混合对流条件下浮升力对环形通道中流动及传热的影响

讨论了混合对流条件下环形通道中浮升力对流动及传热的影响。实验时用LDA测量了水向下流过竖直环形通道时的平均流速和湍流强度。对于逆浮升力方向的流动情况，湍流速度脉动和湍流剪切应力都因浮升力的影响而增加，从而传热得到了增强。当浮升力的影响特别大时。靠近环形内壁的流动出现反向流，在这种情况下即使流动在无浮升力影响时是层流。湍流也会由于浮升力的存在而产生，传热维持较好的效果。     

The study of buoyancy influence on mean flow and heat transfer under conditions of mixed convection in annular channels

Laser Doppler anemometry (LDA) measurements are reported on mean flow and turbulence in water as it flows downwards through a long vertical passage of annular cross‐section having an inner surface which can be uniformly heated and an outer one which is adiabatic. Under buoyancy‐opposed conditions, which can be achieved by heating the core and operating at a reduced mass flow rate, the flow near the inner surface is retarded, turbulent velocity fluctuations and turbulent shear stress are increased and the effectiveness of heat transfer is enhanced. When the influence of buoyancy is very strong, flow reversal occurs near the inner surface. Under such conditions, turbulence is produced very readily and the heat transfer process remains very effective, even when the Reynolds number is reduced to values at which the flow is laminar in the absence of heating. The measurements of turbulence in buoyancy‐opposed flow made in this study provide direct confirmation of the validity of the ideas currently used to explain the influences of buoyancy on mixed convection in vertical passages. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(1): 9–17, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20041     

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

Investigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third-grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third-grade fluids for EMHD flow and heat transfer behavior. The least-square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third-grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third-grade fluid increases.     

G-jitter fully developed combined heat and mass transfer by mixed convection flow in a vertical channel

The effect of g-jitter induced combined heat and mass transfer by mixed convection flow in microgravity for a simple system consisting of two heated vertical parallel infinite flat plates held at constant but different temperatures and concentrations. The governing equations are solved analytically for the induced velocity, temperature and concentration distributions. Graphical results for the velocity profile of the oscillating flow in the channel are presented and discussed for various parametric physical conditions. Despite the simplicity of the problem, it does display some features, which have also been observed in real mixed convection flows, such as flow reversal and flow dependence on the buoyancy parameter ratio.     

Non-axisymmetric forced and free flow in a vertical circular duct

The fully developed laminar mixed convection in a vertical circular duct is studied analytically, with reference to non-axisymmetric boundary conditions such that the fluid temperature does not change along the axial direction. The Boussinesq approximation is applied by taking the average temperature in a duct section as the reference fluid temperature. The dimensionless momentum and energy balance equations are solved by employing Fourier series expansions of the temperature and the velocity fields. The solution shows that the temperature field is not influenced by the velocity distribution and that the Fanning friction factor is not affected by buoyancy. On the other hand, the velocity field is strongly influenced by the buoyancy forces and may display flow reversal phenomena. Two special cases are studied in detail: a duct with a sinusoidal wall temperature distribution; a duct subjected to an external convection heat transfer with two environments having different reference temperatures.     

Analytic solutions for the mixed convection flow of non-newtonian fluids in parallel plate ducts

The modelling of laminar, fully-developed, combined convection flows of non- Newtonian fluids in a vertical parallel-plate duct, where the walls are held at asymmetric uniform temperatures is considered. For this fully-developed flow model, the momentum, continuity and energy equations are solved analytically for the Bingham Plastic rheology and for the limiting case of Power Law fluids. It is shown that different flow configurations exist depending on the buoyancy parameter, Grashof/Reynolds, which include flow reversal for both rheologies, and unsheared plug flow adjacent to the cold wall for the Bingham Plastic.     

Entropy Analysis of a Coupled‐Convection Flow through a Vertical Channel Partially Filled by a Porous Medium with Injection/Suction and Slip Boundary Conditions

Flow fields, thermal fields, and entropy generation have been investigated for fully developed mixed convection flow between two vertical porous plates. The vertical channel is partially filled by a porous medium, and channel walls are subjected to a constant injection velocity at the left wall and constant suction velocity at the right wall. The viscous dissipation effects and velocity slip for the longitudinal component of the velocity at the channel walls are also taken into account. The momentum and energy equations for the mixed convection problem in the vertical channel are solved by means of the perturbation series method, by taking perturbation parameter proportional to the Brinkman number. For the present problem, numerical solution is also obtained and compared with the analytical solution. The effects of various pertinent parameters on the velocity distribution, temperature distribution, entropy generation rate, and Bejan number are investigated and discussed graphically.     

Theory of fully developed mixed convection including flow reversal: A nonlinear Boussinesq approximation approach

In this article, an exact solution is obtained to investigate the role of nonlinear Boussinesq approximation on mixed convection flow in a vertical channel subject to asymmetric wall heating. The nonlinear density variation with temperature (NDT) in the buoyancy term is introduced to the momentum equation and solved exactly by direct integration. During the course of graphical and numerical computations, results show that the role of NDT is to increase fluid velocity as well as skin‐friction while it reduces the rate of heat transfer. In addition, reverse flow formation at the walls is increased due to the inclusion of NDT (nonlinear Boussinesq approximation).     

Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

Exploration of thermal Péclet number,vortex viscosity,and Reynolds number on two-dimensional flow of micropolar fluid through a channel due to mixed convection

The present theoretical investigation is conducted on a micropolar fluid medium channel in the presence of mixed and nonlinear convection with the assumptions of thermal radiation and species reactive agents. The nonlinear governing equations, which describe the micropolar fluid flow and energy, are converted into ordinary differential equations using appropriate similarity variables. With the Runge–Kutta–Fehlberg method, the resultant equations are numerically solved. The physical characteristics of flow restrictions over velocity, microrotation, energy, and concentration profile are plotted and discussed. Further, the impact of several dimensionless parameters on Nusselt and Sherwood numbers is investigated and depicted graphically. In addition to observing flow patterns, contour plots of streamlines are plotted and discussed. It is demonstrated that the dimensionless velocity, temperature, and concentration of micropolar fluid have a maximum value at the center of the channel. However, the microrotation velocity of the micropolar fluid has both maxima and minima. The thermal and solutal properties of micropolar fluid influence heat and mass transport rates, that is, mixed convection and buoyancy parameter boost up the local heat transfer at the surface. Finally, Péclet number and chemically reactive parameters boost up the local mass transfer at the surface.     

Finite element method solution of mixed convection flow of Williamson nanofluid past a radially stretching sheet

This computation reports the mixed convection flow of Williamson fluid past a radially stretching surface with nanoparticles under the effect of first‐order slip and convective boundary conditions. The coupled nonlinear ordinary differential equations (ODEs) are obtained from the partial differential equations, which are derived from the conservation of momentum, energy, and species. Then, utilizing suitable resemblance transformation, these ODEs were changed into dimensionless form and then solved numerically by means of a powerful numerical technique called the Galerkin finite element method. The effect of different parameters on velocity, temperature, and concentration profiles is inspected and thrashed out in depth by graphs and tables. The upshots exhibit that the velocity profile augments as the values of concentration buoyancy and mixed convection parameters are engorged. Also, the results demonstrated that both temperature and concentration profiles are improved with an enhancement in values of thermophoresis parameters. The outcomes also indicate that for finer values of magnetic field parameter and thermophoresis parameter, the numerical value of local Nusselt and Sherwood numbers is reduced.     

Combined boundary and inertia effects for fully developed mixed convection in a vertical channel embedded in porous media

The fully developed laminar mixed convection in a vertical channel embedded in porous media has been solved by using non-Darcy flow model. Through proper manipulation of nondimensional variables and parameters, the governing equations are derived and the thermal boundary conditions on the left and right walls can be prescribed as isothermal-isothermal, isothermal-isoflux, or isoflux-isothermal, respectively. Including the Darcian force, buoyancy force and boundary effect, the exact solutions for temperature and velocity profiles are obtained. Meanwhile, parametric zones for the occurrence of flow reversal based on the analytical solutions are presented. Finally, the numerical solution is also provided to investigate their further influence due to the existence of inertia effect.     

Hydromagnetic mixed convection stagnation flow with suction and blowing

This paper deals with steady, two-dimensional, mixed convection flow of an electrically-conducting and heat-absorbing fluid near a stagnation point on a semi-infinite vertical permeable surface at arbitrary surface heat flux variations in the presence of a magnetic field. Similarity equations are derived and solved numerically by an implicit and accurate finite-difference method. Graphical solutions for the local skin-friction coefficient and the local Nusselt number are presented and discussed for various parametric conditions. These results are presented to illustrate the influence of the Hartmann number, wall mass transfer coefficient, heat absorption coefficient, Prandtl number and the mixed convection or buoyancy parameter.     

Thermal characteristics of forced convection in combined pressure and shear-driven flow of a non-Newtonian third-grade fluid through parallel plates

Heat transfer in a non-Newtonian third-grade fluid, flowing under the action of pressure gradient and shear, through two parallel plates, is considered. The upper plate moves with a constant velocity. Constant wall heat fluxes are applied to the plates. Effect of viscous dissipation is included, which has a major role in heat transfer of non-Newtonian fluids. The governing equations are nonlinear and are solved semi-analytically by using the least-square method (LSM). Then, using the solution for velocity in the energy equation, the solution is obtained by a direct integration process. Further, approximate analytical solutions are obtained by the perturbation method, which validates the results generated by the LSM. The effects of the third-grade fluid parameter on the velocity and temperature and also on the physical quantity, such as Nusselt's number, are discussed. Further, viscous dissipation effects on the temperature distribution have been analyzed. Observations show that the movement of the upper plate results in a significant decrease in temperature near the upper plate. For the unit heat flux ratio, the temperature difference between the surface and fluid is more at the upper surface due to the enhanced convective heat transfer caused by the moving upper plate. Nusselt's number increases significantly with an increase in the heat flux ratio.     

Hydromagnetic free convection of a radiating fluid

Natural convection of an electrically conducting and radiating fluid in the presence of an external magnetic field is investigated numerically. The two opposing side walls are differentially heated with a temperature difference specified, while the top and bottom walls are insulated. The coupled momentum and energy equations associating with the electromagnetic retarding force as well as the buoyancy force terms are solved by an iterative procedure using the SIMPLER algorithm based on control volume approach. Steady-state conditions are assumed. The finite-volume method is utilised to solve the radiation transport adopting the same computational grid as used in solving the flow field, with which the radiating fluids in an enclosure are assumed to be radiatively opaque, transparent and participating, respectively. After validating the numerical procedures, the changes in the buoyant flow patterns and temperature distribution affected by combined radiation and a magnetic field are focused mainly. Comparative results for the velocity profiles and the heat transfer rates are presented too. Based on the results of this study, it was found that the radiation played a significant role in developing the hydromagnetic free convective flow in a differentially heated enclosure.     

Heat transfer in the flow of blood‐gold Carreau nanofluid induced by partial slip and buoyancy

Dynamics of blood containing gold nanoparticles on a syringe and other objects with a nonuniform thickness is of importance to experts in the industry. This study presents the significance of partial slip (i.e. combination of linear stretching and velocity gradient) and buoyancy on the boundary layer flow of blood‐gold Carreau nanofluid over an upper horizontal surface of a paraboloid of revolution (uhspr). In this report, the viscosity of the Carreau fluid corresponding to an infinite shear‐rate is assumed as zero, meanwhile, the viscosity corresponding to zero shear‐rate, density, thermal conductivity, and heat capacity were assumed to vary with the volume fraction of nanoparticles. The governing equation that models the transport phenomenon were non‐dimensionalized and parameterized using suitable similarity variables and solved numerically using classical Runge–Kutta method with shooting techniques and MATLAB bvp4c package for validation. The results show that temperature distribution across the flow decreases more significantly with buoyancy‐related parameter when the influence of partial slip was maximized. Maximum velocity of the flow is ascertained at larger values of partial slip and buoyancy parameters. At smaller values of Deborah number and large values of volume fraction, maximum local skin friction coefficient, and local heat transfer rate are ascertained.     

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

The current study focuses on investigating the influence of transverse magnetic field, variable viscosity, buoyancy, variable Prandtl number, viscous dissipation, Joulian dissipation, and heat generation on the flow of nanofluids over thin needle moving in parallel stream. The theory of nanofluids that includes the Buongiorno model featured by slip mechanism, such as Brownian motion and thermophoresis, has been implemented. Further, convective boundary condition and zero mass flux condition are considered. The nondimensionally developed boundary layer equations have been solved by Runge–Kutta–Fehlberg method with shooting technique for different values of parameters. The most relevant outcomes of the present study are that the augmented magnetic field strength, viscosity parameter, buoyancy ratio parameter, and the size of the needle undermine the flow velocity, establishing thicker velocity boundary layer while Richardson number and Brownian motion show opposite trend. Another most important outcome is that increase in the size of the needle, viscous dissipation, convective heating, and heat generation upsurges the fluid temperature, leading to improvement in thermal boundary layer. The effects of different natural parameters on wall shear stress and heat and mass transfer rates have been discussed.     

Quartic autocatalysis of homogeneous and heterogeneous reactions in the bioconvective flow of radiating micropolar nanofluid between parallel plates

This study deals with the quartic autocatalysis of homogeneous–heterogeneous chemical reaction that occurs in the bioconvective flow of micropolar nanofluid between two horizontally parallel plates. The quartic autocatalysis is found to be more effective than cubic autocatalysis since the concentration of the homogeneous species is substantially high. The upper plate is assumed to be in motion and the lower plate is kept stationary. Such a flow of micropolar fluid finds application in the pharmaceutical industry, microbial enhanced oil recovery, hydrodynamical machines, chemical processing, and so forth. The governing equations for this flow are in the form of the partial differential equation and their corresponding similarity transformation is obtained through Lie group analysis. The governing equations are further transformed to coupled nonlinear differential equations that are linearized through the Successive linearization method and are solved using the Chebyshev Collocation method. The effects of various parameters, such as micropolar coupling parameter, spin gradient parameter, reaction rates, and so forth, are analyzed. It is observed that the fluid flows with a greater velocity away from the channel walls, whereas near the channel walls the velocity decreases with an increase in the coupling parameter. Furthermore, the spin parameter increases the spin gradient viscosity that reduces the microrotation of particles that further decreases the microrotation profile.     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

MHD convective rotating flow of viscoelastic fluid past an infinite vertical oscillating porous plate with Hall effects

It is considered the unsteady and incompressible magnetohydrodynamic rotating free convection flow of viscoelastic fluid with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field and taking Hall current into account. The governing equations of the flow field are then solved by a regular perturbation method for a small elastic parameter. The expressions for the velocity, temperature, and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction on the boundary, the heat flux in terms of the Nusselt number, and the rate of mass transfer in terms of the Sherwood number are also obtained and their behavior discussed. The resultant velocity enhances with increasing Hall parameter and rotation parameter. The reversal behavior is observed with increasing viscoelastic parameters. The resultant velocity enhances and experiences retardation in the flow field with increasing radiation parameters, whereas the secondary velocity component increases with increasing rotation parameters. The temperature diminishes as the Prandtl number and/or the frequency of oscillations. The concentration reduces at all points of the flow field with the increase in the Schmidt number.