Pure Free Convection Research Articles

Cross Diffusion and Internal Heat Generation Effects on Mixed Convection of Non-Newtonian Fluids Flow Adjacent to a Vertical VHF/VMF Wedge in Porous Media: the Entire Regime

The problem of cross diffusion (Soret/Dufour) and internal heat generation effects on combined convection flow of non-Newtonian fluids flow over the vertical wedge in a saturated porous medium with the entire regime is solved numerically. The internal heat generation is assumed to be an exponential decaying form. The power law model of Ostwald-de-Waele for non-Newtonian fluids is considered here. The entire regime of the combined convection is included, as the combined convection parameter varies from 0 (pure free convection) to 1 (pure forced convection). The transformed equations are obtained by using a suitable coordinate transformation and then Keller box method (KBM) is utilized to solve the non-similar equations for the variable heat flux and variable mass flux (VHF/VMF) conditions. Comparisons with the previously published article are performed and the good agreement is achieved. The main numerical results for the dimensionless temperature and concentration distributions, the local Nusselt and Sherwood numbers are obtained.

Aiding and Opposing Re-circulating Mixed Convection Flows in a Square Vented Enclosure

A numerical study is performed to investigate mixed convective flow in a vertically vented square enclosure with heating or cooling one of the vertical walls and the other three walls are insulated. This study is conducted to analyse and clarify the intricate interaction between the buoyancy-induced flow and the pressure-driven external flow in a vertical upward laminar air jet for both assisting and opposing buoyancy situations. The approach of spectral-element that is introduced as a finite-element method with high-order Lagrange polynomials as interpolating functions, is applied to discretise unsteady Navier-Stokes, continuity and energy equations, and for calculating the velocity and temperature fields. The numerical solutions are obtained for air having a Prandtl number of (Pr = 0.7) and for buoyancy parameters which cover the whole mixed convection region, ranging from pure forced convection with a Reynolds number ranging between (10 ⩽Re ⩽350) to pure free convection with a Richardson number ranging between (0 ⩽Ri ⩽30), with a single dimensionless enclosure size. The results reveal that the flow and thermal patterns can be significantly influenced by both aiding and opposing buoyancies. Also, the mean heat transfer rates increase with increasing either the buoyancy force Richardson number or the forced flow Reynolds number in assisting flows. However, in opposing flows, it is found that the mean heat transfer rates decrease with increasing the buoyancy effects for small to moderate (Ri ⩽2) but, they begin rising for higher Richardson number when the free convection starts domination the flow.

Correcting for tube curvature effects on condensation in the presence of a noncondensable gas in laminar regimes

Filmwise vapor condensation in the presence of noncondensable gases (NCG) continues to attract interest due to its widespread range of applications. In studies of NCG effects on condensation over external surfaces, experimentalists and analysts alike usually employ correction factors to transfer tube condensation rates to flat plate equivalents or vice-versa. For laminar flows over vertical cylinders, these factors are estimated from pure convection correlations as a function of the Grashof number and tube curvature only. We show that this procedure is not rigorous and leads to significant errors, especially at low NCG fractions and small tube radii. Indeed, the usual way of correcting for curvature is strictly valid only in the limit where the NCG fraction is so large that convection heat transfer dominates condensation. On the other hand, as the NCG fraction becomes vanishingly small, the vapor condensation rates should tend to values predicted by the Nusselt film theory, and no enhancement due to tube curvature is to be expected.This paper focuses on vapor condensation as the gas mixture moves along a vertical tube in the laminar free convection regime. The gas and liquid film boundary layer equations are coupled at the gas/film interface and a marching solution procedure using local non-similarity is adopted. The methodology is first verified for near pure free convection flows as well as previous analyses of condensation over a flat surface. The model is subsequently validated against data on steam condensation on a square plate in the presence of air. Finally, a correlation is deduced from the parametric numerical results to allow a proper correction for curvature effects when vapor condenses in the presence of a NCG. The proposed correction spans the whole range of NCG fractions, and displays the expected behavior at the extremes of this range.

Heat and Mass Transfer on the Mixed Convection of Non-Newtonian Fluids Over a Vertical Wedge with Soret/Dufour Effects and Internal Heat Generation: Variable Wall Temperature/Concentration

This numerical analysis investigated the effects of heat and mass transfer characteristics on the mixed convection flow of non-Newtonian fluids over the vertical wedge in a saturated porous medium with Soret/Dufour effects and internal heat generation. The numerical modeling of this problem has attracted considerable attention from researchers because it has practical applications in biological sciences, electronic cooling, advanced nuclear systems, etc. The internal heat generation is assumed to be an exponential decaying form. The power-law model of Ostwald–de Waele for non-Newtonian fluids is considered. The surface of the vertical wedge is kept at variable wall temperature and concentration. In the analysis of mixed convection, which included free convection and forced convection, parameter varies from 0 (pure free convection) to 1 (pure forced convection). The transformed equations are obtained by using a suitable coordinate transformation, and then, Keller box method is utilized to solve the non-similar equations. Comparisons with data published previously showed good agreement. Both the local Nusselt number and the local Sherwood number increase with increasing the exponent of variable wall temperature/concentration. Increasing the internal heat generation coefficient decreases (increases) the local Nusselt (Sherwood) number. As the power-law index is increased, the local Nusselt and Sherwood numbers are decreased.

Simulation of a novel hybrid solar photovoltaic/wind system to maintain the cell surface temperature and to generate electricity

A hybrid solar photovoltaic/wind system is proposed and investigated theoretically. The hybrid system is based on attaching a converging inclined duct beneath the photovoltaic (PV) panels and directed upward after the end of the panels. A wind turbine is attached at the exit of the converging duct. The converging duct will capture wind currents that at its inlet and enhances these current by buoyancy effect created by the rejected heat from the panels. The mixed convection air flow is used in cooling the PV panels and in generating electricity by driving the wind turbine at the duct exit. A mathematical model is proposed to describe the system hydrodynamic and thermal behavior. In addition to the mixed convection case, the pure free convection case, when there is no wind speed, has been tested. The design of the wind duct capturing system is not included in this study, which should be carefully manufactured to eliminate the reversed flow. The simulation results show that the integration of both systems not only enhances the performance of PV cell due to the effective cooling but also generates more electric power from the inserted turbine. At low wind speeds, it is found that the ducting system helps more in cooling the panels rather than driving the wind turbine. At these low wind speeds, the buoyancy effect may have a significant effect. However, at high wind speeds, the ducting system acts in both cooling the panels and driving the turbine, and at these high speeds, the buoyancy effect is insignificant.

Coupled radiation and natural convection within an inclined sinusoidal solar collector heated from below

The main objective of this article is to study the effect of coupled mode free convection with surface radiation on the fluid flow behavior inside a tilted solar collector having a flat glass cover and a wavy bottom absorber. The cavity is subject to vertical gradient temperature while its top sidewalls remain thermally insulated. The dimensionless governing equations under Boussinesq approximation are coupled with a radiative model through the boundary conditions and solved by the Finite Volume Method. The numerical results are discussed in terms of streamlines, isotherms, convective and radiative Nusselt number along the cover plate for various aspect ratios, inclination angle, emissivity and Rayleigh number. These results highlighted the condition of the enclosure performance and revealed that the heat and fluid flow fields are affected by surface radiation and the above parameters. In the end, correlations for predicating the convection heat loss in term of averaged Nusselt numbers are developed in both pure free convection and coupled convection-surface radiation modes.

Heat transfer measurement of the cylindrical heat sink with sintered-metal-bead-layers fins and a built-in motor fan

This work sintered 0.5–0.85mm-diameter copper beads smoothly with the radial plate fins of the copper heat sink by thin layers at high temperature to form a LED cooling device with sintered-metal-bead-layer fins. A motor fan could be installed or un-installed into the heat sink, which would result in the mixed convection heat transfer or the pure free convection heat transfer conditions, respectively. This work also experimentally investigated the effect of the sintered-metal-bead layers on the total heat transfer under the above-mentioned two heat transfer conditions. The experimental groups were the plate-shape sintered-metal-bead (Model B) and strip-shape sintered-metal-bead heat sinks (Model C). The pure copper finned heat sink (Model A) was set as the control group. The results demonstrated that the thermal resistances of the Model B and Model C were separately 29% and 16% higher than that of the Model A at the temperature difference between the heated surface and the ambient (ΔT≒30°C) and the pure free convection heat transfer condition (i.e. the heat sink without motor fan). It reveals that the present sintered-metal-bead layers cannot strengthen the free convection heat transfer. However, by comparing with the heat sinks without motor fan, the Model A, Model B and Model C built-in a motor fan had lower thermal resistances reduced separately by about 58%, 78% and 50%. It validates the effect of the built-in motor fan on the heat transfer enhancement, especially for the Model B with the plate-shape sintered-metal-bead layers. The thermal resistance of Model B was 31% lower than that of Model A at the mixed convection heat transfer condition (i.e. the heat sink with a motor fan).

Effect of convection on the Penman–Monteith model estimates of transpiration of hot pepper grown in solar greenhouse

Accurate estimate of transpiration in greenhouses is of great importance for developing water-saving management practices. In this study, we evaluated the performance of the Penman–Monteith (P–M) model using aerodynamic resistance values estimated from heat transfer coefficient (h) to predict transpiration of hot pepper grown in a solar greenhouse based on different convection types. The reference transpiration was measured by sap flow meters. Results showed that heat transfer was conducted through mixed convection in about 81% and 71% of the study period, respectively, for the 2010–2011 and 2011–2012 season, while the rest of the study period was pure free convection which occurred mainly at night and in the early morning when transpiration rates were low and no pure forced convection occurred in the study solar greenhouse. Under pure free convection, the P–M model with h calculated by the McAdams equation tends to underestimate the transpiration, and the model with h calculated by the Stanghellini equation performed similar to the one by the McAdams equation. Under mixed convection, the P–M model with h calculated by the Stanghellini equation can accurately estimate the transpiration of hot pepper. This study shows that the P–M model with h estimated by the Stanghellini equation can well predict the transpiration rates of hot peppers grown in solar greenhouses without distinguishing the convection types.

Exact Solutions for Free Convective Heat Transfer in Nanofluids in a Vertical Channel

The Buongiorno model for convective heat transfer in nanofluids was modified to fully account for the effects of nanoparticle volume fraction distributions on the continuity, momentum and energy equations. A set of exact solutions have been obtained for thermally fully developed laminar free convection of nanofluid in a vertical channel with isothermal hot and cold vertical walls. It has been found that the volume fraction of nanoparticles increases exponentially towards the cold wall over which the downward flow of high effective density is induced. Unlike in forced convective flows of nanofluid in channels and tubes, no anomalous heat transfer enhancement has been observed, so that the Nussult number based on the thermal conductivity of nanofluid stays close to unity as in pure base fluid free convection.

Combined Convective Boundary Layer Flow Over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid

A boundary layer analysis is presented for the mixed convection past a horizontal plate in a porous medium saturated with a nano fluid. The prescribed heat and mass flux boundary conditions are considered. The entire regime of the mixed convection is included, as the mixed convection parameter ξ varies from 0 (pure free convection) to 1 (pure forced convection). The transformed nonlinear system of equations is solved by using an implicit infinite difference method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid: entire regime

A boundary layer analysis is presented for the mixed convection past a vertical wedge in a porous medium saturated with a nanofluid. The entire regime of the mixed convection is included since the mixed convection parameter of ξ varies from zero (pure free convection) to one (pure forced convection). The transformed non-linear system of equations is solved by using an implicit infinite difference method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) on these parameters has been discussed. The results indicate that as Nr and Nt increase, the heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) decrease. As Nb increases, the surface mass transfer rates increase whereas the surface heat transfer rate decreases. As Le increases, the heat transfer rate decreases whereas the mass transfer rate increases. As the wedge angle increases, the heat and mass transfer rates increase.

Network Simulation of Laminar Convective Heat and Mass Transfer over a Vertical Slender Cylinder with Uniform Surface Heat and Mass Flux

The steady, laminar axisymmetric convective heat and mass transfer in boundary layer flow over a vertical thin cylindrical configuration in the presence of significant surface heat and mass flux is studied theoretically and numerically. The governing boundary-layer equations for momentum, energy and species conservation are transformed from a set of partial differential equations in a (x,r) coordinate system to a ([,K) system using a group of similarity transformations. The resulting equations are solved using the Network Simulation Method (NSM) for the buoyancy-assisted pure free convection and also the pure forced convection cases, wherein the effects of Schmidt number, Prandtl number and surface mass parameter on velocity, temperature and concentration distributions in the regime are presented graphically and discussed. For the buoyancy-assisted pure free convection case, nondimensional velocity (wf/wK) is found to increase with a rise in surface mass transfer (S) but decrease with increasing Prandtl number (Pr), particularly in the vicinity of the cylinder surface (small radial coordinate, K). Dimensionless temperature (T) decreases however with increasing S values from the cylinder surface into the free stream; with increasing Prandtl number, temperature is strongly reduced, with the most significant decrease at the cylinder surface. Dimensionless concentration (I) is decreased continuously throughout the boundary layer regime with an increase in S; conversely I is enhanced for all radial coordinate values with an increase in Prandtl number. For the pure forced convection case, velocity increases both with dimensionless axial coordinate ([) and dimensionless radial coordinate (K) but decays smoothly with increasing Prandtl number and increasing Schmidt number, from the cylinder surface to the edge of the boundary layer domain. The model finds applications in industrial metallurgical processes, thermal energy systems, polymer processing, etc.

Artificial boiling heat transfer in the free convection to carbonic acid solution

Free convection phenomenon has been experimentally investigated around a horizontal rod heater in carbonic acid solution. Because of the tendency of the solution to desorb carbon dioxide gas when temperature is increased, bubbles appear when cylinder surface is heated. The bubbles consists mainly carbon dioxide and also a negligible amount of water vapor. The results present that dissolved carbon dioxide in water significantly enhances the heat transfer coefficient in compare to pure free convection regime. This is mainly due to the microscale mixing on the heat transfer surface, which is induced by bubble formation. In this investigation, experiments are performed at different bulk temperatures between 288 and 333K and heat fluxes up to 400kWm−2 at atmospheric pressure. Bubble departure diameter, nucleation site density and heat transfer coefficient have been experimentally measured. A model has been proposed to predict the heat transfer coefficient.

Soret and Dufour effect on double diffusion mixed convection from a vertical surface in a porous medium saturated with a non-Newtonian fluid

A non-similar boundary layer analysis is presented to study the flow, heat and mass transfer characteristics of non-Darcian mixed convection of a non-Newtonian fluid from a vertical isothermal plate embedded in a homogeneous porous medium with the effect of Soret and Dufour and in the presence of either surface injection or suction. The value of the mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonian fluids, from pseudoplastics to dilatant fluids. The numerical solution of the problem is derived using a Runge–Kutta integration scheme with Newton–Raphson shooting technique. Distributions for velocity, temperature and concentration, as well as for the rate of wall heat and mass transfer, have been obtained and discussed for various physical parametric values.

Influence of surface mass transfer on mixed convection flows over non-isothermal horizontal flat plates

Non-similar solution of a steady mixed convection flow over a horizontal flat plate in the presence of surface mass transfer (suction or injection) is obtained when there is power-law variation in surface temperature. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A non-similar mixed convection parameter is considered which covers the whole convection regime, namely from pure free convection to pure forced convection. Numerical results are reported here to account the effects of Prandtl number, surface temperature, surface mass transfer parameter (suction or injection) on velocity and temperature profiles, and skin friction and heat transfer coefficients.

Heat-flux scaling for weakly forced turbulent convection in the atmosphere

Observational data in the atmosphere indicate that conventionally defined drag and heat transfer coefficients increase rapidly as wind speed falls. It is shown here that, at sufficiently low wind speeds, the observed heat flux is nearly independent of wind speed but the drag increases linearly with it. These findings are not consistent with the free-convection limit of the Businger relations for Monin–Obukhov theory, and lend support to the ideas of Ingersoll (1966) and Grachev (1990), till now checked only against laboratory experiments. We propose here that it is useful to define, within the regime of mixed convection, a sub-regime of ‘weakly forced convection’ in which, to a first approximation, the heat flux is determined by temperature differentials as in free convection and the momentum flux by a perturbation, linear in wind, on free convection. It is further proposed that this regime is governed by velocity scales determined by the heat flux (rather than by the friction velocity as in classical turbulent boundary layer theory). Three candidates for the heat-flux velocity scale are considered; novel definitions of the drag and heat exchange coefficients, based on the preferred scale, are found to show very weak dependence on wind speed up to values of about 5–10 m s $^{-1}$ ; but there is some evidence that the usefulness of heat-flux scaling may extend beyond the velocity limits where pure free-convection scaling for heat flux is valid.

Influence of radiation on mixed convection over a wedge in non-Darcy porous medium

The influences of radiation on mixed convection flow of an optically dense viscous fluid along an isothermal wedge embedded in non-Darcy porous medium, in the presence of heat source/sink are numerically investigated. The entire mixed convection regime is covered by a single parameter χ from the pure free convection limit (χ=0) to the pure forced convection limit (χ=1). Forchheimer’s extension is employed to describe the fluid flow in the porous medium and the Rosseland diffusion approximation is considered to describe the radiative heat flux in the energy equation. The governing equations, including internal heat source/sink, are first transformed into a dimensionless form by the nonsimilar transformation and then solved by the Keller box method. The effect of the radiation parameter, mixed convection parameter, Forchheimer number and heat source/sink parameter on the velocity and temperature profiles as well as on the local Nusselt number is presented and analyzed. The results are compared with those known from the literature and excellent agreement between the results is obtained.

Mixed Convection-Radiation in Power-Law Fluids Along a NOn-Isothermal Wedge in a Porous Medium with Variable Permeability

A boundary layer analysis has been presented for the interaction of mixed convection with thermal radiation in laminar boundary flow from a vertical wedge in a porous medium saturated with a power-law type non-Newtonian incorporating the variation of permeability and thermal conductivity. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. The combined convection non-similar parameter we note that χ=0 and 1 correspond to pure free and forced convection cases. The Rosseland approximation is used to describe the radiative heat flux in energy equation. Velocity and temperature profiles as well as the local Nusselt number are presented.

HALL CURRENT AND OHMIC HEATING EFFECTS ON MIXED CONVECTION BOUNDARY LAYER FLOW OF A MICROPOLAR FLUID FROM A ROTATING CONE WITH POWER-LAW VARIATION IN SURFACE TEMPERATURE

The problem of laminar mixed convection boundary layer flow of an electrically conducting micropolar fluid from a constantly rotating cone is analyzed, taking into account the effects of Hall current and Ohmic heating. The flow is subjected to a uniform strong transverse magnetic field normal to the cone surface. In this study, the surface temperature is assumed to vary as a power of the axial coordinate measured along the cone surface. A non-similar mixed convection parameter and a pseudo-similarity variable η are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically. The mixed convection parameter is chosen to cover the entire regime of mixed convection from the pure forced limit to the pure free convection limit. Results for the velocity, angular velocity and thermal functions are displayed for a range of values of magnetic parameter, Hall parameter and Eckert number

Non-Darcy mixed convection in power-law fluids along a non-isothermal horizontal surface in a porous medium

The non-similar non-Darcy mixed convection from a horizontal surface in a porous medium saturated with a power-law type non-Newtonian fluid has been studied. Non-similarity solutions have been obtained for the case of a variable surface temperature of the form T w( x)= T ∞± Ax λ , λ≠1/2. It has been found that for λ=1/2, self-similar solution exists. A single mixed convection parameter has been used which covers the entire regime of mixed convection from pure forced convection to pure free convection limits. Both these limiting flows admit self-similar solutions. The partial differential equations governing the non-similar flow and the ordinary differential equations governing the self-similar flow have been solved numerically. The buoyancy force and the wall temperature have significant influence on the heat transfer and the velocity at the wall. For a fixed buoyancy force, the heat transfer and the velocity at the wall decrease with increasing non-Newtonian parameter, non-Darcy parameter and Peclet number.