Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces

Abstract

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.

Unsteady Mixed Convection Flow in the Stagnation Region of a Heated Vertical Plate Embedded in a Variable Porosity Medium with Thermal Dispersion Effects

“…for the prescribed surface temperature with those of Ramachandra et al [16] and Scshadri et al [17]. The results are found to be almost compatible to a reasonable degree..…”

“…The partial differential equations governing the flow and the heat transfer have been solved numerically using the finite difference scheme by Pereyra [14]. Particular cases of the present results are compared with previously numerical work by Ramachandra et al [16] and Scshadri et al [17]. The problem is formulated in such way that it represented by Rayleigh type of equation at t=0 and for t →∞ it represented by type of Hemennz equation.…”

“…Equations (13), (14) are uncoupled linear equations while equations (15), (16) are coupled nonlinear equations. Equations (13) and (14) Equations (15), (16) do not admit closed form solutions.…”

“…The mixed convection flow becomes important when the buoyancy forces increase due to the temperature difference between the wall and the free stream. The mixed convection flow in the stagnation region of a vertical plate has been investigated by Ramachandra et al [16]. When there is an impulsive change in the velocity field the inviscid flow is developed instantaneously, but the flow in the viscous layer near the wall is developed slowly which becomes fully developed steady flow after a while.…”

Investigation of Unsteady Mixed Convection Flow near the Stagnation Point of a Heated Vertical Plate embedded in a Nanofluid-Saturated Porous Medium by Self-Similar Technique

“…The mixed convection flows become important when the buoyancy forces, due to the temperature difference between the wall and the free stream, become large. The mixed convection flow in the stagnation flow region of a vertical plate has been investigated by Ramachandra et al [1].…”