Combined heat and mass transfer in natural convection between vertical parallel plates

Abstract

This study is to examine the effects of latent heat transfer associated with liquid film vaporization on heat transfer in the natural convection flows driven by the simultaneous presence of combined buoyancy forces of thermal and mass diffusion. Results are especially presented for an air‐water system under various conditions. The influences of channel length and system temperatures on the momentum, heat and mass transfer in the flow are investigated in great detail. The important role of transport of latent heat of vaporization under the situations of buoyancy‐aiding and opposing flows is clearly demonstrated.     

Laminar forced convection in wedge flow with separation

Abstract

A perturbation method is used to study the steady and unsteady laminar boundary layer heat transfer from a wedge with separation for a step‐discontinuity in the surface temperature. The analytic solutions obtained can be used to calculate the steady and unsteady heat transfer rate with arbitrary surface temperature. The effects of the Prandtl number on the temperature distribution and the heat transfer rate are discussed in detail. The solution is valid for large or moderate Prandtl number.     

Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective flow and mass transfer over an accelerating surface with a heat source in the presence of suction and blowing in the case of variable viscosity

Summary. An analysis has been carried out to obtain the thermal-diffusion and the diffusion-thermo effects on the mixed free-forced convective and mass transfer steady laminar boundary-layer flow over an accelerating surface with a heat source in the presence of suction and blowing. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which is solved numerically by applying the shooting method. The results for an impermeable accelerating surface are discussed. The effects of the variable viscosity parameter _r, the thermal diffusion parameter Sr, the diffusion-thermo parameter Df, suction or blowing parameter m, heat flux parameter s and Schmidt number Sc have been examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The effects of varying these parameters are studied in the case of a surface with prescribed wall temperature and a surface with prescribed wall heat flux.     

Mixed convection in micropolar fluid flow over a horizontal plate with surface mass transfer

Combined free and forced convection in the boundary layer flow of a micropolar fluid over a horizontal surface is studied. Buoyancy effects on the flow and temperature fields are discussed. The influence of uniform mass transfer from the surface is also considered. Wall friction and heat transfer results are presented for various cases representing the relative effects of blowing or suction as compared to the combined effects of buoyancy and mass transfer.     

Experimental investigation on heat transfer characteristics of supercritical CO2 cooled in horizontal helically coiled tube

An experimental investigation on the heat transfer characteristics of supercritical CO₂ during gas cooling process in a helically coiled tube is conducted. The experimental data are obtained over a mass flux range of 79.6–238.7 kg m⁻² s⁻¹, an inlet pressure range of 7.5–9.0 MPa and a mean bulk temperature of 23.0–53.0 °C. The effects of mass flux, bulk temperature and pressure on the heat transfer coefficient for helically coiled tubes are investigated. A comparative analysis of the gravitational buoyancy and the heat transfer coefficient is carried out between helically coiled tubes and straight tubes. A new heat transfer correlation of the supercritical CO₂ in the horizontal helically coiled tube is proposed based on the experimental data. The maximum error between the predicted results of the new correlation and the experimental data is 20%.     

Mixed convection near a non-orthogonal stagnation point flow on a vertical plate with uniform surface heat flux

Summary The interaction of a buoyancy induced mixed convection flow and a free stream impinging at some angle of incidence on a vertical flat plate with a prescribed surface heat flux is studied in this paper. The similarity equations are numerically solved for some values of the governing parameters. It is found that the buoyancy force and non-orthogonal mechanisms act to either reinforce or oppose one another. The stagnation point (separation point) is shifted at the left or at the right of the origin and it depends upon the balance between obliqueness and thermal effects.     

Unsteady mixed convection flow at the stagnation point

The unsteady mixed convection flow of an electrically conducting fluid at the stagnation point of a two-dimensional body and an axisymmetric body in the presence of an applied magnetic field has been studied. The effect of induced magnetic field has been included in the analysis. Both prescribed wall temperature and prescribed heat flux conditions have been considered. It is found that if the free stream velocity, applied magnetic field and square root of the wall temperature vary inversely as a linear function of time, i.e. as (1 − λt′)⁻¹, the governing boundary layer equations admit a locally self-similar solution. If surface heat flux is prescribed, it should vary as (1 − λt^*)^−5/2 for the existence of a local self-similar solution. The resulting ordinary differential equations have been solved using a finite element method as well as a shooting method with Newton's corrections for missing initial conditions. The skin friction and heat transfer coefficients and x-component of the induced magnetic field on the surface increase with the applied magnetic field or buoyancy force. Also they are found to change more for decelerating free stream velocity than for accelerating free stream velocity. Furthermore, they change little with the reciprocal of the magnetic Prandtl number. The buoyancy parameter causes overshoot in the velocity profile. For a given Prandtl number, beyond a certain critical value of the dissipation parameter, the hot wall ceases to be cooled due to the “heat cushion” provided by frictional heat.     

Effects of wetted wall on laminar natural convection in vertical annular ducts

Abstract

A detailed numerical analysis is performed to investigate the effects of latent heat exchange, in connection with evaporation of the liquid film on the wall, on the natural convection heat transfer in vertical concentric annuli. Major governing parameters identified are Gr_T, Gr_M, Pr, Sc, and N. Results are specifically presented for an air‐water system under various heating conditions to illustrate the latent heat transport during the evaporation process. The effects of the channel length, ratio of radii N and wetted wall temperature on the momentum, heat and mass transfer are examined in detail. Tremendous enhancement in heat transfer due to the exchange of latent heat was clearly demonstrated.     

A pumped supercritical helium flow loop for heat transfer studies

The construction and operation of a flow loop is described in which a 0.5 ls^? centrifugal pump circulates supercritical helium through a 1 m long, 18 mm id heated test section instrumented with 18 carbon resistance thermometers. Based on the heat transfer measurements obtained (published in detail elsewhere) some observations are made on deviations from the standard Dittus Boelter heat transfer correlation caused by helium's variable properties, and on possible buoyancy induced reductions in heat transfer particularly for radially inward flow in rotating machines.     

Mixed convection boundary layer flow of a micropolar fluid along vertical cylinders and needles

An analysis is presented to investigate the effects of buoyancy and curvature on convection along vertical cylinders and needles placed in a micropolar fluid. The governing equations for momentum, angular momentum and energy are solved numerically by finite difference scheme. The heat transfer results are presented for a range of values of the buoyancy parameters, the curvature parameter and the material parameters of the fluid. The effect of the microrotation boundary conditions on heat transfer is discussed.     

Numerical study of Soret and Dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with variable heat fluxes embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. The buoyancy induced boundary layer adjacent to a vertical surface is analyzed using a non-Darcy flow model. The parameters for inertia, buoyancy ratio, exponent of heat flux, position and diffusion have been examined. The governing differential equations of continuity, momentum, energy and concentration are transformed into a set of coupled equations and solved using similarity analysis with numerical technique. Results show the velocity, temperature and concentration profiles related to local Nusselt and Sherwood numbers at different magnitude of Soret and Dufour numbers.     

Thermal instability of a rotating curved plate subjected to an applied magnetic field

The effect of a magnetic field on thermal instability in mixed convection flow on a heated rotating convex surface is studied in this paper. The onset position characterized by the Goertler number G _δ depends on the Grashof number, the rotational number, the Prandtl number, the magnetic field parameter, and the wave number. The buoyancy force, the centrifugal force, the Lorentz force, and the Coriolis force are found to significantly affect the flow structure and heat transfer of the flow. Negative rotation (clockwise) destabilizes the boundary layer flow on a convex surface. However, the Lorentz force stabilizes the flow. Numerical data in this study show the same order of magnitude like experimental data.     

Combined heat and mass transfer in natural convection on horizontal and inclined plates with variable surface temperature/concentration or heat/mass flux

Summary An analysis is presented to study the heat and mass transfer characteristics of natural convection flow along horizontal and inclined plates with variable surface temperature/concentration or heat/mass flux under the combined buoyancy effects of thermal and mass diffusion. Numerical results are obtained for two values of Schmidt number covering the range of diffusion species of common interest like water vapour, carbon dioxide and naphthalene in air.     

Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption

The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model. The formulation of the flow model is based on basic universal equations of conservation of momentum, energy and mass. The prescribed flow model is converted to non-dimensional form by using suitable scaling. The obtained transformed equations are solved numerically by using finite difference scheme. For the analysis of above said behavior the computed numerical data for fluid velocity, temperature profile, and mass concentration for several constraints that is mixed convection parameter λ_t, modified mixed convection parameter λ_c, Prandtl number Pr, heat generation/absorption parameter δ, Schmidt number Sc, thermophoresis parameter N_t, and thermophoretic coefficient k are sketched in graphical form. Numerical results for skin friction, heat transfer rate and the mass transfer rate are tabulated for various emerging physical parameters. It is reported that in enhancement in heat, generation boosts up the fluid temperature at some positions of the surface of the sphere. As heat absorption parameter is decreased temperature field increases at position X = π/4 on the other hand, no alteration at other considered circumferential positions is noticed.     

Effect of plate orientation on quenching characteristics

Abstract

The effect of position on the face of a steel plate on the quenching process during cooling from a typical austenitisation temperature has been examined. In addition, the effect of plate orientation on the quenching mechanism has been investigated. The most significant effect of these parameters on the quenching process relates to the length of the vapour blanket stage, which is very sensitive to position on the surface of the specimen. This has considerable importance in relation to the production of unhardened regions. A markedly different mechanism of heat transfer during nucleate boiling at different positions on the face did not give rise to corresponding differences in the surface heat transfer coefficients at this stage in the quench. The investigation of heat transfer in the surface of the plate has been supported by still photographs that clearly show the different processes at different positions and orientations of the plate. In particular they show violent disruption of the surrounding quenchant as large packets of vapour are nucleated in quick succession on the underside of a horizontal plate.

MST/3032     

Mould surface roughness and interfacial heat transfer using heat flow model

Abstract

The heat resistance at the metal/mould interface, represented by the interfacial heat transfer coefficient (IHTC), plays an important role in the rate of heat transfer from the metal to the mould. The objective of the present work was to determine the influence of the mould inner surface roughness on the IHTC using steel moulds of diameter 55 mm and height 56 mm with different surface roughnesses to solidify pure zinc with a superheat of 80 K. A computer program solving the heat conduction equation taking into consideration the convection in the molten zinc was used, together with the experimental temperature history, to determine the IHTC at the metal/mould interface. The results show that IHTC decreases as mould surface roughness increases.     

Bandwidth reduction by automatic renumbering

Consider a solid heat conductor with a non-linear constitutive equation for the heat flux. If the material is anisotropic and inhomogeneous, the heat conduction equation to be satisfied by the temperature field θ(x, t) is, Here L (θ, x ) [grad θ] is a vector-valued function of θ, x , grad θ which is linear in grad θ, In the present paper, the application of the finite element method to the solution of this class of problems is demonstrated. General discrete models are developed which enable approximate solutions to be obtained for arbitrary three-dimensional regions and the following boundary and initial conditions: (a) prescribed surface temperature, (b) prescribed heat flux at the surface and (c) linear heat transfer at the surface. Numerical examples involve a homogeneous solid with a dimensionless temperature-diffusivity curve of the form κ = κ₀(l + σT). The resulting system of non-linear differential equations is integrated numerically.     

Mixed convection on a vertical surface with a prescribed heat flux: the solution for small and large Prandtl numbers

The mixed convection boundary-layer flow over a vertical surface with a prescribed surface heat flux is considered for both large and small values of the Prandtl number. The similarity equations are treated first. It is shown that, for large values of the Prandtl number, the solution approaches the forced convection limit with the free convection effects having only a small perturbation on this. The opposite is seen to be the case for small values of the Prandtl number, now free convection becomes the dominant heat transfer mechanism. A consequence of this is seen to be that the range of negative buoyancy parameter (opposed flow) over which a solution can exist decreases to zero as the Prandtl number is decreased.The scalings worked out for the similarity equations are then applied to the general boundary-layer flow, with the particular example of a uniform stream over a flat plate with uniform surface heat flux being treated in detail. Again it is seen that, for large Prandtl numbers, the solution approaches the forced convection limit whereas, for small Prandtl numbers, free convection dominates the flow. The effect of this is seen, for opposed flow, to delay the onset of separation for large Prandtl numbers, and to bring the separation point closer to the leading edge as the Prandtl number is decreased. An estimate for this effect is obtained.     

Estimation of air gap and heat transfer coefficient at different faces of Al and Al–Si castings solidifying in permanent mould

Abstract

In the casting processes, the heat transfer coefficient at the metal/mould interface is an important controlling factor for the solidification rate and the resulting structure and mechanical properties. Several factors interact to determine its value, among which are the type of metal/alloy, the mould material and surface conditions, the mould and pouring temperatures, casting configuration, and the type of gases at the interfacial air gap formed. It is also time dependent. In this work, the air gap formation was computed using a numerical model of solidification, taking into consideration the shrinkage and expansion of the metal and mould, gas film formation, and the metallostatic pressure. The variation of the air gap formation and heat transfer coefficient at the metal mould interface are studied at the top, bottom, and side surfaces of Al and Al–Si castings in a permanent mould in the form of a simple rectangular parallelepiped. The results show that the air gap formation and the heat transfer coefficient are different for the different casting surfaces. The bottom surface where the metallostatic pressure makes for good contact between the metal and the mould exhibits the highest heat transfer coefficient. For the sidewalls, the air gap was found to depend on the casting thickness as the larger the thickness the larger the air gap. The air gap and heat transfer coefficient also depend on the surface roughness of the mould, the alloy type, and the melt superheat. The air gap is relatively large for low values of melt superheat. The better the surface finish, the higher the heat transfer coefficient in the first few seconds after pouring. For Al–Si alloys, the heat transfer coefficient increases with increasing Si content.     

Effect of fluidised bed parameters on quenching of steel sections

Abstract

The effect of fluidised bed parameters on quenching efficiency was examined on two steels for various section sizes. Heat transfer coefficients were determined and the microstructure of some sections was examined. It was found that the heat removal rate by the fluidised bed lies between those of air and oil quenching and a martensitic structure was observed in quenched sections. The fluidising velocity affects greatly the heat transfer coefficient h between the bed and the cooled section. The value of h increases with the velocity to a maximum and then decreases. Higher values of h are obtained in beds of fine particles and wide particle size distribution. The bed/cooled section diameter ratio has an important effect on the heat removal rate. The treated section should be immersed well below the bed surface.

MST/658