Variable Wall Heat Flux Research Articles

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.

Microfluidics analysis of nanoparticle mixing in a microchannel system

The microfluidics of controlled nanodrug delivery to living cells in a representative, partially heated microchannel was analyzed, using a validated computer model. The objective was to achieve uniform nanoparticle exit concentrations at a minimum microchannel length with the aid of simple static mixers, e.g., a multi-baffle-slit or perforated injection micro-mixer. A variable wall heat flux, which influences the local nanofluid properties and carrier-fluid velocities, was added to ensure that mixture delivery to the living cells occurred at the required (body) temperature of 37°C. The results show that both the baffle-slit micro-mixer and the perforated injection micro-mixer aid in decreasing the microchannel length while achieving uniform nanoparticle exit concentrations. The injection micro-mixer not only decreases best the system’s dimension, but also reduces the system power requirement. The baffle-slit micro-mixer also decreases the microchannel length; however, it may add to the power requirement. The imposed wall heat flux aids in enhanced nanoparticle and base-fluid mixing as well.

Effects of free convection on the oscillatory flow of a polar fluid through a porous medium in the presence of variable wall heat flux

The purpose of this work is to study a laminar two-dimensional free convective oscillatory flow of an incompressible polar fluid through a saturated porous medium occupying a semi-infinite region of the space which is bounded by an infinite vertical permeable plate in the presence of oscillating suction and variable wall heat flux. The governing equations are based on the local volume averaging technique. The generalized Darcy equation accounting for polar effects is employed. Analytical expressions for the linear momentum, angular momentum, and energy fields are obtained by using the two-term perturbation technique. The numerically computed results are shown graphically and compared with the corresponding ones for a viscous (Newtonian) fluid. Distribution of the mean velocity of a polar fluid is found to increase as compared to the Newtonian fluid. The analysis reveals multiple boundary-layer structure for velocity.

Natural convection heat and mass transfer of non-Newtonian power law fluids with yield stress in porous media from a vertical plate with variable wall heat and mass fluxes

This work studies the heat and mass transfer by natural convection from a vertical plate with variable wall heat and mass fluxes in a porous medium saturated with a non-Newtonian power law fluid with yield stress for the general case of power law variations in wall heat and mass fluxes. The governing equations are transformed into a dimensionless form by the similarity transformation and then solved by a cubic spline collocation method. Results are presented for velocity, temperature, and concentration profiles, as well as the Nusselt and Sherwood numbers for various parameters of the power law fluid with yield stress in porous media. The existence of threshold pressure gradient in the power law fluids tends to decrease the fluid velocity and the local Nusselt and Sherwood numbers. An increase in the power law exponent increases the local Nusselt and Sherwood numbers.

Free convection in non-newtonian fluids along a horizontal plate in a porous medium

A similarity solution is presented for the problem of free convection boundary layer in power-law type non-Newtonian fluids along a horizontal plate with variable wall temperature or heat flux distribution. The effects of surface mass transfer are included. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Dynamics of single and multiple bubbles and associated heat transfer in nucleate boiling under low gravity conditions.

Experimental studies and numerical simulation of growth and lift-off processes of single bubbles formed on designed nucleation sites have been conducted under low-gravity conditions. Merging of multiple bubbles and lift-off processes during boiling of water in the parabola flights of KC-135 aircraft were also experimentally studied. The heating area of the flat heater surface was discretized and equipped with a number of small heating elements that were separately powered in the temperature-control mode. As such, the wall superheat remained nearly constant during the growth and departure of the bubbles, whereas the local heat flux varied during the boiling process. From numerical calculation it is found that peak of heat flux occurs locally at the contact line of bubble and heater surface. Dry conditions exist inside the bubble base area, which is characterized through a zero heat flux region in the numerical calculation and a lower heat flux period in the experimental results. During the merger of multiple bubbles, dry-out continues. In both the numerical calculations and experimental results, the bubble lift-off is associated with an apparent increase in heat flux. Wall heat flux variation with time and spatial distribution during the growth of a single bubble from numerical simulations are compared with experimental data.

Approche analytique de la convection forcée des fluides de Bingham dans un tube

The asymptotic behaviour of laminar forced convection for Bingham fluid in a circular tube subjected to an axially varying wall heat flux is studied analytically. The effect of viscous dissipation is taken into account while the axial heat conduction in the fluid is considered as negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial wall heat flux distributions which yield a thermally developed region. The results obtained show a diminution in asymptotic Nusselt number when the Brinkman number and the dimensionless radius of the plug flow region increase. Comparisons with the results in the literature for Newtonian fluids show the validity of the present analysis. To cite this article: R. Khatyr et al., C. R. Mecanique 330 (2002) 69–75.

Variable viscosity effects on free and mixed convection boundary-layer flow from a horizontal surface in a saturated porous medium - variable heat flux

In recent years, the study of convective heat transfer from surfaces embedded in porous media has received considerable attention in the literature. The interest for such studies is motivated by several thermal engineering applications, such as geothermal systems, the storage of nuclear wastes, oil extraction, ground water pollution and thermal insulation. The boundary-layer mixed convection flow over horizontal surface with constant or variable wall temperature or heat flux has been studied by many investigators [1-8]. Recently, the flow over an horizontal surface in saturated porous media for the entire regime of forced to free convection has been investigated by Aldoss et al. [9], Chen [10] for Newtonian fluids and by Kumari et al. [11] for non-Newtonian fluids. In all these studies, it was assumed that the thermophysical properties of the fluid are constant. However, it is known that these properties may change with temperature, especially for fluid viscosity. Variable viscosity effects on the stability of flow and temperature fields were considered by Kassoy and Zebib [12], Strans and Schubert [13], Horne and Sullivan [14] and Gary et al. [15]. The effect of variable viscosity for mixed convection flow over a vertical plate with constant wall temperature in saturated porous media has been investigated by Lai and Kulacki [16]. The free or mixed convection flow taking in to account the effect of variable viscosity over a horizontal surface with variable heat flux has not been studied so far.

On the Solution of Multidimensional Inverse Heat Conduction Problems Using an Efficient Sequential Method

An efficient real-time scheme is developed to estimate the unsteady, spatially varying wall heat flux in a two-dimensional heat conduction system from the temperature measurement inside the domain. The algorithm is based on the Kalman filtering and the Karhunen-Loe`ve Galerkin procedure. Although the employment of the Kalman filtering technique allows the derivation of a set of sequential estimation equations, the real-time implementation of these equations is never feasible due to the tremendous requirement of computer time and memory. In the present scheme, this difficulty is circumvented by means of the Karhunen-Loe`ve Galerkin procedure that reduces the governing partial differential equation to a minimal set of ordinary differential equations. The performance of the present technique of inverse heat conduction problems is evaluated by several numerical experiments, and it is found to be very accurate as well as efficient.

Nonsimilar solutions for free convection in non‐Newtonian fluids along a vertical plate in a porous medium

A nonsimilar boundary layer analysis is presented for the problem of free convection in power‐law type non‐Newtonian fluids along a permeable vertical plate with variable wall temperature or heat flux distribution. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Nonsimilar solutions for free convection from a vertical plate in porous media

A nonsimilar boundary layer analysis has been presented for the free convection along a vertical plate embedded in a fluid-saturated porous medium in the presence of surface mass transfer and internal heat generation. The transformed conservation laws are solved numerically for the cases of variable wall temperature and variable wall heat flux boundary conditions. Results are presented for the details of the velocity and temperature fields as well as Nusselt number.

Similarity solution for thermal boundary layer on a stretched surface of a non-Newtonian fluid

Continuum equations governing steady, laminar, boundary-layer flow and heat transfer in a quiescent non-Newtonian, power-law fluid driven by a stretched porous surface are developed. The resulting partial differential equations are nondimensionalized and transformed into ordinary differential equations using similarity transformations for both variable power-law surface temperature and constant wall heat flux cases. The surface is assumed to be moving with a constant velocity. The transformed equations are solved numerically using a standard implicit finite-difference method. Graphical results for the tangential velocity and temperature profiles as well as tabulated results for the skin-friction coefficient and the Nusselt number for various parametric conditions are presented and discussed.

Non-darcy mixed convection over a vertical flat plate in porous media with variable wall heat flux

The problem of non-Darcy mixed convection along a vertical flat plate embedded in a saturated porous medium is analyzed for the case of variable surface heat flux. Based on three different flow models, the influences of non-Darcy flow phenomena on mixed convection from a vertical surface are thoroughly investigated. The wall effect on porosity variation is approximated by an exponential function. The effects of thermal dispersion and variable stagnant thermal conductivity are taken into consideration in the energy equation. The entire regime of mixed convection, including the two limits of pure forced convection and pure free convection, is covered by employing a single nonsimilarity parameter. The resulting nonsimilar system of equations is solved using a finite difference method. Results are presented for temperature and velocity profiles, and local Nusselt number for representative values of different controlling parameters.

Forced convection in the thermal entrance region of a circular duct with slug flow and viscous dissipation

Abstract Slug flow forced convection in a circular duct is studied. The effect of viscous dissipation is analysed in the thermal entrance region. The temperature field and the local Nusselt number are determined analytically for any prescribed axial distribution of wall heat flux. Three examples are considered: a uniform wall heat flux, a linearly varying wall heat flux and an exponentially varying wall heat flux. In the case of a uniform wall heat flux, it is shown that viscous dissipation reduces the value of the local Nusselt number in the whole duct. In the case of a linearly or exponentially increasing wall heat flux, viscous dissipation affects the local Nusselt number only in the thermal entrance region and becomes negligible in the fully developed region.

Mixed Convection in Non-Newtonian Fluids Along a Horizontal Plate in a Porous Medium

The problem of mixed convection from horizontal surfaces in a porous medium saturated with a power-law-type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable wall heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5–1.5.

Possible transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall heat flux

This study derived the transformation of boundary layer equations for two-dimensional steady natural convection on a vertical wall embedded in porous media. Three different kinds of thermal boundary conditions are prescribed for wall heat flux: uniform distribution, power law variation, and exponential variation. The flow pattern contains three subregions based on the distance along the flat plate. When inertia resistance is ignored, similarity solution exists in case wall heat flux is in linear distribution. The known relationships of uniform wall temperature relative to wall heat flux variation and uniform wall heat flux relative to wall temperature variation in both cases of the pure fluid flow and the pure porous flow can all be obtained in the present transformation.

Thermal entrance region for laminar forced convection in a circular tube with a power law wall heat flux

Laminar forced convection in a circular tube is investigated with a boundary condition of prescribed axially varying wall heat flux, under the assumptions of hydrodynamically developed flow and of negligible axial conduction and viscous dissipation in the fluid. A condition on the asymptotic behaviour of the axial distribution of wall heat flux is established which is fulfilled by power-law varying axial distributions and which guarantees the existence of a thermally developed regime. It is proved that for all the axial distributions which fulfil this condition the asymptotic value reached by the local Nusselt number is 48/11, i.e. the same which holds for a uniform wall heat flux. For some power-law varying axial distributions of wall heat flux, a finite difference determination of the thermal entrance region is performed. In every numerical solution, the local Nusselt number tends asymptotically to 48/11.

On the laminar forced convection with axial conduction in a circular tube with exponential wall heat flux

The values of the fully developed Nusselt number for laminar forced convection in a circular tube with axial conduction in the fluid and exponential wall heat flux are determined analytically. Moreover, the distinction between the concepts of bulk temperature and mixing-cup temperature, at low values of the Peclet number, is pointed out. Finally it is shown that, if the Nusselt number is defined with respect to the mixing-cup temperature, then the boundary condition of exponentially varying wall heat flux includes as particular cases the boundary conditions of uniform wall temperature and of convection with an external fluid.

Exact solutions for thermally developing tube flow with variable wall heat flux

Forced convection within circular tubes, subjected to an axially variable wall heat flux, is analytically studied. The integral transform method is employed, in conjunction with a splitting-up procedure, to hield exact expressions for the temperature distributions and related Nusselt numbers along the thermal entry region. Two specific situations of practical interest are considered for illustrating the approach, involving both sinusoidal and exponential variations of the prescribed heat flux along the duct length, for laminar and turbulent flow. The convergence behavior of the proposed solutions is demonstrated and previously reported solutions are critically examined.

Buoyancy-induced flow of non-newtonian fluids in a porous medium past a vertical flat plate with nonuniform surface heat flux

Steady buoyancy-induced flow of a non-Newtonian fluid in a porous medium bounded by a vertical flat plate with prescribed variable wall heat flux is investigated analytically by Karman-Pohlhausen integral method and numerically by similarity method. The results for excess surface temperature obtained from the two methods are found to be in good agreement for all values of power law indices for wall heat flux and non-Newtonian fluid.