Combined heat and mass transfer in laminar gas stream flowing over an evaporating liquid film

A numerical analysis was carried out to study the detailed heat and mass transfer characteristics in laminar gas stream flowing over a falling liquid water film by solving the respective governing equations for the liquid film and gas stream together. It was observed that the cooling of the liquid film is mainly caused by the latent heat transfer connected with the vaporization of the liquid film. Significant liquid cooling results for the system with a high inlet liquid temperature, high gas stream velocity or a low liquid flowrate. Additionally, the predicted Nusselt and Sherwood numbers were correlated.     

Radiative-convective heat transfer in a plane layer of a selectively absorbing mist

This paper deals with the thermal field in a plane layer of selectively absorbing gas which has been injected into a steady turbulent stream of high-temperature gas flowing around a porous plate. The boundary-value problem in terms of the energy equation reduces to a nonlinear integral equation in terms of a dimensionless temperature, and this equation is solved numerically by the Newton-Kantorovich method. The results are presented on graphs of temperature and thermal flux in the absorbing gas layer as functions of the space coordinate. Such a problem has been analyzed in [1] for the case of an injected gray gas.Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 3, pp. 179–182, May–June, 1972.     

Microscale heat transfer in an evaporating moving extended meniscus

The evaporative heat flux distribution in the leading edge region of a moving evaporating thin liquid film of pentane on quartz was obtained by analyzing the measured thickness profile for thicknesses, δ < 2 μm. The profiles in a constrained vapor bubble were obtained using image analyzing interferometry. Although the evaporating meniscus appeared to be benign (i.e., without additional observed motion beyond creeping), high heat fluxes were obtained. Significantly higher heat fluxes are possible. The interfacial slope, curvature, interfacial shear stress, and liquid pressure profiles were also obtained. Results obtained using a continuum model were consistent with those obtained using a control volume model. The measured pressure field profile of the isothermal extended meniscus agreed with the constant pressure field predicted by the augmented Young–Laplace model. For the non-isothermal case, measured thickness gradients lead to disjoining pressure and curvature gradients for fluid flow and evaporation. The experimental results demonstrate that disjoining pressure at the contact line controls fluid flow within an evaporating completely wetting thin curved film and is, therefore, a useful boundary condition. However, in small interfacial systems, non-idealities can have a dramatic effect.     

Turbulent forced convective heat transfer in two-phase evaporating droplet flow through a vertical pipe

A physical model was developed to study heat transfer in turbulent dispersed flow at very high vapor quality in a vertical pipe by numerically solving the coupling governing differential equations for both phases. Major heat transfer mechanisms included in the model were the thermal nonequilibrium effects, droplet vaporization, droplet deposition on the duct wall and thermal radiative transfer. The predicted results indicated that vapor superheating is dominant for the cases with high wall superheat, otherwise droplet vaporization dominates the energy transport processes. Heat transfer during the droplet-wall interaction only exists at low wall superheat but in small amounts.     

Effects of viscous dissipation on heat transfer in an oscillating flow past a flat plate

Theoretical investigation has been carried out of laminar thermal boundary layer response to harmonic oscillations in velocity associated with a progressive wave imposed on a steady free stream velocity and convected in the free stream direction. Series solutions are derived both to velocity and temperature field and the resulting equations are solved numerically. The functions affecting the temperature field are shown graphically for different values of Prandtl number. It is observed that there is more reduction in the rate of heat transfer for P _r<1 and a rise in the rate of heat transfer for P _r>1 due to the presence of oscillatory free-stream.Nomenclature u, v velocity components in the x and y direction - x, y Cartesian coordinate axes - t time - U, U ₀ instantaneous value of and mean free stream velocity - density of fluid - kinematic viscosity - T, T _w, T temperature of the fluid, wall and free stream fluid - c _p specific heat at constant pressure - thermal diffusivity - amplitude of free stream velocity - frequency - _p non-dimensional temperature (T–T /T _w–T ) - P _r Prandtl number (c _p/K) - E _c Eckert number (U ₀ ² /c _p(T _w–T )) - a parameter ( ) - ₀ boundary layer thickness of the oscillation of a harmonic oscillation of frequency ( ) - ordinary boundary layer thickness ( ) - time-averaged, time-independent external velocity - A, B, C, D, E, K, L, M, N, P functions used in expansion for u and - Nu Nusselt number (hx/k) - T _w–% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8V4rqqrFfpeea0Jc9yq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepGe9fr-xfr-x% frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcadaGcaa% qaaiaadAhacaWG4bGaai4laiqadwfagaqeaaWcbeaakiaacMcaaaa!3CA6!\[(\sqrt {vx/\bar U} )\] - k thermal conductivity     

Unsteady radiative-conductive heat transfer in a semitransparent selectively absorbing layer

Results of a numerical solution of the boundary-value problem of radiative-conductive heat transfer in a flat layer of a selectively absorbing and radiating medium are presented. The effect of the optical properties of the medium and the walls, the temperature of the source of radiation, and the relationship between the absorption spectra of the medium and the source of radiation on temperature distribution is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 124–129, March–April, 2000.     

Unsteady radiative-convective heat transfer in a high-temperature gas-particle flow past a semi-transparent plate

Numerical simulations of unsteady radiative-convective heat transfer in a turbulent flow of a mixture of gases and solid particles past a semi-transparent plate are performed. An ablation process is demonstrated to occur on the plate surface in the case of intense radiative heating of the plate by an external source with emission in a limited spectral range. Temperature fields and distributions of heat fluxes in the boundary layer and in the plate are calculated. Calculation results are presented, which allow determining the effect of ablation and reflecting properties of the plate surface on the thermal state of the medium in the system containing the boundary layer and the plate under conditions of plate heating by a high-temperature source of radiation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 140–146, May–June, 2009.     

Unsteady flow past an impulsively started vertical plate with heat and mass transfer

Finite difference solution of the transient free-convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with heat and mass transfer is presented here. The steady state velocity, temperature and concentration profiles are shown graphically. Velocity profiles are compared with exact solution. It has been observed that there is a rise in the velocity due to the presence of a mass diffusion. An increase in Schmidt number, leads to a fall in the velocity. Stability and the convergence of the finite difference scheme are established. Received on 7 January 1998     

Experimental study on effect of relative humidity on heat transfer of an evaporating water droplet in air flow

Dispersed water droplets are often seen in environmental air flows in rain, cloud, mist, sea spray and so on. It is therefore of great importance to precisely estimate heat transfer between water droplets and atmospheric air in developing a reliable climate model. The purpose of this study is to fabricate the measurement system for the temperature of a small water droplet in air flow under the controlled relative humidity condition and to investigate the effect of relative humidity on heat transfer across the surface of an evaporating water droplet in air flow. The results show that the droplet temperature decreases in the low-relative-humidity condition, whereas it increases in the high-relative-humidity condition. Nusselt number on the droplet surface is not affected by the relative humidity.     

Hypersonic flow past a flat body in a regime of intense radiative heat transfer

The paper is devoted to the investigation of hypersonic flow regimes in which radiative transfer plays a significant part. A numerical solution is obtained to the two-dimensional steady problem of hypersonic flow past a flat thermally insulated body of an inviscid radiating gas with allowance for radiative transfer of energy in the approximation of radiative thermal conductivity. It is noted that a heated region is formed around the body, its dimensions exceeding by an order of magnitude those of the body itself; the temperature is effectively equalized, and the gas velocity is close to the velocity of the oncoming flow. Heated gas flows past the body at a moderate Mach number (M ～ 3–6). A thin region of strongly compressed gas is formed directly in front of the body.     

Conjugate heat transfer in the unbounded flow of a viscoelastic fluid past a sphere

This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime (Re = 0.01). The problem is numerically solved with the finite-volume method assuming axisymmetry, absence of natural convection and constant physical properties. The sphere generates heat at a constant and uniform rate, and the analysis is conducted for a range of Deborah (0 ≤ De ≤ 100), Prandtl (10⁰ ≤ Pr ≤ 10⁵) and Brinkman (0 ≤ Br ≤ 100) numbers, in the presence or absence of thermal contact resistance at the solid–fluid interface and for different conductivity ratios (0.1 ≤ κ ≤ 10). The drag coefficient shows a monotonic decrease with De, whereas the normalized stresses on the sphere surface and in the wake first increase and then decrease with De. A negative wake was observed for the two solvent viscosity ratios tested (β = 0.1 and 0.5), being more intense for the more elastic fluid. In the absence of viscous dissipation, the average Nusselt number starts to decrease with De after an initial increase. Heat transfer enhancement relative to an equivalent Newtonian fluid was observed for the whole range of conditions tested. The dimensionless temperature of the sphere decreases and becomes more homogeneous when its thermal conductivity increases in relation to the conductivity of the fluid, although small changes are observed in the Nusselt number. The thermal contact resistance at the interface increases the average temperature of the sphere, without affecting significantly the shape of the temperature profiles inside the sphere. When viscous dissipation is considered, significant changes are observed in the heat transfer process as Br increases. Overall, a simplified PTT fluid can moderately enhance heat transfer compared to a Newtonian fluid, but increasing De does not necessarily improve heat exchange.     

A numerical study of heat transfer during flow of melt in a cylindrical mould

A numerical analysis of transient heat transfer during the flow of a melt in a cylindrical mould is presented. The analysis includes thermal resistance at the melt-mould interface, and axial conduction inside both melt and mould. Energy equations are formulated in a domain that expands continuously due to the advance of the melt inside the empty mould, and solved by the finite difference method using a time-stepping procedure. Calculations are compared to existing analytic results. It is found that axial conduction in the melt can significantly influence the rate of heat loss from the flowing melt, and that analytic approximations, which neglect axial conduction, may give erroneous predictions for the rate of heat loss.     

Radiative heat transfer in a hypersonic gas flow generated a spherical source past a plane

An asymptotic solution of radiative gas-dynamic equations for stationary interaction of two hypersonic gas flows emanating from two identical spherical sources is obtained. Under the assumption that the gas in the shock layer is in local thermodynamic equilibrium and volume emission (energy loss for radiation) occurs there, analytical expressions for the distributions of gas-dynamic functions and temperature are derived. The shock wave shape and the radiant flux on the contact plane are examined as functions of problem parameters.     

Transient couple heat transfer in an absorbing rectangular medium with one semitransparent diffuse boundary

This paper studies 2-D transient coupled radiative and conductive heat transfer in an absorbing non-scattering rectangular medium. The medium have one diffuse semitransparent boundary, and the other three boundaries are black. The reflectivity of the diffuse semitransparent boundary is determined by integrating the reflected energy over the whole hemispherical space according to the Fresnel’s reflective law and Snell’s refractive law based on assuming each bit of the rough surface to be optically smooth.     

Unsteady flow and heat transfer past an axisymmetric permeable shrinking sheet with radiation effect

In this paper, the problem of unsteady axisymmetric boundary layer flow and heat transfer induced by a permeable shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by an implicit finite‐difference scheme known as the Keller‐box method. The influence of radiation, unsteadiness and mass suction parameters on the reduced skin friction coefficient f′′(0) and the heat transfer coefficient ?θ′(0), as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and suction parameter delays the separation of boundary layer. Copyright © 2010 John Wiley & Sons, Ltd.     

Heat transfer in flow past a continuously moving porous flat plate with heat flux

The analysis of the heat transfer in flow past a continuously moving semi-infinite plate in the presence of suction/ injection with heat flux has been presented. Similarity solutions have been derived and the resulting equations are integrated numerically. It has been observed that an increase in suction value leads to an increase in temperature whereas it is opposite in the case of injection.

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Wärmeübergang in einer Strömung hinter einer wärmeabgebenden, kontinuierlich bewegten, porösen Platte

Zusammenfassung Es wird eine Analyse des Wärmeübergangs in einer Strömung hinter einer bewegten, halbunendlichen Platte bei gleichzeitiger Absaugung bzw. Ausströmung präsentiert. Mit Hilfe von Ähnlichkeitsbetrachtungen wurden Lösungen erarbeitet und die daraus resultierenden Gleichungen wurden numerisch integriert. Als Ergebnis zeigte sich, daß zunehmende Absaugung zu einer Erhöhung der Temperatur führt, während bei der Ausströmung das Gegenteil der Fall ist.

     

Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer

In this paper the study of visco-elastic (Walters' liquid B model) flow past a stretching plate with suction is considered. Exact solutions of the boundary layer equations of motion and energy are obtained. The expressions for the coefficient of skin friction and of boundary layer thickness are obtained.