Laminar Free Convection Boundary Layer Research Articles

Theoretical prediction of temperature difference between prefrontal cortex and forehead skin for fever screening

To improve reliability of fever screening, many studies have been conducted on the relationship between forehead skin and core temperatures. However, all studies thus far were based on only statistical analyses of temperature data, and it remains unsolved how forehead skin temperature is determined and controlled by environmental temperature as well as face details of individual. This study examined heat transfer in a free convection thermal boundary layer on the human forehead theoretically and experimentally to propose a theoretical model describing the relationship between prefrontal cortex (PFC) and forehead skin temperatures. Temperature distributions across the forehead boundary layer measured using a resistance thermometer probe showed that the convective heat flux on the forehead, including the case of wearing face mask, could be estimated similarly to that in a laminar free convection boundary layer on a heated vertical plate. It was also shown that the difference between PFC and forehead skin temperatures measured using a zero-heat-flux core-temperature monitoring probe and a thermocouple attached to the forehead was well represented by a simple formula derived from analyses of radiative and convective heat fluxes over a normal range of environmental temperature. Wearing a face mask little affected the temperature difference between PFC and forehead skin. These results provide a scientific basis for fever screening from thermo- and fluid-dynamics viewpoints.

Effects of Junction Flow on the Free Convection Heat Transfer of a Heated Vertical Plate

The present study covers results of non-stationary numerical simulation of three-dimensional flow in the junction region of a low aspect ratio circular cylinder entirely immerged in laminar free convection boundary layer developing over a heated vertical plate. To categorize the effects of the cylinder surface temperature on the dynamics behavior of the forming vortical structure, its size and position both upstream and downstream of the cylinder the results, which prove the presence of a complex coherent vortical structure, are analyzed. In particular, the influence of horseshoe vortex system formed upstream of the cylinder on the free convection heat transfer of the heated vertical plate in the junction area is evaluated. Finally, the importance of the forming vortical structure on the heat transfer computation for the junction region is demonstrated.

HEAT TRANSFER IN VISCOPLASTIC BOUNDARY-LAYER FLOW FROM A VERTICAL PERMEABLE CONE WITH MOMENTUM AND THERMAL WALL SLIP: NUMERICAL STUDY

A mathematical model is presented for the laminar free convection boundary layer flow of Casson viscoplastic non-Newtonian fluid external to a vertical penetrable circular cone in the presence of thermal and hydrodynamic slip conditions. The cone surface is maintained at non-uniform surface temperature. The boundary layer conservation equations, which are parabolic in nature, are transformed into non-dimensional form via appropriate similarity variables, and the emerging boundary value problem is solved computationally with the second order accurate implicit Keller-box finite-difference scheme. The influence of velocity (momentum) slip, thermal slip and Casson non-Newtonian parameter on velocity, temperature, skin friction and Nusselt number are illustrated graphically. Validation of solutions with earlier published work is included. The computations show that the flow near the cone surface is strongly decelerated with increasing momentum slip whereas the temperature and thermal boundary layer thickness are increased. Increasing Casson parameter generally decelerates the flow and also decreases temperatures. Both velocity and thermal boundary layer thickness are reduced with greater Prandtl number. The study is relevant to petro-chemical engineering (polymer) processing systems.

Unsteady MHD Radiative and Chemically Reactive Free Convection Flow near a Moving Vertical Plate in Porous Medium

We have investigated an unsteady flow of a viscous, incompressible electrically conducting, laminar free convection boundary layer flow of a moving infinite vertical plate in a radiative and chemically reactive medium in the presence of a transverse magnetic field. The equations governing the flow are solved by Laplace transform technique. The expressions for velocity, temperature, concentration are derived and based on these quantities the expressions for skin friction; rate of heat transfer and the rate mass transfer near the plate are derived. The effects of various physical parameters on flow quantities, wise magnetic parameter, Grashof number, modified Grashof number, heat source parameter, the chemical reaction parameter, Schmidt number and radiation parameter are studied numerically and the results are discussed with the help of graphs. Some important applications of physical interest for different type motion of the plate like case (i) when the plate is moving with uniform velocity, case (ii) when the plate is moving with single acceleration and case (iii) when the plate is moving with periodic acceleration, are discussed.

Chemically Reacting MHD Boundary Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate in a Porous Medium with Suction

A mathematical model is presented for a two-dimensional, steady, incompressible electrically conducting, laminar free convection boundary layer flow of a continuously moving vertical porous plate in a chemically reactive and porous medium in the presence of a transverse magnetic field. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is tackled numerically using shooting techniques with the forth order RungaKutta method. Pertinent results with respect to embedded parameters are displayed graphically for the velocity, temperature and concentration profiles and were discussed quantitatively.

Heat generation effects on MHD boundary layer flow of a moving vertical plate with suction

This work is focused on the numerical solution of a two-dimensional, steady, incompressible electrically conducting, laminar free convection boundary layer flow of a continuously moving vertical porous plate in the presence of a transverse magnetic field and heat generation. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is solved numerically using shooting techniques with the forth order Runge-Kutta method. The physical behavior of different parameters for velocity, temperature and concentration has been examined graphically and analyzed quantitatively.DOI: http://dx.doi.org/10.3329/jname.v9i2.8550 Journal of Naval Architecture and Marine Engineering 9(2012) 153-167

A comparison of three quantitative schlieren techniques

We compare the results of three quantitative schlieren techniques applied to the measurement and visualization of a two-dimensional laminar free-convection boundary layer. The techniques applied are Schardin's “calibrated” schlieren technique, in which a weak lens in the field-of-view provides a calibration of light deflection angle to facilitate quantitative measurements, “rainbow schlieren”, in which the magnitude of schlieren deflection is coded by hue in the image, and “background-oriented schlieren” (BOS), in which quantitative schlieren-like results are had from measuring the distortion of a background pattern using digital-image-correlation software. In each case computers and software are applied to process the data, thus streamlining and modernizing the quantitative application of schlieren optics. (BOS, in particular, is only possible with digital-image-correlation software.) Very good results are had with the lens-calibrated standard schlieren method in the flow tested here. BOS likewise produces good results and requires less expensive apparatus than the other methods, but lacks the simplification of parallel light that they feature. Rainbow schlieren suffers some unique drawbacks, including the production of the required rainbow cutoff filter, and provides little significant benefit over the calibrated schlieren technique.

Radiation effect on chemically reacting magnetohydrodynamics (MHD) boundary layer flow of heat and mass transfer through a porous vertical flat plate

A mathematical model is presented for a two-dimensional, steady, viscous, incompressible, electrically conducting and laminar free convection boundary layer flow with radiation from a flat plate in a chemically reactive medium in the presence of a transverse magnetic field. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is tackled numerically using shooting techniques with the fourth order Runge-Kutta integration scheme. Pertinent results with respect to embedded parameters are displayed graphically for the velocity, temperature and concentration profiles and discussed quantitatively. Key words: Heat transfer, thermal radiation, magnetic field, chemical species, mixed convection.

Free convection flow about a vertical spinning cone under a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a heated down-pointing cone spinning with a constant angular velocity about the symmetry axis. Boundary-layer velocity and temperature profiles were determined numerically for prescribed surface temperature or heat flux and for various values of the magnetic and spin parameters and the Prandtl number. The spin of the body augments the velocity profiles increasing the skin friction and compresses the temperature profiles toward the surface increasing the surface heat flux for the prescribed surface temperature case and decreasing surface temperature for the prescribed heat flux case. The magnetic field suppresses the velocity profiles and decreases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in lower surface heat flux for the prescribed surface temperature case and higher surface temperature for the prescribed heat flux case.

Free convection flow about a cone under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a vertical down-pointing cone with mixed thermal boundary conditions. Boundary layer velocity and temperature profiles were determined numerically for various values of the magnetic parameter and the Prandtl number. The results show that the magnetic field suppresses the velocity profiles and increases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.

Free-convection flow about a wedge under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a wedge with mixed thermal boundary conditions. Boundary-layer velocity and temperature profiles were determined numerically for various values of the Prandtl number and the magnetic parameter. The results show that the magnetic field retards the velocity profiles and increases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.

FREE CONVECTION BOUNDARY LAYER ON A SPHERE WITH CONSTANT SURFACE HEAT FLUX IN A MICROPOLAR FLUID

The present paper considers the steady laminar free convection boundary layer flow over an a sphere with a surface heat flux placed in a micropolar fluid. The governing boundary layer equations are first transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are then solved numerically using the Keller-box method. Numerical results presented include the local wall temperature distribution and the local skin friction coefficient for a wide range of material parameter K. The Prandtl number is taken to be 0.7 and 7, respectively.

FREE CONVECTION BOUNDARY LAYER ON AN ISOTHERMAL SPHERE IN A MICROPOLAR FLUID

The present paper considers the steady laminar free convection boundary layer flow over an isothermal sphere in a micropolar fluid. The governing boundary layer equations are first transformed into a non-dimensional and the resulting nonlinear system partial differential equations are then solved numerically using the Keller-box method. Numerical results presented include the local wall temperature distribution and the locak skin friction coefficient for a wide range of martial parameter K. The Prandtl is taken to be 0.7 and 7, respectively

UNSTEADY LAMINAR BOUNDARY LAYER FLOW OVER A SPINNING BODY IN FREE CONVECTION

Initial development of the unsteady laminar free-convection boundary-layer flow over an impulsively started spinning isothermal axisymmetrical vertical body is investigated. Stream function, swirl velocity and temperature are obtained in series of functions in powers of time. The general results are applied to a family of downward and upward thickening bodies to investigate the effects of the body shape on the formation of unseparated and separated boundary-layer flow regimes. The onset of flow separation is observed to take place at higher spin rates for downward thickening bodies. The surface heat flux is enhanced by the circulating flow inside the separated region. The series solutions are limited to the small values of the dimensionless time.

Similarity solutions for free convection to power-law fluids from a heated vertical plate

Steady, laminar free-convection boundary-layer flow of a power-law fluid over a vertical heated plate under mixed thermal boundary conditions is investigated. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles is obtained.

Stability of free convection with uniform suction or injection from a vertical flat plate subjected to a constant wall heat flux

A theoretical study is presented for the stability characteristics of the laminar free convection boundary layer flow along a vertical porous (permeable) flat plate subjected to a constant heat flux. The disturbance equations are solved numerically on the basis of the linear stability theory for a wide range of values of the modified Grashof number,G, and some values of the suction or injection parameterX when the Prandtl number, Pr, is 0.73 (air). These solutions indicate the important role of the parametersG andX on the flow and heat transfer characteristics. It is found that the present results are in very good agreement with those from the open literature.

Free convection flow of thermomicropolar fluid along a vertical plate with nonuniform surface temperature and surface heat flux

We determine the effects of micro‐inertia density and the vortex viscosity on laminar free convection boundary layer flow of a thermomicropolar fluid past a vertical plate with exponentially varying surface temperature as well as surface heat flux. The governing nonsimilarity boundary layer equations are analyzed using: first, a series solution for small ξ (a scaled streamwise distribution of micro‐inertia density), second, an asymptotic solution for large ξ and, third, a full numerical solution implicit finite difference method together with Keller‐box scheme. Results are expressed in terms of local skin friction and local Nusselt number. The effects of varying the vortex viscosity parameter, Δ, surface temperature and the surface heat flux gradient n and m respectively against ξ for fluids having Prandtl number equals 0.72 and 7.0 are determined.

Particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder

Consideration is given to analyse the sub-micron deposition from a laminar free convection boundary layer developing on a heated isothermal vertical cylinder. A finite-difference method, as proposed by Cebeci and Smith [28], has been used to theoretically calculate the local cumulative particle deposition, with the thermophoretic velocity being that proposed by Talbot et al. [19]. It was demonstrated that the thermophoresis has a pronounced effect on the particle transfer but only a slight effect on the very smaller particles (<0.01 μm) and that the effect increases with particle size and distance along the cylinder. Experiments were also conducted using mono-disperse flourescent uranin, particles with mean diameter of 0.05 μm. A calibrated flourimeter was used to measure the mass of the particles deposited at different axial locations of the cylinder. Results showed similar trends to the theoretical model, but absolute values of the deposits were greater than theoretical predictions.

Heat transfer response of MHD free convection flow along a vertical plate to surface temperature oscillations

A linearized theory is used to study the heat-transfer response of a laminar free convection boundary layer flow of a viscous incompressible and electrically conducting fluid along a vertical plate to surface temperature oscillations, when the mean surface temperature varies as a power n of distance from the leading edge in the presence of a variable transverse magnetic field. Three distinct methods, namely, the extended series expansion method for low-frequency range and the asymptotic series expansion method of high-frequency range, the local non-similarity method with second level of truncation and the finite difference method for entire frequency range are used. Calculations have been carried out for a wide range of parameters to examine the results obtained from three solutions in terms of amplitude and phase of the surface heat flux. It has been found that the amplitude and phase angle of the surface heat flux predicted by these three methods are in very good agreement in the entire frequency range.

Heat transfer response of free convection flow from a vertical heated plate to an oscillating surface heat flux

An investigation is undertaken of the unsteady response of two-dimensional laminar free convection boundary layer flow of a viscous incompressible fluid along a semi-infinite vertical heated plate where the mean surface heat flux oscillates with a small amplitude about a steady profile. The buoyancy forces are favourable, resulting from a positive flux of heat from the surface of the plate into the fluid. The interaction of the time-periodic heat flux with the usual boundary-layer flow is examined by using a linearized theory. Solutions are obtained using three distinct methods, namely an extended series expansion method for low frequencies, an asymptotic series expansion method for high frequencies and a fully numerical finite difference method for general frequencies. Calculations have been carried out for a wide range of parameters to examine the solutions in terms of the amplitude and phase angle of the fluctuating parts of the surface shear stress and the surface temperature. It has been found that the amplitude and phase angle of both the shear stress and the surface temperature predicted by these three methods are in very good agreement in their respective ranges of validity.