Natural convection over a vertical flat plate due to absorption of thermal radiation

Heat transfer by simultaneous free convection and radiation in a participating fluid has received some attention during the past few years. However most of the previous work has been focussed on gases. The present work investigates the problem of combined radiation and natural convection in liquids. Analysis are given for an optically thick cold fluid layer adjacent to a non-emitting and non-reflecting radiation-transmitting plate. The external surface of the plate is subjected to heat loss to surroundings. The governing differential equations are transformed to a dimensionless form where the solution becomes dependent on the following parameters: the plate absorpitivity,α _p; the dimensionless distance along the plate,ζ; the fluid Prandtl number,Pr; and dimensionless heat loss coefficient to surrounding,N _c. A local non-similar technique is adopted to obtain solutions atPr=6.5 and at a wide range ofα _p,ζ, andN _c. The results showed that both velocity and temperature are non-similar and they are greatly affected by the value ofα _p whenζ is small. At large values of f the effect ofα _p diminishes and for a plate without heat loss the velocity becomes similar, i.e. independent of C The heat loss from the external surface of the plate causes the maximum temperature of the fluid to depart far from the plate. The results also showed that for plates without heat loss the local heat transfer coefficient from the plate depends on the local Grashof number to the power 0.185.     

Natural convection due to heat and mass transfer in a composite system

A numerical study is performed to analyse heat and mass transfer phenomena due to natural convection in a composite cavity containing a fluid layer overlying a porous layer saturated with the same fluid. The flow in the porous region is modelled using Brinkman–Forchheimer-extended Darcy model that includes both the effect of macroscopic shear (Brinkman effect) and flow inertia (Forchheimer effect). The vertical walls of the two-dimensional enclosure are isothermal whilst the horizontal walls are adiabatic. The two regions are coupled by equating the velocity and stress components at the interface. The resulting coupled equations in non-dimensional form are solved by an alternating direction implicit method by transforming them into parabolic form by the addition of false transient terms. The numerical results show that the amount of fluid penetration into the porous layer depends strongly upon the Darcy, thermal and solutal Rayleigh numbers. Average Nusselt number decreases while average Sherwood number increases with an increase of the Lewis number. The transfer of heat and mass on the heated wall near the interface depends strongly on the Darcy number. Received on 11 May 1998     

Mixed convection boundary layer flow over a horizontal plate with thermal radiation

The effects of thermal radiation and thermal buoyancy on the steady, laminar boundary layer flow over a horizontal plate is investigated. The plate temperature is assumed to be inversely proportional to the square root of the distance from the leading edge. The set of similarity equations is solved numerically, and the solutions are given for some values of the radiation and buoyancy parameters for Prandtl number unity. It is found that dual solutions exist for negative values of the buoyancy parameter, up to certain critical values. Beyond these values, the solution does no longer exist. Moreover, it is found that there is no local heat transfer at the surface except in the singular point at the leading edge. The radiation parameter is found to increase the local Stanton number.     

Natural convection heat transfer from round horizontal plate

A new approach to the model of natural convection from a horizontal, isothermal round plate and a simplified analytical solution of this model have been presented. In this model two separate regions with different fluid motions have been distinguished. In the first region, inside the boundary layer, the fluid flows concentrically towards the centre of the plate, while in the second one (stagnation region) the fluid is motionless. The presented theory has been verified experimentally.Ein neuer Lösungsweg für das Modell der freien Konvektion an einer isothermen, kreisförmigen, horizontalen Platte und eine vereinfachte analytische Lösung für dieses Modell werden hier vorgestellt. An diesem Modell wird zwischen zwei Bereichen mit verschiedenen Fluidbewegungen unterschieden. Im ersten Bereich, innerhalb der Grenzschicht, strömt das Fluid konzentrisch in Richtung Plattenmitte, während im zweiten Bereich (Stau-Bereich) die Flüssigkeit in Ruhe ist. Diese Theorie wurde experimentell überprüft.     

Natural convection in a reservoir sidearm subject to solar radiation: experimental observations

The natural convection in a reservoir sidearm induced by solar radiation is visualised using a shadowgraph technique. The flow visualisation reveals three stages of the flow development, namely an initial growth stage, a transitional stage and a quasi-steady stage. At the initial growth stage, a distinct thermal boundary layer grows rapidly along the sloping bottom. The transitional stage is characterised by the onset of convective instability in a form of rising plumes. At the quasi-steady state, the mean temperature across the enclosure increases steadily in time and the flow is sighted with quasi-regular presence of instabilities with reduced intensities. Received: 3 July 2001/Accepted: 10 December 2001     

Laminar forced convection conjugate heat transfer over a flat plate

Coupled heat transfer between laminar forced convection along and conduction inside a flat plate wall is theoretically studied. The laminar convective boundary layer is analyzed by employing the integral technique. The energy equations for the fluid and the plate wall are combined under the condition of the continuity in the temperature and heat flux at the fluid-solid interface. The analysis results in a simple formal solution. Expressions have been obtained for calculating local Nusselt number, wall heat flux and temperature along the plate, all are functions of the local Brun number, Br _x , which is a measure of the ratio of the thermal resistance of the plate to that of the convective boundary layer. The results indicate that for Br _x ≥0.15, neglecting the plate resistance will results in an error of more than 5% in Nusselt number. Comparison of the present solution with other previous studies has been made. The solution may be of a considerable theoretical and practical interest. Received on 19 August 1998     

黏弹性纳米流体在垂直板上的自然对流与传热分析

基于分数阶Maxwell模型和分数阶Fourier定律构建黏弹性纳米流体在垂直板上的非定常二维边界层自然对流与传热控制方程,利用有限差分和L1算法获得数值稳定解,对不同物理参数下的速度、温度、平均表面摩擦系数和平均Nusselt数的变化趋势进行图形化分析。结果显示,速度和温度边界层均表现出短暂记忆和延迟特性;速度分数导数参数削弱了自然对流,而速度松弛时间的影响却相反;温度分数导数参数削弱了自然对流和热传导,而温度松弛时间的影响却相反。     

Development of mixed convection flow over a vertical plate due to an impulsive motion

The development of the mixed convection flow of an incompressible laminar viscous fluid over a semi-infinite vertical plate has been investigated when the fluid in the external stream is set into motion impulsively, and at the same the surface temperature is suddenly raised from its ambient temperature. The problem is formulated in such a way that at time t = 0, it reduces to Rayleigh type of equation and as time t , it tends to Blasius type of equation. The scale of time has been selected such that the traditional infinite region of integration becomes finite which significantly reduces the computational time. The nonlinear coupled singular parabolic partial differential equations governing the unsteady mixed convection flow have been solved numerically by using an implicit finite-difference scheme. The surface shear stress and the heat transfer increase or decrease with time when the buoyancy parameter is greater or less than a certain valve. There is a smooth transition from the initial steady state to the final steady state. The skin friction and heat transfer for the constant heat flux case are more than those of the constant wall temperature case. Also they increase with the buoyancy force.     

Natural convection effects on impulsively started inclined plate with heat and mass transfer

The present investigation, involving the simultaneous heat and mass transfer is concerned with a numerical study of transient natural convection flow past an impulsively started inclined plate. Crank-Nicolson implicit finite difference method is used to solve the unsteady, non-linear and coupled governing equations. In order to check the accuracy of the numerical results, the present study is compared with available exact solution and are found to be in good agreement. Numerical results are obtained for various parameters. The steady-state velocity, temperature and concentration profiles, local and average skin friction, local and average Nusselt number, local and average Sherwood number are shown graphically. It is observed that local wall shear stress decreases as an angle of inclination { decreases.     

Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux

The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter (N _b), the Buoyancy ratio (N _r), the thermophoresis parameter (N _t), and the Lewis number (Le). The variations of the reduced Nusselt number and the reduced Sherwood number with N _b and N _t for various values of Le and N _r are discussed in detail. Simulation results depict that the increase in N _b, N _t, or N _r decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.     

Enhance of heat transfer on unsteady Hiemenz flow of nanofluid over a porous wedge with heat source/sink due to solar energy radiation with variable stream condition

Nanofluid-based direct solar receivers, where nanoparticles in a liquid medium can scatter and absorb solar radiation, have recently received interest to efficiently distribute and store the thermal energy. The objective of the present work is to investigate theoretically the unsteady homogeneous Hiemenz flow of an incompressible viscous nanofluid past a porous wedge due to solar energy (incident radiation). The conclusion is drawn that the temperature is significantly influenced by magnetic strength, nanoparticle volume fraction, convective radiation and porosity of the wedge sheet.     

Natural convection near a vertical plate with ramped wall temperature

The unsteady natural convective flow of an incompressible viscous fluid near a vertical plate has been considered. It is assumed that the bounding plate has a ramped temperature profile. The exact solutions of the energy and momentum equations, under the usual Boussinesq approximation, have been obtained in closed form. There are two different solutions for the fluid velocity—one valid for the fluids of Prandtl numbers different from unity, and the other for which the Prandtl number is unity. The variations of the fluid temperature, velocity as well as the Nusselt number and wall skin friction have been presented graphically. The natural convection near a ramped temperature plate has also been compared with the flow near a plate with constant temperature.     

Natural convection with surface radiation from a planar heat generating element mounted freely in a vertical channel

Experiments and numerical simulations have been conducted to study the conjugate heat transfer by natural convection and surface radiation from a planar heat generating element placed centrally between two adiabatic vertical plates. The relevant problem dependent parameters considered in this study are modified Rayleigh number, channel aspect ratio, stream-wise location of the heat generating element, and surface emissivities of the heat generating element and the adiabatic side plates. Experiments are conducted for different values of modified Rayleigh number ranging from 3.2 × 10⁵ to 1.6 × 10⁷ and surface emissivities 0.05, 0.55, 0.75 and 0.85. The interdependence between the heat transfer mechanism and the flow field under the influence of surface radiation on natural convection is explored and discussed. Experimental correlations for total and convective Nusselt number, and dimensionless temperature in terms of relevant parameters have been developed. The mathematical model governing the problem has been numerically solved using a commercial computational fluid dynamics package FLUENT 6.3 and the numerical predictions substantiate the experimental observations.     

Transient heat conduction with uniform heat generation in a slab subjected to convection and radiation cooling

A finite difference scheme with fourth order Runge-Kutta method is employed to determine the unsteady state temperature distribution in a plane slab with uniform heat generation. The plane slab is insulated on one face and subjected to convective and radiative cooling at the other face. The plane slab has a uniform initial temperature and the ambient environment as well as the fluid temperatures are assumed to be constant. Heat conduction is considered to be one dimensional. Results are presented in dimensionless charts over a wide range of parameters.

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Instationäre Wärmeleitung mit gleichförmiger Wärmeerzeugung in einer Platte bei Kühlung durch Konvektion und Abstrahlung

Zusammenfassung Zur Ermittlung der instationären Temperaturverteilung in einer Platte mit gleichförmiger Wärmeerzeugung wird ein Differenzverfahren vierter Ordnung nach Runge-Kutta angewendet. Die ebene Platte ist einseitig isoliert und wird auf der anderen Seite durch Konvektion und Abstrahlung gekühlt. Zu Beginn befindet sich die Platte gleichförmig auf einer bestimmten Anfangstemperatur, die Temperaturen der umgebenden Objekte sowie des Fluids sind ebenfalls konstant. Der Wärmeleitungsvorgang sei eindimensional. Die Ergebnisse sind in dimensionsloser Form für einen weiten Parameterbereich in Diagrammform dargestellt.

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Nomenclature Bi Biot number - c specific heat - h heat transfer coefficient - k thermal conductivity - L half thickness of plate - Nr Radiation number - T absolute temperature - t time - F _o dimensionless time - T _e environment temperature - T _f fluid temperature - T _i initial plate temperature - u internal energy generation number - u internal energy generation - x space coordinate - x* dimensionless space coordinate Greek symbols thermal diffusivity - emissivity - dimensionless temperature - density - Stephan-Boltzman constant     

Natural convection and radiation heat transfer of an externally-finned tube vertically placed in a chamber

A three-dimensional numerical study was made to investigate effects of fin angle, fin surface emissivity, and tube wall temperature on heat transfer enhancement for a longitudinal externally-finned tube placed vertically in a small chamber. The numerical model was first validated through comparison with experimental measurements and the appropriateness of general boundary conditions was examined. The numerical results show that the mean Nusselt number increases with Rayleigh number for all the fin angles investigated. The maximum heat transfer rate per mass occurs when the fin angle is about 60° for fin surface emissivity between 0.7 and 0.8 and 55° when the surface emissivity increases to 0.9. With increasing tube wall temperature, both the natural convection and radiation heat transfer are enhanced, but the fraction of radiation heat transfer decreases in the temperature range studied. Radiation fraction increases with increasing fin surface emissivity. Both convection and radiation heat transfer modes are important.     

Natural convection flow over a vertical frustum of a cone for constant wall heat flux

Laminar natural convection flow and heat transfer over a vertical frustum of a cone has been studied. The governing boundary layer equations are solved using local non-similarity method for constant wall heat flux. The local similarity and the local non-similarity two and three-equation models are constructed and the resulting equations are solved numerically. Results obtained from two and three-equation models are in good agreement. The numerical values of the flow and temperature functions required to calculate the surface skin friction and heat transfer rate are reported for various values of Prandtl numbers.     

Experiments on convection from a horizontal plate with and without background rotation

Laboratory experiments are described on convection driven by a finite-sized circular heating plate in the bottom of a horizontal fluid layer, both with and without background rotation. For the non-rotating case the various observations are arranged in a regime diagram, in which the different flow types are presented as a function of the governing parameters, being the Rayleigh number and the ratio of plate size and fluid depth. For the case = O(1) it is found that the finiteness of the heating disk has a significant effect on the convective flow structure, in the sense that an inflow is established which tends to stabilize the convection above the plate. The flow pattern changes drastically in the presence of background rotation, the effect of which is characterized by the Rossby number Ro. In the geostrophic limit (Ro « 1) one observes the flow to be organized in an array of axially-aligned vortices, as found in earlier studies. In the Ro = O(1) regime, however, the horizontal inflow along the bottom causes an intense vortex to arise above the heating disk. This vortex appears to be unstable, and it was seen to continuously change from a spiral mode to a toroidal mode and vice versa.     

Mixed convection effects on heat and mass transfer in a non Newtonian fluid with chemical reaction over a vertical plate

This paper studies mixed convection, double dispersion and chemical reaction effects on heat and mass transfer in a non-Darcy non-Newtonian fluid over a vertical surface in a porous medium under the constant temperature and concentration. The governing boundary layer equations, namely, momentum, energy and concentration, are converted to ordinary differential equations by introducing similarity variables and then are solved numerically by means of fourth-order Runge-Kutta method coupled with double-shooting technique. The velocity, temperature concentration, heat and mass transfer profiles are presented graphically for various values of the parameters, and the influence of viscosity index n, thermal and solute dispersion, chemical reaction parameter χ are observed.