Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition

Abstract

The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. m = 1 5 is found to be a transitional case with different behaviour depending on whether m > 1 5 or m < 1 5 . For m > 1 5 , there is a critical value λ c with solutions only for λ ≥ λ c , a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For 0 < m < 1 5 , there is a value of B where there is a change in behaviour from that seen for m > 1 5 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m < 0, though still in the range when there is a solution to the Falkner-Skan, λ = 0, problem, the behaviour is similar to that seen for m > 1 5 .

Ingham Problem for Mixed Convection Flow of a Nanofluid over a Moving Vertical Plate with Suction and Injection Effects

“…In contrast to Devi et al (1991) and Ramachandran et al (1988), Ishak et al (2010) and Rhida (1996) reported that dual solutions existed in both the opposing and the assisting flow regions. This finding was supported by Nazar and Pop (2004), Rahman et al (2015), Roşca et al (2014) and recently by Abbasbandy et al (2017), who similarly demonstrated the existence of dual solutions in the mixed convection boundary layer flow.…”

Impact of Nonlinear Thermal Radiation on the Time-Dependent Flow of Non-Newtonian Nanoliquid over a Permeable Shrinking Surface

“…Holding the system of Equations (18)- (26) as an IVP numerically, we need the value for y 2 (0), θ(0), and p(0), i.e., β 1 , β 2 , and β 3 , respectively. However, these values are not mentioned in Equation (25). The initial estimated values for y 2 (0), θ(0), and p(0) are speculated and bvp4c was obtained via the MATLAB software to achieve accurate results.…”

“…Yao et al [24] investigated flow with a permeable convectively heated shrinking and stretching wall and found an exact result. Rahman et al [25] utilized the convective condition to find the solution numerically for mixed convective flow through an upright flat plate in a convective condition. Mustafa et al [26] analyzed Maxwell liquid and an exponential stretched surface with a convective condition engrossed in a nanoliquid.…”

Three-Dimensional Magnetohydrodynamic Mixed Convection Flow of Nanofluids over a Nonlinearly Permeable Stretching/Shrinking Sheet with Velocity and Thermal Slip

“…They also examined the existence of dual solutions in both opposing and assisting flows for two cases: permeable and impermeable. Moreover, several other published papers have reported the existence of dual solutions in mixed convection flow (see [7][8][9][10] for more details).…”