Bassem F. Armaly

Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces

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.

Natural Convection on Horizontal, Inclined, and Vertical Plates with Variable Surface Temperature or Heat Flux

Abstract An analysis is performed to study the flow and heat transfer characteristics of laminar free convection in boundary layer flows from horizontal, inclined, and vertical flat plates in which the wall temperature T w ( x ) or the surface heat flux q w ( x ) varies as the power of the axial coordinate in the form T w ( x ) = T ∞ + ax n or q w = bx m . The governing equations are first cast into a dimensionless form by a nonsimilar transformation and the resulting equations are then solved by a finite-difference scheme. Numerical results for fluids with Prandtl numbers of 0.7 and 7 are presented for three representative exponent values under each of the nonuniform surface heating conditions. It has been found that both the local wall shear stress and the local surface heat transfer rate increase as the angle of inclination from the horizontal γ increases or as the local Grashof number increases. An increase in the value of the exponent n or m enhances the surface heat transfer rate, but it causes a decrease in the wall shear stress. Correlation equations for the local and average Nusselt numbers are obtained for the special cases of uniform wall temperature (UWT) and uniform surface heat flux (UHF). Comparisons are also made of the local Nusselt numbers between the present results and available experimental data for the UHF case, and a good agreement is found to exist between the two.

Nonsimilarity solutions for mixed convection from vertical surfaces in porous media : variable surface temperature or heat flux

Abstract Nonsimilarity solutions for mixed convection from a vertical flat plate embedded in a porous medium are reported for two surface heating conditions: variable wall temperature (VWT) and variable surface heat flux (VHF) of the power-law form. The entire mixed convection regime is divided into two regions. One region covers the forced convection dominated regime and the other one covers the free convection dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finite-difference scheme. Four nonsimilarity parameters are introduced. The parameters Rax/Pex and Rax*/Pex3/2 characterize the effect of buoyancy forces on the forced convection for the VWT and VHF cases, respectively; while the parameters Pex/Rax and Pex/Rax*2/3 characterize the effect of forced flow on the free convection for VWT and VHF cases, respectively. Numerical results for both heating conditions are presented. Correlation equations for the local and average Nusselt numbers are also presented.

Three-dimensional convective flow adjacent to backward-facing step - effects of step height

Abstract Three-dimensional simulations are presented for incompressible laminar forced convection flow adjacent to backward-facing step in rectangular duct and the effects of step height on the flow and heat transfer characteristics are investigated. Reynolds number, ducts width, and ducts height downstream from the step are kept constant at Re =343, W =0.08 m, and H =0.02 m, respectively. The selection of the values for these parameters is motivated by the fact that measurements are available for this geometry and they can be used to validate the flow simulation code. Uniform and constant heat flux is specified at the stepped wall downstream from the step, while other walls are treated as adiabatic. The size of the primary recirculation region and the maximum that develops in the Nusselt number distribution increase as the step height increases. The “jet-like” flow that develops near the sidewall within the separating shear layer impinges on the stepped wall causing a minimum to develop in the reattachment length and a maximum to develop in the Nusselt number near the sidewall. The maximum Nusselt number, in the spanwise distribution, develops generally in the same region where the reattachment length is minimum. The maximum in the friction coefficient distribution on the stepped wall increases with increasing step height inside the primary recirculation flow region, but that trend is reversed downstream from reattachment. The three-dimensional behavior and sidewall effects increase with increasing step height.

Mixed convection in buoyancy-assisting, vertical backward-facing step flows

Abstract Mixed convective heat transfer results for laminar, buoyancy-assisting, two-dimensional flow in a vertical duct with a backward-facing step are reported. The present numerical study examines a wide range of inlet flow and wall temperature conditions to cover the domain from pure forced convective flow, where the buoyancy force effects are not present, to the inlet starved convective flow where the buoyancy force effects are significant and where the average inlet velocity is smaller than the corresponding natural convective value. The results compare very favorably with existing, but limited, experimental and numerical data. This study focuses on a backward-facing step geometry with an expansion ratio of 2, but the general observed behaviors are applicable to similar geometries with different expansion ratios. The buoyancy-induced flow decreases the reattachment length and pushes the recirculating region away from the heated wall. Velocity and temperature distributions along with Nusselt numbers and wall friction coefficients are presented for wide ranges of flow and temperature parameters.

Measurements in three-dimensional laminar separated flow

Abstract Velocity measurements are reported for three-dimensional laminar separated airflow adjacent to a backward-facing step using two-component laser Doppler velocimeter. The backward-facing step, with a height of S =1.0 cm, is mounted in a rectangular duct that has an upstream height of h =0.98 cm, downstream height of H =2 cm, and a width of W =8 cm. This geometry provides an aspect ratio of AR=8 and an expansion ratio of ER=2.02. The flow measurements covered a Reynolds number range between 98.5⩽ Re ⩽525. Measurements of velocity distributions reveal that a swirling “jet-like” flow develops near the sidewall in the separating shear layer, and the impingement of that flow on the stepped wall causes a minimum to develop in the spanwise distribution of the reattachment region. Reverse and recirculation flow regions develop adjacent to both the sidewall and the step, and these regions increase in size as the Reynolds number increases. Velocity distributions that were measured at various planes downstream from the step are presented, and predictions compare favorably with these measurements. The results show some interesting flow behaviors that could not be deduced from two-dimensional studies.

Laminar mixed convection in a duct with a backward-facing step: the effects of inclination angle and Prandtl number

Abstract Mixed convective heat transfer results for two-dimensional laminar flow in an inclined duct with a backward-facing step are presented for both the buoyancy assisting and the buoyancy opposing flow conditions. The wall downstream of the step is maintained at a uniform heat flux, while the straight wall that forms the other side of the duct is maintained at a constant temperature equivalent to the inlet fluid temperature. The wall upstream of the step and the backward-facing step are considered as adiabatic surfaces. The inlet flow is fully developed and is at a uniform temperature. The effects of the inclination angle and Prandtl number on the velocity and temperature distributions are reported.

Correlations for Laminar Mixed Convection Flows on Vertical, Inclined, and Horizontal Flat Plates

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.

Natural Convection Along Slender Vertical Cylinders With Variable Surface Temperature

Natural convection in laminar boundary layers along slender vertical cylinders is analyzed for the situation in which the wall temperature T{sub w}(x) varies arbitrarily with the axial coordinate x. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation technique. As an example, numerical results were obtained for the case of T{sub w}(x) = T{infinity} + ax{sup n}, a power-law wall temperature variation. They cover Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of values of the surface curvature parameter. Representative local Nusselt number as well as velocity and temperature profiles are presented. Correlation equations for the local and average Nusselt numbers are also given.

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} = 1) to pure free convection ({chi} = 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. Local Nusselt numbers are presented for 0.1 {le} Pr {le} 100 that cover 0 {le} {chi} {le} 1 ({infinity} {ge} {Omega}{sub x} {ge} 0) and 0 {le} {Lambda} {le} 50. For needles ({Lambda} {ge} 5), the local Nusselt numbers (Nu{sub x}/Re{sub x}{sup 1/2} + Gr{sub x}{sup 1/5}*) are found to be nearly independent of the buoyancy parameter {chi}. Correlation equations for the local Nusselt numbers are also presented.