Steady Mixed Convection Boundary-layer Flow Research Articles

Magnetohydrodynamic flow and heat transfer of a Jeffrey fluid towards a stretching vertical surface

This study investigates the steady-mixed convection boundary layer flow near a stagnation point that runs about a linearly stretched vertical surface filled with a Jeffery fluid in the presence of a transverse magnetic field. It is assumed that the external velocity impinges normally to the wall and the wall temperature varies linearly with the distance from the stagnation point. The governing partial differential equations that govern the fluid flow are transformed into a set of coupled ordinary differential equations, which are then solved numerically using a finite-difference scheme. The numerical results are presented for some values of parameters, namely the Deborah number ?, the Prandtl number Pr, the magnetic parameter M and the mixed convection parameter ?, for both assisting and opposing flows.

EXISTENCE AND NON-UNIQUENESS OF SOLUTION FOR A MIXED CONVECTION FLOW THROUGH A POROUS MEDIUM

In this paper we reconsider the problem of steady mixed convection boundary-layer flow over a vertical flat plate studied in [6],[7] and [13]. Under favorable assumptions, we prove existence of multiple similarity solutions, we study also their asymptotic behavior. Numerical solutions are carried out using a shooting integration scheme.

Mixed convection boundary-layer flow past a horizontal circular cylinder embedded in a porous medium filled with a nanofluid under convective boundary condition

The steady mixed convection boundary-layer flow past a horizontal circular cylinder in a stream flowing vertically upwards embedded in porous medium filled with a nanofluid is studied, taking into account the thermal convective boundary condition is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticle volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.

Mixed convection boundary-layer flow on a horizontal flat surface with a convective boundary condition

The steady mixed convection boundary-layer flow on an upward facing horizontal surface heated convectively is considered. The problem is reduced to similarity form, a necessary requirement for which is that the outer flow and surface heat transfer coefficient are spatially dependent. The resulting similarity equations involve, apart from the Prandtl number, two dimensionless parameters, a measure of the relative strength of the outer flow M and a heat transfer coefficient γ. The free convection, M=0, case is considered with the asymptotic limits of large and small γ being derived. Results for the general, M>0, case are presented and the asymptotic limit of large M being treated.

Mixed Convection Boundary-Layer Flow Along a Vertical Cylinder Embedded in a Porous Medium Filled by a Nanofluid

The steady mixed convection boundary-layer flow on a vertical circular cylinder embedded in a porous medium filled by a nanofluid is studied for both cases of a heated and a cooled cylinder. The governing system of partial differential equations is reduced to ordinary differential equations by assuming that the surface temperature of the cylinder and the velocity of the external (inviscid) flow vary linearly with the axial distance x measured from the leading edge. Solutions of the resulting ordinary differential equations for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction \({\phi}\), the mixed convection or buoyancy parameter λ and the curvature parameter γ. Results are presented for the specific case of copper nanoparticles. A critical value λc of λ with λc λc for both aiding, λ > 0 and opposing, λ < 0, flows. Asymptotic solutions are also determined for both the free convection limit \({(\lambda \gg 1)}\) and for large curvature parameter \({(\gamma \gg 1)}\).

Non-Darcy mixed convection from a horizontal plate embedded in a nanofluid saturated porous media

The problem of steady mixed convection boundary-layer flow over an impermeable horizontal flat plate embedded in a porous medium saturated by a nanofluid is numerically studied. The model used for the nanofluid incorporates only the effect of the volume fraction parameter. The surface of the plate is maintained at a constant temperature and a constant nano-particle volume fraction. The resulting governing partial differential equations are transformed into a set of two ordinary (similar) equations, which are solved using the bvp4c function from Matlab. A comparison is made with the available results in the literature, and the present results are in very good agreement with the known results. A representative set of numerical results for the reduced heat transfer from the plate, dimensionless velocity and temperature profiles is graphically and tabularly presented. Also, the salient features of the results are analyzed and discussed.

Mixed convection boundary-layer flow about an isothermal solid sphere in a nanofluid

The steady mixed convection boundary-layer flow of a nanofluid about a solid sphere with constant surface temperature has been studied for cases of both assisting and opposing flows. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions for the flow and heat-transfer characteristics are evaluated numerically for various values of the parameters, namely the nanoparticle volume fraction φ and the mixed convection parameter λ at Prandtl numbers Pr=0.7 and 6.2. The three different types of nanoparticles considered are Al2O3, Cu and TiO2, using water-based fluid with Pr=6.2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the skin friction coefficient and the heat-transfer rate at the surface also increase. This leads to an increase in the value of the mixed convection parameter λ, which at first gives no separation.

Mixed Convection Boundary-Layer Flow in a Porous Medium Filled with Water Close to its Maximum Density

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.

Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C: variable surface heat flux

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4°C (maximum density) when the surface heat flux varies as xm and the velocity outside the boundary layer varies as x(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter λ is greater than some critical value λc (dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λc is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and the limits as m → ∞ and as m → −1.