Combined heat and mass transfer along a vertical moving cylinder with a free stream

The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u _w/(u _w + u _∞), where u _w and u _∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1 it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution. For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction decreases as the relative velocity between the surface and free stream decreases. Received on 17 May 1999     

Influence of lateral mass flux on mixed convection heat and mass transfer over inclined surfaces in porous media

 The effect of lateral mass flux on mixed convection heat and mass transfer in a saturated porous medium adjacent to an inclined permeable surface is analyzed. A similarity solution is obtained when surface temperature and concentration, free stream velocity and injection/suction velocity of fluid are prescribed as power functions of distance from the leading edge. The cases when the flow and buoyancy forces are in the same and opposite directions are discussed both for aiding and opposing buoyancy effects. The governing parameters are the mixed convection parameter Gr, the Lewis number Le, the buoyancy ratio N, the lateral mass flux parameter f _w, representing the effects of injection or withdrawal of fluid at the wall, and λ which specifies three cases of the inclined plate. The interactive effect of these parameters on heat and mass transfer rates are presented. It is observed that the diffusion ratio (Le) has a more pronounced effect on concentration field than on flow and temperature fields. It is found that the rates of heat and mass transfer increase with suction and decrease with injection of the fluid. Received on 31 August 2000 / Published online: 29 November 2001     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

Calculation of heat and mass transfer of tobacco on band coolers

 The heat and mass transfer from moist tobacco on a band cooler was mathematically examined. The fibrous tobacco particles are 10 to 20 mm long and cut to about 1 mm width, with a leaf thickness of approx. 0.1 mm. The tobacco is loosely heaped on a band and cooled after the drying process. The cooling is carried out by cross flow operation with ambient air. Furthermore tobacco is subjected to moisture loss in the course of cooling. The mass transfer is affected upon the initial conditions as well as the considered drying mechanism (first and second drying period). The cooling process on the band cooler is calculated by applying a two dimensional stationary cross flow model as shown. Received on 28 March 2001     

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number.     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.     

Coupled heat and mass transfer in mixed convection over a vertical flat plate embedded in saturated porous media: PST/PSC or PHF/PMF

A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N ^*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases) the local heat (mass) transfer rate. Received on 8 December 1997     

Combined heat and mass transfer by laminar natural convection from a vertical plate

Simultaneous heat and mass transfer in buoyancy-induced laminar boundary-layer flow along a vertical plate is studied for any ratio of the solutal buoyancy force to the thermal buoyancy force by using a new similarity transformation. The effects of the buoyancy ratio and Lewis number on the rates of heat and mass transfer are presented explicitly for most practical gaseous solutions (Pr=0.7, 0.21≤Sc≤2.1) and aqueous solutions (Pr=7, 140≤Sc≤1400). Very accurate correlations of the mass transfer and heat transfer rates are developed for the cases of single and combined buoyancy forces.     

Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel

An experimental study was conducted of incompressible, moderate Reynolds number flow of air over heated rectangular blocks in a two-dimensional, horizontal channel. Holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in self- sustained oscillatory flow. Experiments were conducted in the laminar, transitional and turbulent flow regimes for Reynolds numbers in the range from Re = 520 to Re = 6600. Interferometric measurements were obtained in the thermally and fluiddynamically periodically fully developed flow region on the ninth heated block. Flow oscillations were first observed between Re = 1054 and Re = 1318. The period of oscillations, wavelength and propagation speed of the Tollmien–Schlichting waves in the main channel were measured at two characteristic flow velocities, Re = 1580 and Re = 2370. For these Reynolds numbers it was observed that two to three waves span one geometric periodicity length. At Re = 1580 the dominant oscillation frequency was found to be around 26 Hz and at Re = 2370 the frequency distribution formed a band around 125 Hz. Results regarding heat transfer and pressure drop are presented as a function of the Reynolds number, in terms of the block-average Nusselt number and the local Nusselt number as well as the friction factor. Measurements of the local Nusselt number together with visual observations indicate that the lateral mixing caused by flow instabilities is most pronounced along the upstream vertical wall of the heated block in the groove region, and it is accompanied by high heat transfer coefficients. At Reynolds numbers beyond the onset of oscillations the heat transfer in the grooved channel exceeds the performance of the reference geometry, the asymmetrically heated parallel plate channel. Received on 26 April 2000     

Heat transfer by laminar flow in a vertical pipe with twisted-tape inserts

Heat transfer for laminar flow of water in an air-cooled vertical copper pipe with four twisted-tape inserts was determined experimentally. The tests were executed for laminar flow within 110 ≤ Re ≤ 1500, 8.1 ≤ Gz ≤  82.0 and 1.62 ≤ y ≤ 5.29. The correlation equation for heat transfer was defined for the tested range. The obtained results were compared to the results of other authors. Received on 28 April 1998     

T-RANS Simulations of Subcritical Flow with Heat Transfer Past a Circular Cylinder Surrounded by a Thin Porous Layer

We study flow and heat transfer to a cylinder in cross flow at Re = 3,900–80,000 by means of three-dimensional transient RANS (T-RANS) simulations, employing an RNG k − ε turbulence model. Both the case of a bare solid cylinder and that of a solid cylinder surrounded at some fixed distance by a thin porous layer have been studied. The latter configuration is a standard test geometry for measuring the insulating and protective performance of garments. In this geometry, the flow in the space between the solid cylinder and the porous layer is laminar but periodic, whereas the outer flow is transitional and characterized by vortex shedding in the wake of the cylinder. The results from the T-RANS simulations are validated against data from Direct Numerical Simulations and experiments. It is found that T-RANS is very well suited for simulating this type of flow. The transient nature of the flow underneath the porous layer is well reproduced, as well as the influence of vortex shedding on the heat transfer in the downstream stagnation zone. T-RANS results are found to be in much better agreement with DNS and experimental data than results from steady-state RANS.     

Comparative evaluation of three heat transfer enhancement strategies in a grooved channel

 Results of a comparative evaluation of three heat transfer enhancement strategies for forced convection cooling of a parallel plate channel populated with heated blocks, representing electronic components mounted on printed circuit boards, are reported. Heat transfer in the reference geometry, the asymmetrically heated parallel plate channel, is compared with that for the basic grooved channel, and the same geometry enhanced by cylinders and vanes placed above the downstream edge of each heated block. In addition to conventional heat transfer and pressure drop measurements, holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in the self-sustained oscillatory flow. The locations of increased heat transfer within one channel periodicity depend on the enhancement technique applied, and were identified by analyzing the unsteady temperature distributions visualized by holographic interferometry. This approach allowed gaining insight into the mechanisms responsible for heat transfer enhancement. Experiments were conducted at moderate flow velocities in the laminar, transitional and turbulent flow regimes. Reynolds numbers were varied in the range Re = 200–6500, corresponding to flow velocities from 0.076 to 2.36 m/s. Flow oscillations were first observed between Re = 1050 and 1320 for the basic grooved channel, and around Re = 350 and 450 for the grooved channels equipped with cylinders and vanes, respectively. At Reynolds numbers above the onset of oscillations and in the transitional flow regime, heat transfer rates in the investigated grooved channels exceeded the performance of the reference geometry, the asymmetrically heated parallel plate channel. Heat transfer in the grooved channels enhanced with cylinders and vanes showed an increase by a factor of 1.2–1.8 and 1.5–3.5, respectively, when compared to data obtained for the basic grooved channel; however, the accompanying pressure drop penalties also increased significantly. Received on 5 April 2001     

Mass transfer effects on the non-Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux

 The present study is devoted to investigate the influences of mass transfer on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solution for the transformed governing equations is obtained with prescribed variable surface heat flux. Numerical results for the details of the velocity, temperature and concentration profiles are shown on graphs. Excess surface temperature as well as concentration gradient at the wall associated with heat flux distributions, which are entered in tables, have been presented for different values of the power-law index n, buoyancy ration B and the exponent λ as well as Lewis number Le. Received on 26 April 2000     

Flow of a viscous incompressible fluid of temperature dependent viscosity past a permeable wedge with uniform surface heat flux

 The effect of uniform suction on the steady two-dimensional laminar forced flow of a viscous incompressible fluid of temperature dependent viscosity past a wedge with uniform surface heat flux is considered. The governing equations for the flow are obtained by using suitable transformations and are solved by using an implicit finite difference method. Perturbation solutions are also obtained near the leading edge and in the downstream regime. The results are obtained in terms of the local skin friction coefficient and the rate of heat transfer for various values of the pertinent parameters, such as the Prandtl number, Pr, the velocity gradient parameter, m, the local suction parameter, ξ, and the viscosity variation parameter, ɛ. Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement. The effect of ξ, m and ɛ on the dimensionless velocity profiles and viscosity distribution are also presented graphically for Pr = 0.7 and 7.0, which are the appropriate values for gases and water respectively. Received on 22 July 1999     

Transient free convection flow between long vertical parallel plates with ramped wall temperature at one boundary in the presence of thermal radiation and constant mass diffusion

The unsteady laminar free convection flow between two long vertical parallel plates with ramped wall temperature at one boundary has been investigated in the presence of thermal radiation and chemical species concentration. The exact solutions of the momentum, energy and concentration equations have been obtained using the Laplace transform technique. The velocity and temperature profiles, skin-friction and Nusselt number variations are shown graphically and the numerical values of the volume flow rate, the total heat rate and species rate added to the fluid are presented in a table. The influence of different system parameters such as the radiation parameter (R), buoyancy ratio parameter (N), Schmidt number (Sc) and time (t) has been analyzed carefully. A critical analysis of the coupled heat and mass transfer phenomena is provided. The free convective flow due to ramped wall temperature has also been compared with the baseline case of flow due to constant wall temperature.     

Heat and mass transfer for micropolar flow with radiation effect past a nonlinearly stretching sheet

In this study, an analysis has been performed for heat and mass transfer with radiation effect of a steady laminar boundary-layer flow of a micropolar flow past a nonlinearly stretching sheet. Parameters n, K, k ₀, Pr, Ec, and Sc represent the dominance of the nonlinearly effect, material effect, radiation effect, heat and mass transfer effects which have presented in governing equations, respectively. The similar transformation, the finite-difference method and Runge–Kutta method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles, the wall unknown values of θ′(0) and ϕ′(0) for calculating the heat and mass transfer of the similar boundary-layer flow are carried out as functions of n, Ec, k ₀, Pr, Sc. The value of n, k ₀, Pr and Sc parameters are important factors in this study. It will produce greater heat transfer efficiency with a larger value of those parameters, but the viscous dissipation parameter Ec and material parameter K may reduce the heat transfer efficiency. On the other hand, for mass transfer, the value of Sc parameter is important factor in this study. It will produce greater heat transfer efficiency with a larger value of Sc.     

Effect of viscous dissipation on mixed convection heat transfer in a vertical tube with uniform wall heat flux

 The laminar and parallel flow of a Newtonian fluid in a vertical cylindrical duct with circular cross section has been analysed. Both the viscous dissipation effect and the buoyancy effect have been taken into account. The momentum balance equation and the energy balance equation have been solved by means of a perturbation method, in the case of a uniform heat flux prescribed at the wall of the duct. The velocity distribution, the temperature distribution, the Nusselt number and the Fanning friction factor have been evaluated analytically. Moreover, the velocity and temperature of the fluid have been compared with those obtained in two special cases: forced convection with viscous dissipation (i.e. negligible buoyancy effect); mixed convection with negligible effects of viscous dissipation. Received on 26 June 2000     

Combined heat and mass transfer by laminar natural convection from a vertical plate with uniform heat flux and concentration

This paper studies combined heat and mass transfer by laminar natural convection from a vertical plate maintained with uniform surface heat flux and species concentration. Very accurate finite-difference solutions of a set of nonsimilarity equations have been obtained for most practical gaseous solutions (Pr?=?0.7, 0.21 ≤ Sc ≤ 2.1) and aqueous solutions (Pr?=?7, 140 ≤ Sc ≤ 1400). Variations of heat and mass transfer rates with buoyancy ratio and Lewis number are presented. Precise correlations have been developed for predicting heat and mass transfer rates of natural convection arising from single (solutal or thermal) buoyancy force and dual buoyancy forces.     

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.