Non-dimensional Heat Transfer Coefficient Research Articles

Influence of Viscous Dissipation on Mixed Convection in a Non-Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid-saturated non-Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far-field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite-difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non-dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21083

Generalized Models for Laminar Developing Flows in Heat Sinks and Heat Exchangers

Recent models for laminar friction and heat transfer in non-circular ducts and channels are reviewed. Models for both hydrodynamically and thermally developing flows are presented. These models are based on the superposition of asymptotic characteristics for short and long ducts. The non-dimensional mean wall shear stress (friction factor-Reynolds number product) and non-dimensional heat transfer coefficient (Nusselt number) are shown to be only functions of the dimensionless hydrodynamic or thermal duct length, respectively, and the duct aspect ratio. This is achieved by means of using a new transversal length scale, the square root of cross-sectional area, rather than the hydraulic diameter. Additional definitions more appropriate to single fluid devices such as heat sinks are also discussed.

MOMENTUM INTEGRAL METHOD FOR FORCED CONVECTION IN THERMAL NONEQUILIBRIUM POWER-LAW FLUID-SATURATED POROUS MEDIA

Forced convection heat transfer for power-law fluid flow in porous media was studied analytically. The analytical solutions were obtained based on the Brinkman-extended Darcy model for fluid flow and the two-equation model for forced convection heat transfer. As a closed-form exact velocity profile is unobtainable for the general power-law index, an approximate velocity profile based on the parabolic model is proposed by subscribing to the momentum boundary layer integral method. Heat transfer analysis is based on the two-equation model by considering local thermal nonequilibrium between fluid and solid phases and constant heat flux boundary conditions. The velocity and temperature distributions obtained based on the parabolic model were verified to be reasonably accurate and improvement is justified compared to the linear model. The expression for the overall Nusselt number was derived based on the proposed parabolic model. The effects of the governing parameters of engineering importance such as Darcy number, power-law index, nondimensional interfacial heat transfer coefficient, and effective thermal conductivity ratio on the convective heat transfer characteristics of non-Newtonian fluids in porous media are analyzed and discussed.

Modeling water droplet condensation and evaporation in DNS of turbulent channel flow

In this paper a point particle model for two-way coupling in water droplet-laden incompressible turbulent flow of air is proposed. The model is based on conservation laws and semi-empirical correlations. It has been implemented and tested in a DNS code based for turbulent channel flow with an Eulerian-Lagrangian approach. The two-way coupling is investigated in terms of the effects of mass and heat transfer on the droplets distributions along the channel wall-normal direction and by comparison of the droplet temperature statistics with respect to the case without evaporation and condensation. A remarkable conclusion is that the presence of evaporating and condensing droplets results in an increase in the non-dimensional heat transfer coefficient of the channel flow represented by the Nusselt number.

Heat Transfer Behind a Step in High-Enthalpy Laminar Hypersonic Flow

The parameters that are involved in heat transfer behind a step in high-enthalpy laminar hypersonic flow are investigated. The nondimensional wall heat transfer coefficient such as the Stanton Number depends on a group of dimensionless parameters characteristic of the flow. The flow enthalpies (h ) ranged from 1.5 MJ/kg to 26 MJ/kg, thus covering both undissociated and mildly to moderately dissociated freestreams. The gas phase, Damkohler number, ranged from 0 (undissociated flow) to 0.133. The dissociated freestream may be frozen as a result of nozzle expansion in shock tunnel and expansion tube flows. The part of the freestream total enthalpy may be stored as chemical potential enthalpy, which would be result in reduced heat transfer.

Soret and Dufour effects on free convection along a vertical wavy surface in a fluid saturated Darcy porous medium

In this article, free convection of heat and mass transfer along a vertical wavy surface in a Newtonian fluid saturated Darcy porous medium is studied by considering cross diffusion (namely the Soret and the Dufour effects) in the medium. The vertical wavy wall and the flow governing equations are transformed to a plane geometry case by using a suitable transformation. Then a similarity solution to this problem is presented under the large Darcy–Rayleigh number assumption. The governing partial differential equations are reduced to a set of ordinary differential equations that are integrated using numerical methods to study the nature of the non-dimensional heat and mass transfer coefficients in the medium. The results are presented for a range of the flow governing parameters such as the diffusivity ratio parameter, the buoyancy ratio parameter, the Soret parameter, the Dufour parameter and the amplitude of the wavy surface.

Heat Transfer Coefficients of Film Cooling on a Rotating Turbine Blade Model—Part I: Effect of Blowing Ratio

Experimental investigations were performed to measure the local heat transfer coefficient (hg) distributions of film cooling over a flat blade under both stationary and rotating conditions. Film cooling was via a straight circular hole of 4 mm in diameter located in the middle section of the blade angled 30 deg along the streamwise direction and 90 deg along the spanwise direction. The Reynolds (ReD) number based on the mainstream velocity and the film hole diameter was fixed at 3191, and the rotating speed (ω) was either 0 rpm or 800 rpm; the film cooling blowing ratios ranged from 0.4 to 2.0, and two averaged density ratios of 1.02 and 1.53 were employed with air and carbon dioxide (CO2) as the coolant, respectively. Thermochromic liquid crystal was used to measure the solid surface temperature distributions. Experimental results showed the following: (1) In the stationary case, the blowing ratio has a significant influence on the nondimensional heat transfer coefficient (hg/h0) especially in the near hole region. (2) The film trajectory in rotation had an obvious deflection in the spanwise direction, and the deflection angles on the suction surface are larger than those on the pressure surface. This was attributed to the combined action of the Coriolis force and centrifugal force. (3) In the rotating case, for CO2 injection, the magnitude of heat transfer coefficient on the pressure surface is reduced compared with the stationary case, and the blowing ratio has smaller effects on hg/h0 distribution. However, on the suction surface, the heat transfer coefficient at x/D<1.0 is enhanced and then rapidly reduced to be also below the stationary values. For air injection, rotation also depresses the hg/h0 for both the pressure and the suction surface. (4) The density ratio shows a considerable effect on the streamwise heat transfer coefficient distributions especially for the rotating cases.

Analytical Solution of Nonequilibrium Heat Conduction in Porous Medium Incorporating a Variable Porosity Model With Heat Generation

This paper is concerned with the conduction heat transfer between two parallel plates filled with a porous medium with uniform heat generation under a nonequilibrium condition. Analytical solution is obtained for both fluid and solid temperature fields at constant porosity incorporating the effects of thermal conductivity ratio, porosity, and a nondimensional heat transfer coefficient at pore level. The two coupled energy equations for the case of variable porosity condition are transformed into a third order ordinary equation for each phase, which is solved numerically. This transformation is a valuable solution for heat conduction regime for any distribution of porosity in the channel. The effects of the variable porosity on temperature distribution are shown and compared with the constant porosity model. For the case of the exponential decaying porosity distribution, the numerical results lead to a correlation incorporating conductivity ratio and interstitial heat transfer coefficient.

Thermophoresis particle deposition in a non-Darcy porous medium under the influence of Soret, Dufour effects

Thermophoresis particle deposition in free convection on a vertical plate embedded in a fluid saturated non-Darcy porous medium is studied using similarity solution technique. The effect of Soret and Dufour parameters on concentration distribution, wall thermophoretic deposition velocity, heat transfer and mass transfer is discussed in detail for different values of dispersion parameters (Raγ, Raξ) inertial parameter F and Lewis number Le. The result indicates that the Soret effect is more influential in increasing the concentration distribution in both aiding as well as opposing buoyancies. Also, the non-dimensional heat transfer coefficient and non-dimensional mass transfer coefficient changes according to different values of thermophoretic coefficient k.

Thermal-fluid transports in a five-layer membrane-electrode assembly of a PEM fuel cell

Thermal-fluid transport phenomena in a membrane-electrode assembly (MEA) of a polymer electrolyte membrane (PEM) fuel cell attached to interdigitated gas distributors are studied numerically. The MEA consists of two porous catalyst layers, two porous gas diffusion layers, and an impermeable PEM. In the catalyst layers, the overpotential heating by the electrochemical reaction under thermal equilibrium conditions produces heat that is removed by the fluids as well as the solid matrices. In the diffusion layers, the difference in the heat conductivities between the solid matrices and the fluids causes a thermal non-equilibrium in the porous medium. A two-equation approach is used to resolve the temperature difference between the solid matrices and the fluids. The effects of the porous Reynolds number, interfacial heat transfer coefficient, and overpotential heating are examined. It is found that the local maximum temperature occurs inside the cathodic catalyst layer. In addition, the temperature difference between the solid matrices and the fluids in the diffusion layers decreases with increasing the non-dimensional interfacial heat transfer coefficient. The present results have provided comprehensive heat transfer information that is helpful in understanding of the mechanisms responsible for thermal pathways in a PEM fuel cell.

Free Convective Heat and Mass Transfer in a Doubly Stratified Non-Darcy Porous Medium

Free convective heat and mass transfer from a vertical surface embedded in a doubly stratified non-Darcy porous medium has been analyzed. The wall temperature and concentration are constant and the medium is linearly stratified in the vertical direction with respect to both temperature, and concentration. A series approximation is made for stream function, temperature, and concentration in terms of the stratification parameter. The flow, temperature, and concentration fields are affected by the complex interactions among the diffusion ratio Le, buoyancy ratio N and stratification ratio Sr in addition to the inertia parameter Fc. The effect of double stratification of the medium on nondimensional heat and mass transfer coefficients is discussed.

Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface

The mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent fluid is analyzed using similarity solution technique. Wall temperature and stretching velocity are assumed to have specific exponential function forms. The influence of buoyancy along with viscous dissipation on the convective transport in the boundary layer region is analyzed in both aiding and opposing flow situations. The flow is governed by the mixed convection parameter Gr/Re2. The velocity and temperature inside the boundary layer are observed to be influenced by the parameters like Prandtl number Pr, Gebhart number Gb. Significant changes are observed in non-dimensional skin friction and heat transfer coefficients due to viscous dissipation in the medium. The flow and temperature distributions inside the boundary layer are analyzed and the results for non-dimensional skin friction and heat transfer coefficients are discussed through computer generated plots.

Heat and mass transfer by natural convection in a non-Darcy porous medium

The Forchheimer free convection heat and mass transfer near a vertical surface embedded in a fluid saturated porous medium has been analyzed. A similarity solution is presented for constant wall temperature and concentration distributions with specified power function form (Ax−1/2) of mass flux parameter. The effect of Grashof number (Gr), the buoyancy ratio (N), the Lewis number (Le) and the surface mass flux (fw) on the nondimensional heat and mass transfer coefficients are presented.

Gravity-assisted melting in a spherical enclosure: Effects of natural convection

A theoretical model of graivity-assisted melting in a spherical enclosure is discussed in this paper. A sphere with a phase change material initially in the solid phase at its melting temperature is instantaneously exposed to a uniform higher temperature at the wall. The solid phase is assumed to have a higher density as compared to the liquid and drops down as it melts. The effects of natural convection on the melting process have been considered in this analysis. Suitable simplications have been made where necessary, in order to reduce computational effort and time. The non-dimensional melt time and heat transfer coefficient have been obtained as a function of the property values, operating temperatures and physical size for Md ⪡ 1, Ste ⪡ 1, 10 4 ⩽ Gr ⩽ 10 6, 10 ⩽ Pr ⩽ 100, 0.5 ⩽ Mt ⩽5.0,0 ⩽ Sb ⩽ 0.75, 0.01 ⩽ 1/ Prα 0 ⩽ 1.0 and 0.01 ⩽ Ste/ c 0 p ⩽ 0.2. Natural convection is found to limit the range of applicability of previously published correlations.

Surface mounted heat flux sensors

AbstractThe dual integral equations describing heat flow about a circular Heat Flux Sensor on the surface of a layered medium are derived and discussed, together with the extent to which the Heat Flux Sensor measures the heat flow which would occur in the absence of a Heat Flux Sensor. An asymptotic analysis provides new analytical results supporting those derived previously by numerical methods.It is suggested that some properties of the general problem of a Heat Flux Sensor on the surface of a multiply-layered medium can be approximated by a lumped-parameter model depending on only four non-dimensional numbers: namely, two non-dimensional linear heat transfer coefficients, and essentially two non-dimensional thermal resistances. Some support for the lumped parameter model is provided.

Natural Convective Heat Transfer in an Inclined Rectangular Cavity

Experiments of the convective heat transfer in an inclined air filled rectangular cavity were carried out under the conditions of angle of inclination from 0° to 180° and a wide range of aspect-ratios (H/W = 5 ∼ 83). Depending on the angle of inclination, three flow pattern modes of a three-dimensional Benard cellular flow, a screw type flow with the axis parallel to the direction of inclination and a two-dimensional boundary layer flow were identified by visual observations of two directions. In addition, useful correlations of non-dimensional heat transfer coefficients were derived in the relations between Nusselt number NuW and modified Rayleigh number RaW cosθ or NuW and RaW sineθ.

Heat Transfer From Combustion Gases to a Single Row of Closely Spaced Tubes in a Swirl Crossflow Stirling Engine Heater

This paper describes an experimental program to determine the heat-transfer characteristics of a combustor and heat-exchanger system in a hybrid solar receiver which utilizes a Stirling engine. The system consists of a swirl combustor with a crossflow heat exchanger composed of a single row of 48 closely spaced curved tubes. In the present study, heat-transfer characteristics of the combustor/heat-exchanger system without a Stirling engine have been studied over a range of operating conditions and output levels using water as the working fluid. Non-dimensional heat-transfer coefficients based on total heat transfer have been obtained and are compared with available literature data. The results show significantly enhanced heat transfer for the present geometry and test conditions. Also, heat transfer along the length of the tubes is found to vary, the effect depending upon test condition.

Numerical Prediction of the Flow Field and Impingement Heat Transfer Caused by a Laminar Slot Jet

The effects of uniform suction and nozzle exit velocity profile on the flow and heat-transfer characteristics of a semiconfined laminar impinging slot jet were investigated numerically. The full Navier-Stokes and energy equations were solved using a hybrid or upwind finite-difference representation of the equations cast into their vorticity-stream-function form. The importance of the nozzle exit profile is shown by comparison of the computed heat-transfer distribution with the available experimental data in the laminar range. Application of suction at the impingement surface is shown to enhance the local heat-transfer rates by a constant amount. The nondimensional heat-transfer coefficient and skin friction at the plate are computed as functions of the nozzle Reynolds number, the suction rate, and the nozzle velocity profile. The effect of temperature-dependent physical properties is included in the analysis.

Heat transfer across a turbulent boundary layer: Application of a profile method to the step-wall-temperature problem

a cdnstant ; exponent in the temperature profile ; local drag coefficient; a constant; a constant; laminar Prandtl number; turbulent Prandtl number ; Stanton number; non-dimensional heat-transfer coefficient (12); temperature ; non-dimensional velocity along the walq non-dimensional distance along the wall ; non-dimensional distance (5); non-dimensional distance normal to the wall ; non-dimensional thickness of the temperature profile ; non-dimensional temperature (10) ; non-dimensional distance (4) ; turbulent contribution to the non-dimensional total viscosity.

Experimental Investigation of Free Convection in a Liquid Metal in Long Tubes

This paper reports an extension of a previously published investigation into the natural convection process in a liquid metal (4), using circular tubes closed at their lower ends, operating on the thermosyphon principle of heat transfer. In this work longer tubes were used than previously and two distinct regimes of flow were observed. At low heating rates the non-dimensional heat transfer coefficient was found to be a linear function of the temperature difference, and the fluid at the lower end of the tube appeared to be stagnant, contributing negligibly to the overall heat transfer process. At higher heat transfer rates, the data followed the general trends of the previously observed flows in a liquid metal, although The Heat Transfer Rates Were At Least 17 Per Cent Less Than With Normal Boundary Layer Flow, and More Dependent Upon The Surface Geometry. This Was Due To Interference Between The Heated Boundary Layer and The Core of Cooler Fluid, and This Caused Violent Oscillations In The Temperature of The System Which Persisted Throughout The Entire Test Programme.