The steady boundary-layer flow near the stagnation point on an impermeable vertical surface with slip that is embedded in a fluid-saturated porous medium is investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary differential equations. This system is then solved numerically. The features of the flow and the heat transfer characteristics for different values of the governing parameters, namely, the Darcy–Brinkman, Γ, mixed convection, λ, and slip, γ, parameters, are analysed and discussed in detail for the cases of assisting and opposing flows. It is found that dual solutions exist for assisting flows, as well as those usually reported in the literature for opposing flows. A stability analysis of the steady flow solutions encountered for different values of the mixed convection parameter λ is performed using a linear temporal stability analysis. This analysis reveals that for γ = 0 (slip absent) and Γ = 1 the lower solution branch is unstable while the upper solution branch is stable.

Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip

Studies of heat and mass exchange between leaves and their local environment are central to our understanding of plant-atmosphere interactions. The transfer across aerodynamic leaf boundary layers is generally described by non-dimensional expressions which reflect largely empirical adaptations of engineering models derived for flat plates. This paper reviews studies on leaves, and leaf models with varying degrees of abstraction, in free and forced convection. It discusses implecations of finding for leaf morphology as it affects – and is affected by – the local microclimate. Predictions of transfer from many leaves in plant communities are complicated by physical and physiological feedback mechanisms between leaves and their environment. Some common approaches, and the current challenge of integrating leaf-atmosphere interactions into models of global relevance, are also briefly addressed.

Tansley Review No. 59 Leaf boundary layers

Dual solutions for mixed convective stagnation-point flow of an aqueous silica-alumina hybrid nanofluid

The stagnation point flow toward a stretching vertical sheet is investigated in this study. The temperature and velocity of the sheet as well as the velocity of the external flow are assumed to vary in a power law with the distance from the stagnation point. The governing system of equations is first transformed into a dimensionless form, and then the resulting equations are solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that, for opposing flow, dual solutions exist in the neighborhood of the separation region, whereas for assisting flow the solution is unique.

Mixed Convection on the Stagnation Point Flow Toward a Vertical, Continuously Stretching Sheet

Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface

Laminar mixed convection in two-dimensional stagnation flows around heated surfaces is analyzed for both cases of an arbitrary wall temperature and arbitrary surface heat flux variations. The two-dimensional Navier-Stokes equations and the energy equation governing the flow and thermal fields are reduced to a dimensionless form by appropriate transformations and the resulting system of ordinary differential equations is solved in the buoyancy assisting and opposing regions. Numerical results are obtained for the special cases for which locally similar solutions exist as a function of the buoyancy parameter. Local wall shear stress and heat transfer rates as well as velocity and temperature distributions are presented. It is found that the local Nusselt number and wall shear stress increase as the value of the buoyancy parameter increases in the buoyancy assisting flow region. A reverse flow region develops in the buoyancy opposing flow region, and dual solutions are found to exist in that flow regime for a certain range of the buoyancy parameter.

Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces

Local Nusselt numbers for laminar mixed convection flows along isothermal vertical, inclined, and horizontal flat plates are presented for the entire mixed convection regime for a wide range of Prandtl numbers, 0.1 ≤ Pr ≤ 100. Simple correlation equations for the local and average mixed convection Nusselt numbers are developed, which are found to agree well with the numerically predicted values and available experimental data for both buoyancy assisting and opposing flow conditions. The threshold values of significant buoyancy effects on forced convection and forced flow effects on free convection, as well as the maximum increase in the local mixed convection Nusselt number from the respective pure convection limits, are also presented for all flow configurations. It is found that the buoyancy or forced flow effect can increase the surface heat transfer rate from pure forced or pure free convection by about 20 percent.

N. Ramachandran

Papers

Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces

Correlations for laminar mixed convection flows on vertical, inclined, and horizontal flat plates

Measurements and Predictions of Laminar Mixed Convection Flow Adjacent to a Vertical Surface

Mixed Convection Over a Horizontal Plate

Correlations for laminar mixed convection on vertical, inclined and horizontal flat plates with uniform surface heat flux