Buoyancy Effects in Forced Laminar Convection Flow Over a Horizontal Flat Plate

The effects of buoyancy-induced streamwise pressure gradients on laminar forced convective flow and heat transfer over a horizontal flat plate are studied analytically by the local similarity and local nonsimilarity methods of solution. Numerical results for the local surface heat transfer, wall shear stress, and velocity and temperature distributions are presented for gases having a Prandtl number of 0.7. It is found that both the local Nusselt number and the friction factor increase with increasing buoyancy forces for aiding flow and decrease with increasing buoyancy forces for opposing flow. With regard to the heat transfer results, significant buoyancy effects were encountered for Grx/Rex5/2 > 0.05 and < −0.03, respectively, for aiding and opposing flows. The buoyancy-affected velocity profiles for the aiding-flow case exhibited an overshoot beyond the free stream velocity. Results from previously reported series solutions and from an integral momentum/energy solution were found to be accurate only when the buoyancy effects are small. The present study provides results for intermediate range buoyancy force effects, which have not been reported previously.

The laminar, steady, horizontal flow past a hot or cold two-dimensional body is examined; the fluid is unbounded, diffusive, and viscous. The presence of significant ambient stable temperature (or density) stratification, or significant buoyancy-induced convection, or both, is considered. A detailed understanding of the fundamental structure of such flows is obtained by developing effective analytical and numerical solution procedures. Chapter 2: This chapter considers the general problem of stably stratified, Oseen flow at large distances upstream and downstream of a body which is represented as a line sink of horizontal or vertical momentum, or as a line heat source or heat dipole. The analysis is focused on the general properties of the horizontal velocity component, as well as on explicit calculation of the horizontal velocity profiles and disturbance streamfunction fields for varying degrees of stratification. For stable stratifications, the flow fields for all four types of singularities exhibit the common feature of multiple recirculating rotors of finite thicknesses, which leads to an alternating jet structure. both upstream and downstream for the horizontal velocity component and to lee-waves in the overall flow. Self-similar formulae for the velocity, temperature, and pressure at very large distances upstream and downstream are also derived and compared with the Oseen solutions Chapter 3: The simultaneous forced and free convection flow of a neutrally- or stably-stratified fluid past a hot or cold horizontal flat plate is investigated by numerically solving the full equations of motion and thermal energy subject only to the Boussinesq approximation. The solutions span the parameter ranges 10 ≤ Re ≤ 100, 0.1 ≤ Pr ≤ 10, -2.215 ≤ Gr/Re5/2 ≤ +2.215, and O ≤ Ri ≤ 6.325, where Re, Pr, Gr, and Ri are based on the overall plate length ℓ and the ambient free stream fluid properties evaluated at the plate level. For all degrees of stratification a hot plate causes an acceleration of the boundary flow near the plate surface relative to the corresponding forced convection flow, thereby increasing both the local skin friction and heat transfer coefficients. On the other hand, the boundary flow adjacent to a cold plate is decelerated and the local skin friction and heat transfer rate are decreased. This deceleration effect is enhanced by either further cooling or increasing the amount of ambient stratification, Ri, leading to boundary-layer separation in some cases. When the effect of the ambient stratification dominates that of local heating or cooling, the boundary-layer displacement increases for decreasing Ri, due to the buoyancy restoring force lessening, thus diminishing the drag. The dimunition in the drag, for the same decrease in Ri, lessens (increases) by slightly heating (cooling) the plate. When the effect of local heating or cooling dominates that of the ambient stratification, the drag is diminished by increasing Ri. A wave-structure exists only for stably-stratified fluids, with the amplitudes and wavelengths of the waves being decreased for increasing Ri.

The mixed convection boundary layer flow over a heated horizontal plate is studied using high accuracy numerical method. Present analysis is valid when the buoyancy force effects are small compared to forced convection effects. The mixed convection boundary layer equations are given with the buoyancy term represented by Boussinesq approximation. The non-similar mixed convection boundary layer equations are solved directly using direct integration method without any approximation for non-similar terms. Numerical results are reported for assisting and opposing mixed convection flows for air. Reported results show that both the local Nusselt number and local friction factor values are increasing with increase in buoyancy parameter for assisting mixed convection flows and decreases with increasing buoyancy parameter for opposing mixed convection flows. Reported results reveal that both the local Nusselt number and the local friction factor values are high compared to local similarity and local non-similarity methods for assisting mixed convection flows and less compared to local similarity and local non-similarity methods for opposing mixed convection flows. Reported results show that velocity and temperature profiles in the boundary layer are exactly matches compared to local similarity method for low value of buoyancy parameter (I¾). For assisting mixed convection flows, the significant buoyancy effects are encountered for I¾ ≥ 0.05 and the velocity exhibit an overshoot beyond the free stream velocity for high values of I¾. For opposing mixed convection flows, the effect of buoyancy is to reduce the velocity compared to pure forced convection. The thickness of thermal boundary layer decreases with increasing buoyancy parameter for assisting mixed convection flows and increases with increasing buoyancy parameter for opposing mixed convection flows. Present study provides an accurate numerical approach to solve non-similar mixed convection boundary flows. © 2010 by Begell House, Inc.

Laminar mixed convection over horizontal flat plate embedded in a non-Darcian porous medium with suction and injection

For the moment, coolants that are composed of aqueous solutions of propylene glycol are widely used in chillers. Such coolants have some advantages over brines or ethylene glycol solutions: non-toxicity, low corrosivity, low crystallization temperature. However, aqueous solutions of the propylene glycol have poor heat transfer efficiency in heat exchangers at low temperatures. One of methods to improve the thermophysical properties of the propylene glycol based coolants and also increasing the heat transfer coefficient in forced convection flow in a tube is an addition of the metal or metal oxides nanoparticles. The prospects of nanoparticle additives to coolants for application in refrigeration systems have been studied. The method of preparation of the nanocoolants based on aqueous solutions of propylene glycol and Al2O3 nanoparticles has been considered. The aggregative stability of Al2O3 nanoparticles (0.53 and 1.03 % mass.) in nanocoolant has been investigated. The results of complex experimental investigation of the thermophysical properties of nanocoolant in temperature range 253-313 К are reported. The comparative analysis of thermophysical properties of nanocoolant and base fluid (aqueous solution of propylene glycol) has been carried out. The results of experimental investigation of the heat transfer coefficient in laminar flow forced convection of coolant and nanocoolant in pipe are presented. It was shown that the heat transfer coefficients for various values of the Reynolds number typical for laminar flow for the traditional coolant was generally less than for the nanocoolant.

Numerical Heat Transfer Analysis in Vertical Rectangular Channels in the Core of a Typical Nuclear Research Reactor The heat transfer characteristics for the case of turbulent forced and mixed convection flow of water through narrow vertical rectangular heated channel simulating a cooling channel of a typical material testing reactor (MTR) have been analysed and numerically investigated. Numerical solutions are performed on demineralized water as coolant passing under atmospheric pressure through narrow rectangular channel of 80 cm length, 7 cm width, and 2.7 mm gap thickness under different heat fluxes that covers almost all possible heat fluxes in the single-phase liquid. Qualitative results are presented for the normalized temperature and velocity profiles in the transverse direction with a comparison between the forced and mixed convection flow for the cases of upward directions. The effect of the axial locations and the parameter Gr/Re on the variation of the normalized temperature profiles in the transverse direction for both the regions of forced and mixed convection and for the upward and downward flow directions are obtained. The normalized velocity profiles in the transverse directions are also determined at different inlet velocities and heat fluxes for the previous cases. A Computational Fluid Dynamics (CFD) study will bring much understanding of the phenomena for the different situations.

Combined forced and free convection flow on vertical surfaces

The problem of combined forced and free convection heat transfer in boundary-layer flow past a heated or cooled, horizontal flat plate is studied in the limits of large and small Prandtl number using the technique of matched asymptotic expansions. It is found that the effects of natural convection are confined to small changes in the basic forced convection velocity and temperature fields providedGr/Re5/2Pr2/3≪1 forPr≫1, orGr/Re5/2Pr1/2≪1 forPr≪1. The governing similarity equations at the first two orders in these small parameters are solved and the results compared with the numerical solutions of Sparrow and Minkowycz (1962).

Mixed convection boundary layer flow of a micropolar fluid on a horizontal flat plate with power law variation in surface temperature

In this paper, natural convection heat transfer over a vertical plate in a Darcy porous medium saturated with a nanofluid subject to heat generation/absorption was theoretically studied. The governing partial differential equations were transformed to a set of ordinary differential equations using similarity transformations and solved using finite difference method. The influence of parametric variation of the Brownian motion parameter, thermophoresis parameter and heat generation/absorption parameter on velocity, temperature and nanoparticles concentration profiles was graphically shown. Impact of non-dimensional parameters on the reduced Nusselt number and reduced Sherwood number was also investigated. The results showed that an increase in the heat generation/absorption parameter would increase temperature and velocity profiles; but, it would decrease concentration profiles. Increase of thermophoresis parameter increased magnitude of concentration profiles while not showing any significant effect on velocity and temperature profiles. The results also indicated that increase of Brownian motion parameter did not demonstrate any significant effect on the magnitude of velocity and temperature profiles. It was found that an increase in the heat generation/absorption parameter decreased the reduced Nusselt number whereas it increased the reduced Sherwood number. For negative values of the Brownian motion parameter, increase of the thermophoresis parameter increased the reduced Nusselt and Sherwood numbers.

Laminar boundary-layer flows with small buoyancy effects

This paper presents a numerical investigation for laminar forced convection flow of a radiating gas in a rectangular duct with a solid element that makes a backward facing step. The fluid is treated as a gray, absorbing, emitting and scattering medium. The governing differential equations consisting the continuity, momentum and energy are solved numerically by the computational fluid dynamics techniques. Since the present problem is a conjugate one and both gas and solid elements are considered in the computational domain, simultaneously, the numerical solution of Laplace equation is obtained in the solid element for temperature calculation in this area. Discretized forms of these equations are obtained using the finite volume method and solved by the SIMPLE algorithm. The radiative transfer equation (RTE) is also solved numerically by the discrete ordinate method (DOM) for computation of the radiative term in the gas energy equation.The streamline and isotherm plots in the gas flow and the distributions of convective, radiative and total Nusselt numbers along the solid-gas interface are presented. Besides, the effects of radiation conduction parameter and also solid to gas conduction ratio as two important parameters on thermo hydrodynamic characteristics of such thermal system are explored. It is revealed that the radiative Nusselt number on the interface surface is much affected by RC parameter but the radiation conduction parameter has not considerable effect on the convective Nusselt number. Comparison between the present numerical results with those obtained by other investigators for the case of non-conjugate problems shows good consistency.

The configuration and the performance of louvered fins for compact automotive radiators is a subject matter widely studied [1–7]. The effect of buoyancy on the performance of these fins, however, is assumed to be negligible because fanned radiators normally operate at higher Reynolds numbers. This paper explores the possibility of radiators operating with acceptable performance at lower Reynolds numbers and presents a series of scaling simulations to measure the effect of buoyancy force on the performance of plain and louvered fins. The simulations are generated from a finite element model of a single fin with attached base surfaces and periodic boundary conditions. Transient calculations are performed until the model reaches steady or quasi-steady state, at which point the effect of buoyancy force is quantified for Reynolds numbers between 45 and 2,179 and Froude numbers between 0.4 and 18.9 by intentionally varying the inlet velocity and the gravity constant. At higher Reynolds numbers, the result is consistent with the published reports in the literature, validating the model to an extent. At lower Reynolds numbers, the result shows that the Stanton number scales with Froude numbers, indicating that natural convection is a significant force of the heat transferred. Natural convection is observed coming from the bottom base surface of the fin rather than the fin itself. As the fin is vertical while the base surface horizontal, this effect depends on the orientation of the radiator. On the amount of heat transferred, Nusselt number has a local saddle point at the transition between natural convection and force convection (Fr = 3 ~ 7). The performance at this point is lower because airflow pattern for each mode of convection differs and, at the transition, neither mode of convection dominates the airflow.

Measurements and predictions of laminar mixed forced and free convection air flow adjacent to an isothermally heated vertical flat surface are reported. Local Nusselt numbers and the velocity and temperature distributions are presented for both the buoyancy assisting and opposing flow cases over the entire mixed convection regime, from the pure forced convection limit (buoyancy parameter ξ = Grx/Rex2 = 0) to the pure free convection limit (ξ = ∞). The measurements are in very good agreement with predictions and deviate from the pure forced and free convection regimes for buoyancy assisting flow in the region of 0.01 ≤ ξ ≤ 10 and for opposing flow in the region of 0.01<ξ< 0.2. The local Nusselt number increases for buoyancy assisting flow and decreases for opposing flow with increasing value of the buoyancy parameter. The mixed convection Nusselt numbers are larger than the corresponding pure forced and pure free convection limits for buoyancy assisting flow and are smaller than these limits for opposing flow. For buoyancy assisting flow, the velocity overshoot and wall shear stress increase, whereas the temperature decreases but the temperature gradient at the wall increases as the buoyancy parameter increases. The reverse trend is observed for the opposing flow. Flow reversal near the wall was detected for the buoyancy opposing flow case at a buoyancy parameter of about ξ = 0.20.

Swirl and buoyancy effects on mixing performance of baffle-plate-type miniature confined multijet