Transient heat transfer behaviors in cylindrical porous beds at relatively large Reynolds numbers

The transient behavior of heat transfer in a cylindrical porous bed was examined experimentally under various factors (flow rate, diameter of spherical solid particle, temperature of flowing fluid and physical properties of porous bed). In these factors, it was understood that especially flow rate and the diameter of the particled have important role in evaluating the transient behavior of heat transfer in the porous bed. That is, as the flow rate and the diameter of the particle under a constant diameterD of the cylindrical bed are increased, mean heat transfer coefficient between flowing fluid and the solid particles is increased and the time period to reach a thermally steady state is decreased. The useful experimental correlation equations of mean heat transfer coefficient and the time period to reach the steady state were derived with the functional relationships of Nusselt numberNu _d =f(d/D, Reynolds numberRe _d ) and Fourier numberFo =f (modified Prandtl numberPr*, d/D, Re _d ).     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).     

Velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium

In this paper the velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium are obtained for the governing equations (Kaviany [7]) following the technique adopted by Chandrashekara [2] which are concerned with the interesting situations of the existence of transverse, velocity and thermal boundary layers. Here the pressure gradient is just balanced by the first and second order solid matrix resistances for small permeability and observed that by increasing of the flow resistance the asymptotic value for the heat transfer rate increases. Further we concluded that the transverse boundary layers are thicker than that of axial boundary layers. Hence we evaluated the expressions for the boundary layer thickness, the shear stress at the semi-infinite plate and _T (the ratio of the thicknesses of the thermal boundary layer and momentum boundary layer). The variations of these quantities for different values of the porous parameterB and the flow resistanceF have been discussed in detail with the help of tables. The curves for velocity and temperature distributions have been plotted for different values ofB andF.Lastly we have evaluated the heat fluxq(x) and found that it depends entirely upon the Reynolds numberRe, Prandtl numberPr,B andF.     

Effects of anisotropy in permeability on the two-phase flow and heat transfer in a porous cavity

This paper reports on the results of a numerical study of convection flow and heat transfer in a rectangular porous cavity filled with a phase change material under steady state conditions. The two vertical walls of the cavity are subject respectively to temperatures below and above the melting point of the PCM while adiabatic conditions are imposed on the horizontal walls. The porous medium is characterized by an anisotropic permeability tensor with the principal axes arbitrarily oriented with respect to the gravity vector. The problem is governed by the aspect ratioA, the Rayleigh numberRa, the anisotropy ratioR and the orientation angle θ of the permeability tensor. Attention is focused on these two latter parameters in order to investigate the effects of the anisotropic permeability on the fluid flow and heat transfer of the liquid/solid phase change process. The method of solution is based on the control volume approach in conjunction with the Landau-transformation to map the irregular flow domain into a rectangular one. The results are obtained for the flow field, temperature distribution, interface position and heat transfer rate forA=2.5,Ra=40, 0≤θ≤π, 0.25≤R≤4. It was found that the equilibrium state of the solid/liquid phase change process may be strongly influenced by the anisotropy ratioR as well as by the orientation angle θ of the permeability tensor. First, for a given set of parametersA,Ra andR, there exists an optimum orientation θ_max for which the flow strength, the liquid volume and the heat transfer rate are maximum. There also exists an orientation θ_min=θ_max+π/2 for which these quantities are minimum. Second, when an anisotropic medium is oriented along the optimum direction θ_max, an increase of the permeability component along that direction will increase the flow and heat transfer rate in a same order while an increase of the other permeability component only has a negligible effect. For the parameter ranges considered in the present study, it was found that the optimum direction is lying between the gravity vector and the dominant flow direction.     

Boundary layer development on a continuous moving surface with a parallel free stream due to impulsive motion

The development of the momentum and thermal boundary layers over a semi-infinite flat plate has been studied when the external stream as well as the plate are impulsively moved with constant velocities. At the same time the temperature of the wall is suddenly raised from T_∞, the temperature of the surrounding fluid, toT _w and maintained at this temperature. The problem has been formulated in a new system of scaled coordinates such that fort?=0 it reduces to Rayleigh type of equation and fort? → ∞ it reduces to Blasius or Sakiadis type of equation. A new scale of time has been used which reduces the region of integration from an infinite region to a finite region which reduces the computational time considerably. The governing singular parabolic partial differential equations have been solved numerically using an implicit finite difference scheme. For some particular cases, analytical solutions have been obtained. The results show that there is a smooth transition from Rayleigh solution to Blasius or Sakiadis solution as the dimensionless timeξ increases from zero to one. The shear stress at the wall is negative for the friction parameterλ<0.5, positive forλ>0.5 and zero forλ=0.5. The zero shear stress at the wall does not imply separation but corresponds to the parallel flow. The surface heat transfer is strongly dependent on the Prandtl numberPr and increases with it. Also forPr<Pr ₀, the surface heat transfer is enhanced as the friction parameterλ increases, but forPr>Pr ₀ it get reduced.     

Similarity solution of mixed convection over a horizontal moving plate

Investigation to the mixed convective heat and mass transfer over a horizontal plate has been carried out. By applying transformation group theory to analysis of the governing equations of continuity, momentum, energy and diffusion, we show the existence of similarity solution for the problem provided that the temperature and concentration at the wall are proportional to x ^4/(7-5n) and that the moving speed of the plate is proportional to x ^(3-n)/(7-5n), and further obtain a similarity representation of the problem. The similarity equations have been solved numerically by a fourth-order Runge–Kutta scheme. The numerical results obtained for Pr=0.72 and various values of the parameters Sc, K ₁, K ₂ and K ₃ reveals the influence of the parameters on the flow, heat and mass transfer behavior.     

A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed. The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu _m at the bottom surface of both cavity models tends generally to increase with increasing Re_HorGr _w/Re _H ² . However, in the flow region ofRe _H & 500 for DOF-cavity, theNu _m for 0.4 ≦ D₂/D₁ ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe _H.     

Two-dimensional performance of convecting-radiating fins of different profile shapes

A finite element approach is used to investigate the two-dimensional performance of convecting-radiating fins of rectangular, trapezoidal, triangular, and concave parabolic shapes. The heat transfer rate depends on fin size parameter α, Biot numberBi, radiation-conduction parameterN _r , and environment temperatures θ_∞ and θ _r . Numerical results for the heat transfer rate and the error due to one-dimensional assumption are presented and discussed for each geometry. The highest heat dissipation is achieved with the concave parabolic shape and the lowest with the rectangular shape with the trapezoidal and triangular shapes falling in between. The maximum error of +144 percent is noted for a short and thick rectangular fin (α=1) and ?47 percent for a long thin triangular fin (α=20).     

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.     

Boundary effects on the Bénard-Marangoni instability under an electric field

This article theoretically studies the Bénard-Marangoni instability problem for a liquid layer with a free upper surface, which is heated from below by a heating coil through a solid plate in ana.c. electric field. The boundary effects of the solid plate, which include its thermal conductivity, electric conductivity and thickness, have great influences on the onset of convective instability in the liquid layer. The stability analysis in this study is based on the linear stability theory. The eigenvalue equations obtained from the analysis are solved by using the fourth order Runge-Kutta-Gill's method with the shooting technique. The results indicate that the solid plate with a higher thermal or electric conductivity and a bigger thickness tends to stabilize the system. It is also found that the critical Rayleigh numberR _c, the critical Marangoni numberM _c, and the criticala.c. Rayleigh numberE _ac become smaller as the intensity of thea.c. electric field increases.     

Influence of spanwise pitch on local heat transfer distribution for in-line arrays of circular jets with spent air flow in two opposite directions

Effect of spanwise jet-to-jet spacing on local heat transfer distribution due to an in-line rectangular array of confined multiple circular air jets impinging on a surface parallel to the jet plate are studied experimentally. Length-to-diameter ratio of nozzles of the jet plate is 1.0. The flow, after impingement, is constrained to exit in two opposite directions from the confined passage formed between jet plate and target plate. Mean jet Reynolds numbers based on the nozzle exit diameter (d) covered are 3000, 5000, 7500 and 10,000 and jet-to-plate spacings studied are d, 2d and 3d. Spanwise pitches considered are 2d, 4d and 6d in steps of 2d keeping the streamwise pitch at 5d. For all the configurations, the jet-plates have ten spanwise rows in streamwise direction and six jets in each spanwise row. Flat heat transfer surface is made of thin stainless steel metal foil. Local temperature distribution on a target plate is measured using thermal infrared camera. Wall static pressure on the target plate is measured in the streamwise direction to estimate crossflow velocities and individual jet velocities. Heat transfer characteristics are explained on the basis of the flow distribution. A simple correlation to predict streamwise distribution of heat transfer coefficients averaged over each spanwise strip resolved to one jet hole is developed.     

A transition phenomenon of ice formation in water flow between two horizontal parallel plates

Experiments have been performed to investigate the icetransition profiles and heat-transfer characteristics for water flows between two horizontal parallel plates. The experiments are carried out under the condition that upper plate is cooled at uniform temperature kept less than freezing temperature of water, while the lower plate is heated at uniform temperature kept higher than the temperature of water flow. The temperatures of the upper and lower plates range from ?8 to ?14°C and from 10 to 60 °C, respectively, with inlet-water temperature varied from 1.5 to 4.5 °C. The cooling and heating temperature ratios, θ_c and θ_h, are ranging from 1.78 to 9.33 and from 1.22 to 39, respectively. By using three kinds of heightH of 16, 30 and 40 mm between the horizontal parallel plates, the Reynolds and Grashof numbers are varied from 3.2 × 10² to 1.5 × 10⁴ and from 3.4 × 10³ to 8.97 × 10⁶, respectively. As a result of this investigation two ice-transition modes are observed. The first ice-transition mode is due to an interruption of upper and lower thermal boundary layers, while the second mode is due to an instability of laminar boundary layer formed on water-ice interface. In order to determine the kind of ice-transition mode, criterion correlation formulas including the Reynolds numberRe _H , Grashof numberGr _H , and heating temperature ratio θ_h are determined and may be written as follows: For thermal icetransition mode (th.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23<1.6×10^?3 and for hydrodynamical ice-transition mode (hy.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23>2.3×10^?3 By introducing the freezing parameterB _f , correlation equations for local and mean Nusselt numbers along the water-ice interface at steady-state condition are determined. From the current experimental results it is found that the local Nusselt number may be described as the following equation:Nu _x =0.835 Re _H ^0.278 · B _f ^0.834 ·x/H)^?0.139     

Mixed convection adjacent to inclined flat surfaces embedded in a porous medium

An analysis is performed to study the flow and heat transfer characteristics of laminar mixed convection boundary layer flows from inclined (including horizontal and vertical) surfaces embedded in a saturated porous medium with constant aiding external flows and uniform surface temperature. Both the streamwise and normal components of the buoyancy forces are retained in the momentum equations. Nondimensionalization of the boundary layer equations results in the following three governing parameter: (1)Gr/Re, the ratio of the Grashof number to the Reynolds number; (2)Pe _x =Re _x Pr, the Peclet number; (3) φ, the angle of inclination from the horizontal. The resulting nonsimilar equations are solved by an efficient implicit finite-difference scheme. Numerical results are presented for flows with different values ofGr/Re in the range of 0 to 50, over a wide range of the Peclet numbersPe _x, and various values of φ ranging from 0 to 90 degrees. It is found that the local surface heat transfer rate increases with increasing the local Peclet number. In addition, as the plate is tilted from the horizontal to the vertical orientation, the local Nusselt number increases for a given Peclet number and the effect of the buoyancy force on the surface heat transfer rate increases.     

Mixed convection in the presence of horizontal impermeable surfaces in saturated porous media with variable permeability

Boundary layer approximation is applied for mixed convection about a horizontal flat plate in a saturated porous medium with aiding external flows. Similarity solutions are obtained, incorporating the variation of permeabilty, for 1) horizontal flat plate at zero angle of attack with constant heat flux; 2) stagnation point flows about horizontal flat plates with wall temperature varying asT _w ∝x ². The temperature and velocity profiles for different values of Ra/(RePr)^3/2 and the parameters governing the flow are obtained. The heat transfer rate is calculated and its implications in a geothermal application is discussed. Further, the criteria for pure mixed convection about horizontal flat plates in a porous media are established.     

Computational study of combined effects of conduction-radiation and hydromagnetics on natural convection flow past magnetized permeable plate

The computational study of the combined effects of radiation and hydromagnetics on the natural convection flow of a viscous,incompressible,and electrically conducting fluid past a magnetized permeable vertical plate is presented.The governing non-similar equations are numerically solved by using a finite difference method for all values of the suction parameter ξ and the asymptotic solution for small and large values of ξ.The effects of varying the Prandtl number P r,the magnetic Prandtl number P r m,the magnetic force parameter S,the radiation parameter R d,and the surface temperature θ w on the coefficients of the skin friction,the rate of heat transfer,and the current density are shown graphically and in tables.An attempt is made to examine the effects of the above mentioned physical parameters on the velocity profile,the temperature distribution,and the transverse component of the magnetic field.     

Leading edge bluntness effect on the flow in a model air-inlet

Flow in an idealized air-inlet with plane walls and a rectangular cross-section is experimentally investigated. The air-inlet is mounted on a plate, at a distance well removed from its leading edge. The experiments were conducted in a Ludwig tube at M_∞ = 5 and Re_∞L = 23×10⁶ and 13×10⁶. A panoramic (optical) technique of measuring the heat transfer coefficient is for the first time applied to study the internal flow in an air-inlet. The data on the effect of the bluntness of the leading edges of the plate and the air-inlet cowl on the heat transfer coefficient distribution and the flow structure within the air-inlet are obtained. It is shown that in an air-inlet with large channel constriction an even small bluntness of the plate or the cowl can lead to global changes in the flow structure.     

Mixed convection heat transfer in horizontal channel filled with nanofluids

The laminar fully developed nanofluid flow and heat transfer in a horizonal channel are investigated. Highly accurate solutions for the temperature and nanoparticle concentration distributions are obtained. The effects of the Brownian motion parameter N _b, the thermophoresis parameter N _t, and the Lewis number Le on the temperature and nanoparticle concentration distributions are discussed. The current analysis shows that the nanoparticles can improve the heat transfer characteristics significantly for this flow problem.     

Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer

An analysis is carried out to study the momentum, mass and heat transfer characteristics on the flow of visco-elastic fluid (Walter's liquid-B model) past a stretching sheet in the presence of a transverse magnetic field.In heat transfer, two cases are considered:

1.

The sheet with prescribed surface temperature (PST case); and

2.

The sheet with prescribed wall heat flux (PHF case).

The solution of equations of momentum, mass and heat transfer are obtained analytically. Emphasis has been laid to study the effects of various parameters like magnetic parameter Mn, visco-elastic parameter k₁, Schmidt number Sc, and Prandtl number Pr on flow, heat and mass transfer characteristics.     

Diffusion-Thermo and Radiation Effects on Unsteady MHD Flow Through Porous Medium Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion

The objective of this study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity u ₀ in the vertical upward direction against to the gravitational field. At the same time, the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to ${{C}_{\rm w}^{\prime}}$ . A magnetic field of uniform strength B ₀ is applied normal to the direction to the flow. The dimensionless governing equations are solved in closed form by Laplace transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.     

Heat transfer in an inner loop reactor

General expressions for evaluating heat transfer in reactors with a draft tube have been derived. Theoretical results show that heat transfer can be enhanced for flow pattern (A) compared with that in an open duct whenK ₁ is not departed from 0.5. The competition of the residence time and the volumetric flow rate of the fluids in the annulus and in the draft tube may be used to explain the fluid behaviors. For flow patterns (B) and (C) as in a loop reactor, introduce of recycling can augment the heat transfer rate for large Graetz number, especially whenK ₁,K ₂ orR increases. The competition between the premixing and the residence time effects of the fluid may be used to describe the fluid behaviors. Moreover, asymptotic solutions for all flow patterns were also derived.