Heat transfer on a cylinder in accelerated slip flow

The axisymmetric laminar boundary layer flow along the entire length of a semi-infinite stationary cylinder under an accelerated free-stream is investigated. Considering flow at reduced dimensions, the boundary layer equations are developed with the conventional no-slip boundary condition for tangential velocity and temperature replaced by a linear slip-jump boundary condition. Asymptotic series solutions are obtained for the heat transfer coefficient in terms of the Nusselt number. These solutions correspond to prescribed values of the momentum and temperature slip coefficients and the index of acceleration. Heat transfer at both small and large axial distances is determined in the form of series solutions; whereas at intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the heat transfer along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.     

Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure

 A collocated, non-orthogonal grid based finite volume technique has been applied for investigating the two dimensional natural convective flow and heat transfer around a heated cylinder kept in a square enclosure. The effects of different enclosure wall thermal boundary conditions, fluid Prandtl number and the ratio between enclosure and cylinder dimensions (aspect ratio) upon the flow and thermal features, have been systematically studied. It is observed that the patterns of recirculatory flow and thermal stratification in the fluid are significantly modified, if any of these parameters is varied. The overall heat transfer rates are also affected due to the changes in the flow and temperature patterns. The study presents useful observations regarding the variation of local Nusselt number along each wall, for the different cases considered. Received on 2 August 2000 / Published online: 29 November 2001     

Nonsimilar Boundary Layer Analysis of Free Convection Heat Transfer Over a Vertical Cylinder in Bidisperse Porous Media

This work presents a boundary layer analysis for the free convection heat transfer from a vertical cylinder in bidisperse porous media with constant wall temperature. A boundary layer analysis and the two-velocity two-temperature formulation are used to derive the nonsimilar governing equations. The transformed governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The effects of inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Results show that an increase in the modified thermal conductivity ratio and the permeability ratio can effectively enhance the free convection heat transfer of the vertical cylinder in a bidisperse porous medium. Moreover, the thermal nonequilibrium effects are strong for low values of the inter-phase heat transfer parameter.     

Untersuchungen der Kristallisation an wärmeübertragenden Wänden mit Hilfe der holografischen Interferometrie

The holographic interferometry was used for investigations on temperature and concentration boundary layers during the crystallization of salts from aqueous solutions. Results are discussed for aqueous solutions of sodium sulfate and potassium nitrate. The Nusselt numbers derived from temperature profiles coincide very good with calculated results from heat transfer relations. However, no significant changes of concentration in the vicinity of the surface could be found. Investigations with a dissolving crystallization layer show a distinctive diffusion boundary layer. The measured results led to Sherwood numbers 24% higher than published. On the other hand no diffusion boundary layer could be detected for progressive crystallization. This means that the crystal layer grows is reaction controlled. Microscopical pictures of the crystal layer surface show a strongly rugged surface with steps of about 6o pm height. These coarse structures disturb the formation of a boundary layer and prevent the light beam which passes through the test channel. Therefore an existant diffusion boundary layer maybe covered up by the crystal layer.     

A numerical investigation of primary surface rounded cross wavy ducts

 A three-dimensional numerical study was conducted to assess the hydraulic and heat transfer performance of primary surface type heat exchanger surfaces, called cross wavy (CW) ducts aimed for recuperators. The governing equations, i.e., the mass conservation equation, Navier–Stokes equations and the energy equation, are solved numerically by a finite volume method for boundary fitted coordinates. Periodic boundary conditions are imposed in the main flow direction. In this particular case laminar convective flow and heat transfer prevail. Details of the recuperator ducts and the numerical method as well as relevant results are presented. Received on 4 January 2001 / Published online: 29 November 2001     

Control of a liquid–liquid heat exchanger

 The analytical solutions of equations describing the dynamics of distributed parameter systems are usually complicated in form and derivations and inconvenient to use for simulation and control system design. The liquid–liquid counter flow heat exchanger is an example of these disturbed parameter systems. An analytical solution of the dynamics of a symmetrically operated counter flow heat exchanger in the form of transfer function matrix is investigated in open-loop and close-loop conditions. The resulting non-linear model was linearized using perturbation approach. A feed-forward path controller to counteract at any disturbances in the boundary temperature and a non-interactive controller to decouple the outputs were implemented. Received on 22 February 2001 / Published online: 29 November 2001     

Heat and mass transfer in a visco–elastic fluid flow over an accelerating surface with heat source/sink and viscous dissipation

 In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco–elastic fluid flow over an accelerating stretching sheet in the presence of heat source/sink, viscous dissipation and suction/blowing. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles are obtained in the form of confluent hypergeometric (Kummer's) functions for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature and second order power law concentration (PST), and (ii) wall with prescribed second order power law heat flux and second order power law mass flux (PHF). The effect of various physical parameters like visco–elasticity, Eckert number, Prandtl number, heat source/sink, Schmidt number and suction/blowing parameter on temperature and concentration profiles are analysed. The effects of all these parameters on wall temperature gradient and wall concentration gradient are also discussed. Received on 23 March 2000 / Published online: 29 November 2001     

Flow of Casson fluid with nanoparticles

The boundary layer flow of a Casson fluid due to a stretching cylinder is discussed in the presence of nanoparticles and thermal radiation. All physical properties of the Casson fluid except the thermal conductivity are taken constant. Appropriate transformations yield the nonlinear ordinary differential systems. Convergent series solutions are developed and analyzed. The numerical results for the local Nusselt and Sherwood numbers are demonstrated. It is found that an increase in the strength of the Brownian motion decays the temperature noticeably. However, the rate of heat transfer and the concentration of the nanoparticles at the surface increase for larger Brownian motion parameters.     

Heat transfer studies of the oblique impingement of round jets upon a curved surface

 The effect of jet inclination of the local heat transfer under an obliquely impinging round air jet striking on isothermal circular cylinder is experimentally investigated. The circumferential heat transfer distribution as well as axial Nusselt number is measured. The considered parameters are jet Reynolds number in range of 3800–40,000, and jet inclination angle, ranging from 90 to 20. The experiments are carried out for nozzle sizes, d=3, 5 and 7 mm, and separation distance from 7 to 30 of the nozzle diameter. The output results indicated that the point of maximum heat transfer along the x-axis is shifted upstream and the local heat transfer distribution changed as a function of jet inclination. The magnitude of the shift was found to be significantly higher than that observe for a flat plate. The increasing inclination caused increasing asymmetry around the point of maximum heat transfer, with the upstream side of heat transfer profile dropping off more rapidly than the downstream side. Correlations of both the magnitude and shift of maximum heat transfer point are presented. The surface average heat transfer rate is calculated and compared with the normal impingement. Received on 5 June 2000 / Published online: 29 November 2001     

Combined heat and mass transfer by hydromagnetic natural convection over a cone embedded in a non-Darcian porous medium with heat generation/absorption effects

 The problem of combined heat and mass transfer by natural convection over a permeable cone embedded in a uniform porous medium in the presence of an external magnetic field and internal heat generation or absorption effects is formulated. The cone surface is maintained at either constant temperature and constant concentration or uniform heat and mass fluxes. In addition, the cone surface is assumed permeable in order to allow for possible fluid wall suction or blowing. The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved numerically by an implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement between the results is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the temperature and concentration profiles as well as the local Nusselt number and the Sherwood number is illustrated graphically to show special trends of the solutions. Received on 5 June 2000 / Published online: 29 November 2001     

Experimental results of pure and simultaneous heat and mass transfer by free convection about a vertical cylinder for Pr=0.71 and Sc=0.63

In this paper experimental results are given concerning stationary heat and mass transfer in the laminar boundary layer of a vertical cylinder placed in still air. The combined effect is considered as well as the two separate effects. Measurements are carried out on heat transfer and evaporation of water. Results are in close agreement with the classical free convection boundary layer theory for a vertical flat plate, if only a small cylinder correction is applied.     

Analytical study of heat transfer from circular cylinder in liquid metals

In this study the influence of a thin hydrodynamic boundary layer on the heat transfer from a single circular cylinder in liquid metals having low Prandtl number (0.004–0.03) is investigated under isothermal and isoflux boundary conditions. Two separate analytical heat transfer models, viscous and inviscid, are developed to clarify the discrepancy between previous results. For both models, integral approach of the boundary layer analysis is employed to derive closed form expressions for the calculation of the average heat transfer coefficients. For an inviscid model, the energy equation is solved using potential flow velocity only whereas for a viscous model, a fourth-order velocity profile is used in the hydrodynamic boundary layer and potential flow velocity is used outside the boundary layer. The third-order temperature profile is used inside the thermal boundary layer for both models. It is shown that the inviscid model gives higher heat transfer coefficients whereas viscous flow model gives heat transfer results in a fairly good agreement with the previous experimental/numerical results.     

Mixed convection from a cylinder oscillating vertically in a quiescent fluid

 The problem of heat convection from a vertically oscillating cylinder in a quiescent fluid is investigated. The governing equations of motion and energy are solved numerically in a non-inertial frame of references to determine the flow field and heat transfer characteristics under different conditions. The main dominating parameters are Keulegan–Carpenter number, KC, frequency parameter, β, Grashof number, Gr and Prandtl number, Pr. The ranges considered for these parameters are KC ≤ 10, β≤40 and Gr ≤ 10⁵ while Prandtl number is kept constant. The study revealed that the effect of amplitude and frequency of oscillation on heat transfer is strongly influenced by the Grashof number range. In the forced convection regime (Gr = 0), the increase of KC creates extensive vortex motion at all cylinder positions that leads to a significant increase in heat transfer. A similar trend, but with a lesser extent, is also observed for the increase of β. However, at high Grashof numbers, the effect of oscillation on heat convection is only significant at large values of KC. Received on 5 June 2000 / Published online: 29 November 2001     

Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Simultaneous removal of acetone and ethanol from aqueous solutions by membrane distillation: prediction using the Fick's and the exact and approximate Stefan-Maxwell relations

The simultaneous removal of dilute acetone and ethanol from aqueous solutions by air gap membrane distillation is theoretically investigated. A combined heat and mass transfer model that includes temperature and concentration polarization effects as well as temperature and concentration variation along the module length is employed to predict the flux and selectivity of acetone and ethanol under the relevant process operating conditions. Three mass transfer solutions are considered in the model, namely; the exact Stefan-Maxwell (S-M), the approximate Stefan-Maxwell and the Fickian binary solution. Although, qualitatively, the three solutions exhibit the same trends, quantitatively some differences exist between the Fickian-based solution on one hand and the Stefan-Maxwell solutions on the other hand. The exact and approximate solutions of the Stefan-Maxwell equation showed similar capability in predicting the process performance under all process conditions. Predictions showed that acetone selectivity and flux were strongly dependent on feed conditions and air gap width. Received on 29 December 1998     

Analytische Untersuchung von freier Konvektion und Filmsieden in laminaren Grenzschichten mit temperaturabhÄngigen Stoffwerten

A two-dimensional, stationary boundary layer modell is derived which allows the treatment of free convection and film boiling on vertical plate and horizontal cylinder under complete consideration of temperature dependent thermophysical properties. Some qualities of these boundary layer solutions are discussed by eleminating the influences of geometry. For horizontal cylinders, a correction of heat transfer for small diameters is given.     

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.     

Forced Convection Heat Transfer from a Finite-Height Cylinder

This paper presents a large eddy simulation of forced convection heat transfer in the flow around a surface-mounted finite-height circular cylinder. The study was carried out for a cylinder with height-to-diameter ratio of 2.5, a Reynolds number based on the cylinder diameter of 44 000 and a Prandtl number of 1. Only the surface of the cylinder is heated while the bottom wall and the inflow are kept at a lower fixed temperature. The approach flow boundary layer had a thickness of about 10% of the cylinder height. Local and averaged heat transfer coefficients are presented. The heat transfer coefficient is strongly affected by the free-end of the cylinder. As a result of the flow over the top being downwashed behind the cylinder, a vortex-shedding process does not occur in the upper part, leading to a lower value of the local heat transfer coefficient in that region. In the lower region, vortex-shedding takes place leading to higher values of the local heat transfer coefficient. The circumferentially averaged heat transfer coefficient is 20 % higher near the ground than near the top of the cylinder. The spreading and dilution of the mean temperature field in the wake of the cylinder are also discussed.     

Experimental and numerical investigations on slot air jet impingement cooling of a heated cylindrical concave surface

Experimental and numerical studies have been carried out for slot air jet impingement on a heated concave surface of a partially opened-top horizontal cylinder of length L = 20 cm. The slot jet is situated at the symmetry line of the partially opened-top cylinder along the gravity vector and impinges to the bottom of the cylinder which is designated as θ = 0°. The width of the opening at the top of the horizontal cylinder is W = 3 cm which corresponds to a circumferential angle Δθ = 50.8°. The experiments are performed by a Mach–Zehnder interferometer which enables to measure the local convection heat transfer coefficient. Also, a finite volume method based on the SIMPLE algorithm and non-orthogonal grid discretization scheme is used to solve the continuity, momentum, and energy equations. The Poisson equations are solved for (x, y) to find the grid points which are distributed in a non-uniform manner with higher concentration close to the solid regions. The effects of jet Reynolds number (Re _j) in the range from 190 to 1,600 and the ratio of spacing between nozzle and cylinder surface to the jet width from H = 1.5 to H = 10.7 on the local and average Nusselt numbers are examined. It is observed that maximum Nusselt number occurs at the stagnation point at (θ = 0°) and the local heat transfer coefficient decreases on the circumferential surface of the cylinder with increase of θ as a result of thermal boundary layer thickness growth. Also results show that the local and average heat transfer coefficients are raised by increasing the jet Reynolds number and by decreasing the nozzle-to-surface spacing.     

Unsteady natural convective flow past a moving vertical cylinder with heat and mass transfer

Transient natural convection boundary layer flow of an incompressible viscous fluid past an impulsively moving semi- infinite vertical cylinder is considered. The temperature and concentration of the cylinder surface are taken to be uniform. The unsteady, nonlinear and coupled governing equations of the flow are solved using an implicit finite difference scheme. The finite difference scheme is unconditionally stable and accurate. Numerical results are presented with various sets of parameters for both air and water. Transient effects of velocity, temperature and concentration profiles are analyzed. Local and average skin friction, rates of heat and mass transfer are shown graphically. Received on 1 November 1999