperature as well as to a power‐law wall concentration, in a parallel free stream.

Convective heat and mass transfer over a vertical stretching sheet in a parallel stream is very important for various design of technological process are hot rolling, wire drawing, glass‐fiber paper production, both metal and polymer sheets, for instance, in cooling of an infinite metallic plate in a cooling bath, the boundary layer along material handling conveyors, etc.

The paper studies the combined effects of thermal and mass diffusion over a vertical stretching sheet with surface mass transfer.

The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.

The nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.

The effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.

The present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.