Mixed Convection Along Vertical Cylinders and Needles with Uniform Surface Heat Flux

Mixed convection along vertical cylinders and needles with uniform surface heat flux is investigated for the entire mixed convection regime. A single modified buoyancy parameter chi and a single curvature parameter lambda are employed in the analysis such that a smooth transition from pure forced convection ( chi equals 1) to pure free convection ( chi equals 0) can be accomplished. For large values of the curvature parameter and/or Prandtl number, the governing transformed equations become stiff. Thus, a numerically stable finite-difference method is employed in the numerical solution in conjunction with the cubic spline interpolation scheme to overcome the difficulties that arise from the stiffness of the equations

Non-Parallel Wave Instability of Mixed Convection Flow on Inclined Flat Plates

A non-parallel flow analysis by an order-of-magnitude approach is performed to investigate the linear wave instability of mixed convection flow along an isothermal inclined flat plate. This analysis removes the previous restriction on the weak dependence of the streamwise variation of disturbance quantities. The resulting non-homogeneous, coupled equations for the momentum and temperature disturbances are solved by a superposition technique along with a modified Thomas transformation method. Critical Reynolds numbers are presented for inclination angles in the range of 0° ≤ γ ≤ 90° (with γ being measured from the horizontal) covering the bouyancy parameter range of -0.15 ≤ Grx/Rex2 ≤ 1 for Prandtl numbers of 0.7 and 7. It is found that the net effect of buoyancy force on the critical Reynolds number is essentially zero at γ = 1.05° when the plate is almost horizontal. For γ \u3e 1.05°, an increase in the value of Grx/Rex2 stabilizes the flow. This behavior is reversed for γ \u3c 1.05°. © 1988

Wave Instability Characteristics for the Entire Regime of Mixed Convection Flow Along Vertical Flat Plates

Wave instability of mixed convection flow along an isothermal vertical flat plate is analyzed by the linear theory for the entire mixed convection regime (0 ≤ χ ≤ 1, χ = [1 + ( Grx Rex2)1 4]-1) for fluids with Prandtl number of 0.7 and 7. In the analysis, the domain beyond the mainflow boundary layer edge (η ≥ η∞) is solved analytically to provide boundary conditions at η = η∞ instead of those at η = ∞. This treatment is important in the use of the modified Thomas transformation when λ(λ = Rex1 2 + Grx1 4) is small. Dual solutions of critical λ* values are seen to exist in the range of 0 ≤ χ ≤ 0.5. The results show that the two limiting neutral stability curves, one for the Blasius flow (χ = 1 or Grx = 0, with λ* = 290.6) and the other for the pure free convection flow (χ = 0 or Rex = 0, with λ* = 33.33), correspond to two different modes. © 1987

Nonparallel Wave Instability Analysis of Boundary-Layer Flows

An order-of-magnitude approach is employed to analyze the linear nonparallel wave instability of boundary-layer flows. This analysis removes the restriction imposed by previous investigators on the weak dependence of the streamwise variation of disturbance quantities. A superposition technique along with a modified Thomas transformation is employed to solve the resulting nonhomogeneous equation for the amplitude function of the disturbance without the use of an adjoint eigenfunction, which is needed in conventional approaches. All of the eigenfunctions are treated in their general forms. The growing rate of the disturbance intensity is found to depend on both streamwise and transverse coordinates

New Finite-Difference Solution Methods for Wave Instability Problems

Two finite-difference methods are proposed for solving wave instability problems with and without coupling between momentum and energy equations. Neutral critical stability results are compared with those generated by the Runge-Kutta integration method in conjunction with an orthonormalization procedure. The new finite-difference methods are found to be very accurate, timesaving, and easy to program. They can also be applied to solve systems of high-order ordinary differential equations