Unsteady Mixed Convection Boundary Layer Research Articles

A Fourth Order Numerical Scheme for Unsteady Mixed Convection Boundary Layer Flow: A Comparative Computational Study

In this paper, a three-stage fourth-order numerical scheme is proposed. The first and second stages of the proposed scheme are explicit, whereas the third stage is implicit. A fourth-order compact scheme is considered to discretize space-involved terms. The stability of the fourth-order scheme in space and time is checked using the von Neumann stability criterion for the scalar case. The stability region obtained by the scheme is more than the one given by explicit Runge–Kutta methods. The convergence conditions are found for the system of partial differential equations, which are non-dimensional equations of heat transfer of Stokes first and second problems. The comparison of the proposed scheme is made with the existing Crank–Nicolson scheme. From this comparison, it can be concluded that the proposed scheme converges faster than the Crank–Nicolson scheme. It also produces less relative error than the Crank–Nicolson method for time-dependent problems.

Thermal radiation effect on unsteady mixed convection boundary layer flow and heat transfer of nanofluid over permeable stretching surface through porous medium in the presence of heat generation.

Here, we study the effect of mixed convection and thermal radiation on unsteady boundary layer of heat transfer and nanofluid flow over permeable moving surface through a porous medium. The effect of heat generation is also discussed. The equations governing the system are the continuity equation, momentum equation and the heat transfer equation. These governing equations transformed into a system of nondimensional equations contain many physical parameters that describe the study. The transformed equations are solved numerically using an implicit finite difference technique with Newton's linearization method. The thermo-physical parameters describe the study are the mixed convection parameter α, , the Radiation parameter Rd, , porous medium parameter k, , the nanoparticles volume ,, the suction or injection parameter fw, , the unsteadiness parameter At, and the heat source parameter λ = 0.5 .The influence of the thermo-physical parameters is obtained analytically and displayed graphically. Comparisons of some special cases of the present study are performed with previously published studies and a good agreement is obtained.

Analytical and Numerical Study on Cross Diffusion Effects on Magneto-Convection of a Chemically Reacting Fluid with Suction/Injection and Convective Boundary Condition

The purpose of this paper is to investigate the Soret and Dufour effects on unsteady mixed convective boundary layer flow of a viscous fluid over a stretching surface in a porous medium in the presence of magnetic field with heat generation/absorption, chemical reaction, suction/injection and convective boundary condition. The governing time-dependent partial differential equations are transformed into non-linear ordinarydifferential equations using similarity transformations. These equations subject to the appropriate boundary conditions are solved analytically by homotopy analysis method (HAM) and numerically by Runge-Kutta fourth order method and shooting technique.The numerical solution is compared with analytical solution. The influence of the different parameters on velocity, temperature and concentration profiles are discussed in graphical as well as in tabular form. It is observed that the fluid velocity and temperature increase on increasing the buoyancy ratio parameter and heat generation/absorption parameter. Also found that the surface heat and mass transfer rates increase on increasingthe suction/injection and heat generation/absorption parameters.

MHD Effect on Unsteady Mixed Convection Boundary Layer Flow past a Circular Cylinder with Constant Wall Temperature

Magnetohydrodynamic (MHD) effect is a study on motion of electrical-conducting fluid under magnetic fields. This effect has great intention due to its applications such as design of heat exchanger and nuclear reactor. In the problem in fluid motion, flow of separation can reduced the effectiveness of the system as well as can increased the energy lost. This study will present the results on reducing the flow separation by considering magnetic effect. In this study, unsteady mixed convection boundary layer flow past a circular cylinder is given attention. Focus of study is on the separation times that affected by the magnetic fields. The mathematical models in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. The effect of magnetic parameter on velocity and temperature profiles as well as skin friction and Nusselt number are studied.

On a Bivariate Spectral Homotopy Analysis Method for Unsteady Mixed Convection Boundary Layer Flow, Heat, and Mass Transfer due to a Stretching Surface in a Rotating Fluid

A bivariate spectral homotopy analysis method (BSHAM) is extended to solutions of systems of nonlinear coupled partial differential equations (PDEs). The method has been used successfully to solve a nonlinear PDE and is now tested with systems. The method is based on a new idea of finding solutions that obey a rule of solution expression that is defined in terms of the bivariate Lagrange interpolation polynomials. The BSHAM is used to solve a system of coupled nonlinear partial differential equations modeling the unsteady mixed convection boundary layer flow, heat, and mass transfer due to a stretching surface in a rotating fluid, taking into consideration the effect of buoyancy forces. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The effects of the flow parameters on the local skin-friction coefficient, the Nusselt number, and the Sherwood number were presented in graphs.

Buoyancy-Driven Radiative Unsteady Magnetohydrodynamic Heat Transfer over a Stretching Sheet with non-Uniform Heat Source/sink

In the present study an unsteady mixed convection boundary layer flow of an electrically conduct- ing fluid over an stretching permeable sheet in the presence of transverse magnetic field, thermal radiation and non-uniform heat source/sink effects is investigated. The unsteadiness in the flow and temperature fields is due to the time-dependent nature of the stretching velocity and the surface temperature. Both opposing and assisting flows are considered. The dimensionless governing or- dinary non-linear differential equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. The effects of unsteadiness parameter, buoyancy parameter, thermal radiation, Eckert number, Prandtl number and non-uniform heat source/sink parameter on the flow and heat transfer characteristics are thoroughly examined. Comparisons of the present results with previously published results for the steady case are found to be excellent.

Radiation Effect on Unsteady Mixed Convection Boundary Layer Flow, Heat and Mass Transfer over a Wedge

This paper concerns the unsteady mixed convection laminar boundary layer flow past a vertical wedge in the presence of thermal radiation. The governing equations have been solved by the straightforward finite difference method for the entire frequency range. We observe that the Richardson’s number, Ri, strongly affects the skin friction, heat transfer and mass transfer. The effect of the Schmidt number, Sc, on the mass transfer is significant, whereas the skin friction and the heat transfer are almost unaffected by it. Also the heat transfer is considerably dependent on the conduction-radiation parameter, Rd, but the influence of this parameter on the skin friction and the mass transfer is rather weak.Dhaka Univ. J. Sci. 64(1): 59-64, 2016 (January)

Similarity Solutions of Unsteady Mixed Convective Boundary Layer Flow of Viscous Incompressible Fluid along Isothermal Horizontal Plate

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

Dual solutions for unsteady mixed convection flow of MHD micropolar fluid over a stretching/shrinking sheet with non-uniform heat source/sink

The aim of the present study is to investigate the influence of non-uniform heat source/sink, mass transfer and chemical reaction on an unsteady mixed convection boundary layer flow of a magneto-micropolar fluid past a stretching/shrinking sheet in the presence of viscous dissipation and suction/injection. The governing equations of the flow, heat and mass transfer are transformed into system of nonlinear ordinary differential equations by using similarity transformation and then solved numerically using Shooting technique with Matlab Package. The influence of non-dimensional governing parameters on velocity, microrotation, temperature and concentration profiles are discussed and presented with the help of their graphical representations. Also, friction factor, heat and mass transfer rates have been computed and presented through tables. Under some special conditions, present results are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.

Unsteady mixed convection boundary layer flow along a symmetric wedge with variable surface temperature embedded in a saturated porous medium

Purpose – The purpose of this paper is to study laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past a symmetric wedge embedded in a porous medium in the presence of the first and second orders resistances. Design/methodology/approach – The governing boundary-layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations were solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. The obtained results will be compared with earlier papers on special cases of the problem to examine validity of the method of solution. Findings – The effects of various parameters on the fluid velocity and fluid temperature as well as the wall heat transfer rate and skin-friction coefficient are presented graphically and in tabulated form. Originality/value – The study of heat transfer in porous media has been attracted the attention of many researchers in recent times due to the utmost importance in many different applications, including physical, geophysical and chemical applications. Also in different areas of engineering and modern purposes as oil refining, pollution of the air with poison gas, the process of mineral extraction, the design water tanks and study volcanic activity. Also has many uses in medicine, modern science, food products, textiles and ion exchange.

Unsteady Heat and Mass Transfer Near the Stagnation-point on a Vertical Permeable Surface: a Comprehensive Report of Dual Solutions

In this paper, the problem of unsteady mixed convection boundary layer flow of a viscous incompressible fluid near the stagnation-point on a vertical permeable plate with both cases of prescribed wall temperature and prescribed wall heat flux is investigated numerically. Here, both assisting and opposing buoyancy forces are considered and studied. The non-linear coupled partial differential equations governing the flow, thermal and concentration fields are first transformed into a set of non-linear coupled ordinary differential equations by a set of suitable similarity transformations. The resulting system of coupled non-linear ordinary differential equations is solved numerically by using the Runge–Kutta scheme coupled with a conventional shooting procedure. Numerical results are obtained for the skin-friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for some values of the governing parameters, namely, the unsteadiness parameter A, permeability parameter f0 and mixed convection parameter λ. It is found that dual solutions exist for both assisting and opposing flows, and the range of the mixed convection parameter for which the solution exists, increases with suction and unsteadiness parameters.

G-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

Effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a wedge with heat generation/absorption in the presence of suction or injection

The purpose of this work is to study the effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a vertical wedge with heat generation/absorption in the presence of uniform suction or injection. The fluid is assumed to be viscous and incompressible. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Both accelerating and decelerating free stream flows are considered. Non-similar solutions are obtained numerically by using an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are carried out for different values of dimensionless parameters on velocity, temperature and concentration profiles graphically reported in the present study. Also, numerical results are presented for the local skin friction coefficient, the local Nusselt number and the local Sherwood number. Results indicate that the time effect is crucial on velocity, temperature and concentration profiles, and on the local skin friction coefficient, the local Nusselt and Sherwood numbers. The buoyancy assisting force causes overshoot in the velocity profile for lower Prandtl number fluids. Results are compared with previously published work and are found to be in an excellent agreement.

Unsteady mixed convection boundary layer flow over a vertical cone with non-uniform slot suction (injection)

The non-similar solution of an unsteady mixed convection laminar boundary layer flow over a vertical cone in the presence of non-uniform surface mass transfer through slot has been obtained while the axis of cone is inline with the flow. The unsteadiness is caused by the time dependent free stream velocity. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting coupled non-linear partial differential equations have been solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity and temperature profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are reported to display the effects of non-uniform single and double slot suction (injection) on skin friction and heat transfer coefficients at the wall. Further, the effects of Prandtl number, buoyancy and mass transfer (suction or injection) parameters at different stream-wise locations for various times on velocity and temperature profiles, and on skin friction and heat transfer coefficients are also presented in this paper.

Non-uniform slot suction (injection) on an unsteady mixed convection flow over a wedge with chemical reaction and heat generation or absorption

The aim of this work is to study the effect non-uniform single and double slot suction (injection) on an unsteady mixed convection boundary layer flow over a vertical wedge with chemical reaction and heat generation or absorption. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Non-similar solutions are obtained by solving the coupled non-linear partial differential equations using the quasi-linearization technique in combination with an implicit finite-difference scheme and numerical computations are carried out for different values of dimensionless parameters to display the effects of non-uniform single and double slot suction (injection) along with chemical reaction and heat generation or absorption. Results indicate that the skin friction, heat and mass transfer coefficients increase with non-uniform slot suction but the effect of non-uniform slot injection is just the opposite. As the slot moves in downstream direction, the skin friction, heat and mass transfer coefficients decrease by non-uniform slot suction whereas non-uniform slot injection has the reverse effect.

Heat Generation, Thermal Radiation and Chemical Reaction Effects on MHD Mixed Convection Flow over an Unsteady Stretching Permeable Surface

Magnetohydrodynamics; Thermal radiation; Heat generation; Chemical reaction; Mixed Convective flow; Unsteady flow; Stretching permeable surface The unsteady MHD mixed convective laminar boundary layer flow of an incompressible viscous fluid over continuously stretching permeable surface in the presence of thermal radiation, heat generation and chemical reaction is studied. The unsteadiness in the momentum, temperature and concentration fields is because of the time-dependent stretching velocity and surface temperature and concentration. Similarity transformations are used to convert the governing time dependent boundary layer equations into to a system of nonlinear ordinary coupled differential equations containing Magnetic parameter, Thermal convective parameter, Mass convective parameter, Suction parameter, Radiation parameter, Eckert number, Prandtl number, Heat source parameter, Chemical reaction parameter, Schmidt number, Soret number and Unsteadiness parameter. TheNactsheim-Swigert shooting technique together with Runge-Kutta six order iteration schemes has been used for numerical procedure. Comparisons with previously published work are performed and are found to be in excellent agreement. The effects on the velocity, temperature and concentration distributions as well as skin-friction coefficients, Nusselt number and Sherwood number of the various important parameters are discussed graphically.

A Further Note on the Unsteady Mixed Convection Boundary Layer in a Porous Medium with Temperature Slip: An Exact Solution

The aim of this Letter is to show that a further exact solution of the problem on unsteady mixed convection boundary layer in a porous medium with temperature slip can be obtained in addition of that reported very recently by Fang et al. (2012).

Unsteady mixed convection boundary layer flow and heat transfer of nanofluids due to stretching sheet

Abstract The term of nanofluid refers to a solid–liquid mixture with a continuous phase which is a nanometer sized nanoparticle dispersed in conventional base fluids. A numerical analysis has been presented to investigate the unsteady mixed convection boundary layer flow and heat transfer due to uncertainties of thermal conductivity and dynamic viscosity of nanofluid over a stretching vertical surface. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching velocity and the surface temperature. The governing partial differential equations with the auxiliary conditions are converted to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. Different water-based nanofluids containing Cu, Ag, CuO, Al2O3, and TiO2 are taken into consideration. The effects of pertinent parameters such as the solid volume fraction of nanoparticles, Prandtl number, mixed convection parameter, and the unsteadiness parameter have been discussed. Furthermore, different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics is discussed. Comparison with known results for steady state flow is presented and it found to be in excellent agreement.

Unsteady effects on mixed convection boundary layer flow from a permeable slender cylinder due to non-linearly power law stretching

An unsteady mixed convection boundary layer flow over a permeable non-linearly stretching vertical slender cylinder is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of surface mass transfer, where the slender cylinder is in line with the flow. The unsteadiness in the flow and temperature fields is caused by the continuously non-linearly stretching vertical slender cylinder. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are performed to understand the physical situations of linear and non-linearly stretching surface for different values of parameters to display the velocity and temperature profiles graphically. The obtained results show that the buoyancy parameter λ and the Prandtl number Pr enhance the skin friction coefficient and the local Nusselt number. It is also shown that the suction parameter A (>0) is to decrease the velocity and temperature profiles, but injection parameter A (<0) does the reverse. Results are compared with previously published work and are found to be in excellent agreement.

Effects of slip on unsteady mixed convective flow and heat transfer past a porous stretching surface

This paper investigates the unsteady mixed convective boundary layer flow and heat transfer over a porous stretching vertical surface in presence of slip. Similarity solutions for the transformed governing equations are obtained and the reduced equations are then solved numerically. With increasing values of the unsteadiness parameter, fluid velocity and the temperature are found to decrease in both the presence and absence of slip at the boundary. Fluid velocity decreases due to increasing values of the velocity slip parameter resulting an increase in the temperature field. Skin-friction decreases with the velocity slip parameter whereas it increases with unsteadiness parameter. The rate of heat transfer decreases with the velocity slip parameter while increases with unsteadiness parameter. Same feature is also noticed for thermal slip parameter. Effects of increasing mixed convection parameter on the velocity boundary layer is to increase the velocity field and the temperature decreases in this case.