T. S. Chen

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.

Combined heat and mass transfer in natural convection along a vertical cylinder

Abstract An analytical study is performed to examine the heat- and mass-transfer characteristics of natural convection flow along a vertical cylinder under the combined buoyancy force effects of thermal and species diffusion. The analysis is restricted to processes in which the diffusion-thermo and thermo-diffusion effects as well as the interfacial velocities arising from species diffusion are negligible. The surface of the cylinder is either maintained at a uniform temperature/concentration or subjected to a uniform heat/mass flux. Among the major parameters of the problem are curvature of cylinder, Prandtl and Schmidt numbers, thermal and concentration Grashof numbers, and the relative buoyancy force effect between species and thermal diffusion. Numerical results are obtained and presented for species diffusion of interest in air and water. For both heating/diffusing conditions, the local wall shear stress, the local Nusselt number, and the local Sherwood number increase with increasing curvature of the cylinder. In addition, the first two quantities are found to increase and decrease as the buoyancy force from species diffusion assists and opposes, respectively, the thermal buoyancy force. The mass-transfer parameter or the local Sherwood number is enhanced as the thermal buoyancy force increases. Finally, the combined buoyancy force from thermal and species diffusion provides larger Nusselt and Sherwood numbers for uniform surface heat/mass flux than for uniform wall temperature/concentration.

Analysis of mixed forced and free convection about a sphere

Abstract An analysis is performed to study the flow- and heat-transfer characteristics of laminar mixed forced and free convection about a sphere. The transformed conservation equations of the nonsimilar boundary layers are solved by a finite difference method. Numerical results for gases having a Prandtl number of 0.7 are presented for buoyancy parameters which cover the entire regime of mixed convection, ranging from pure forced convection to pure free convection. In general, it is found that both the local-friction factor and the local Nusselt number increase with increasing buoyancy force for aiding flow and decrease with increasing buoyancy force for opposing flow. The effects of the variation of the local free stream velocities on the wall shear and surface heat-transfer results are also examined. With respect to the heat-transfer results, the buoyancy force effects on forced convection become significant for Gr/Re 2 > 1.67 and 2 /Gr > 0.01. The buoyancy-affected velocity profiles exhibit an overshoot beyond the local free stream velocity for aiding flow and an S-shape for opposing flow.

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.

Combined heat and mass transfer in natural convection on inclined surfaces

The combined heat and mass transfer characteristics of natural convection flow along inclined surfaces are studied analytically. The buoyancy forces arise from both temperature and concentration variations in the fluid. In the analysis, the diffusion-thermo and thermo-diffusion effects are neglected, as are the interfacial velocities resulting from mass diffusion. The surfaces are either maintained at a uniform temperature/concentration or subjected to a uniform heat/mass flux. The important parameters of the problem include Prandtl and Schmidt numbers, thermal and concentration Grashof numbers, the relative buoyancy force effect between species and thermal diffusion, and the angle of inclination from the vertical. Numerical results are presented for diffusion of common species into air and water. For both heating/diffusing conditions, the wall shear stress and the local Nusselt number are found to increase and decrease as the buoyancy force from species diffusion assists and opposes, respectively, the th...

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.

Bouyancy Effects on Forced Convection Along a Vertical Cylinder

The effects of buoyancy forces on the longitudinal forced convective flow and heat transfer along an isothermal vertical cylinder are studied analytically. This problem does not admit similarity solutions, the nonsimilarity arising both from the transverse curvature ξ = (4/r0 ) (νx/u∞)1/2 of the cylindrical surface and from the buoyancy effect expressible as Ω = Grx /Rex2 where Grx and Rex are, respectively, the Grashof and Reynolds numbers. The governing equations are solved by the local nonsimilarity method in which all the nonsimilar terms are retained in the conservation equations and only in the derived subsidiary equations are terms selectively neglected according to the two-equation or three-equation model. Numerical results for the velocity and temperature profiles, wall shear stress, and surface heat transfer for the case of assisting flow are presented for gases having a Prandtl number of 0.7 over a wide range of values of ξ from 0 (i.e., a flat plate) to 4.0 and Ω from 0 (i.e., pure forced convection) to 2.0. It is found that the wall shear and surface heat transfer rate increase with increasing buoyancy force and increasing curvature of the surface.

Mixed Convection on Inclined Surfaces

An analysis is performed to study the effects of buoyancy force on the heat transfer characteristics of laminar forced convection flow over an inclined flat surface which is either maintained at a uniform temperature or subjected to a uniform heat flux. Numerical results are presented for Prandtl numbers of 0.7 and 7 over a wide range of values of the buoyancy force parameters, with the angle of inclination ranging from 0 to 90 deg from the vertical. In general, it is found that for both surface heating conditions, the local friction factor and the local Nusselt number increase with increasing buoyancy force for assisting flow and decrease with increasing buoyancy force for opposing flow. In addition, the effects of the buoyancy force on these two quantities are found to diminish as the angle of inclination increases. A comparison is also made of the results between the case of uniform wall temperature and the case of uniform surface heat flux.

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.