Streamwise Heat Conduction Research Articles

On the fluid flow and heat transfer between a cone and a disk both stationary or rotating

The present paper investigates the role that the radial component of heat conduction plays in a cone-plate viscometer. The cone and the disk may be taken as stationary or in action; both co-rotating or counter-rotating. Hydrodynamic and thermal fields are resolved by means of computationally simulating the resulting systems of equations. Upon working out the well-documented velocity field in the gap region from the similarity governing equations, the rates of heat transfer at both surfaces are calculated from an amended energy equation by further adding radial diffusive terms, which were missing in the previous data published in the literature. It is shown that addition of such physical streamwise heat conduction terms into the energy equation much influences the well-known results of heat transfer rates, particularly when the conical gap section is not small. The missing heat transfer rates pertaining to the cone wall are also presented here. In particular, it is demonstrated that the best cooling of cone-disk apparatus can be achieved for a rotating disk with a stationary cone, provided that the wall temperatures are kept as uniformly constant. The critical power index of passage from cooling to heating is determined to be 1.54492.

Jeffery-Hamel slip flow in a convergent microchannel with uniform wall temperature and streamwise heat conduction

This work is devoted to the determination of the analytical solution of the problem of the laminar forced convection of the Jeffery-Hamel slip flow through a convergent microchannel. The analytical solution is obtained by using a self-adjoint formalism of the functional analysis. The solution represents an extension of the solution obtained in the conventional continuum flow by considering the boundaries slip conditions at the wall and the streamwise heat conduction. This extension has been done by using a new matrix operator of three dimensions in the Hilbert space. The results show that the thermal characteristics are strongly influenced by the Reynolds, Prandtl and Knudsen numbers, the aperture angle of the channel and the streamwise heat conduction.

Axial heat conduction effects in the thermal entrance region for flows in concentric annular ducts: Correlations for the local bulk-temperature and the Nusselt number at the outer wall

Streamwise heat conduction in the flow can affect the heat transfer in ducts. This is mainly relevant for flows with small Prandtl numbers or in micro-channels. In both situations the Péclet number is small, so axial heat conduction in the fluid cannot be neglected. In literature analytical solutions of this so called extended Graetz problem are well documented. In the present paper correlations are developed for the local bulk-temperature and the local Nusselt number at the outer wall in the thermal entrance region of concentric annular ducts. Correlations are given for laminar and turbulent fully-developed flow and different thermal boundary conditions. The correlations also consider the effect of different ratios of the inner radius to the outer radius of the annular ducts.

The analytical investigation of premixed combustion in cylindrical micro-combustor

In this study, an analytical model for heat recirculation in cylindrical micro-combustors is presented, including the effects of heat transfer from the product gas stream in the reaction zone and post-flame region to the reactant in the preheat zone, structural heat conduction through the combustor walls and heat loss to ambient. Eventually, the explicit expression for the flame speed in non-adiabatic condition and the implicit expression for adiabatic condition are obtained in this research. In addition, comparison is made between adiabatic and non-adiabatic flame speeds. It is demonstrated that the streamwise heat conduction through the structure of combustor plays an important role in the flame broadening in both adiabatic and non-adiabatic conditions. Moreover, it is shown that reducing the size of the combustor to a submillimetre scale extremely increases the surface-to-volume ratio, leading to the decrease in the flame speed and flame quenching.

A Numerical Investigation of the Heat Transfer in a Parallel Plate Channel With Piecewise Constant Wall Temperature Boundary Conditions

For turbulent flows in ducts, streamwise heat conduction effects within the flow can be important for low Prandtl number fluids (liquid metals). The paper presents a numerical investigation of the influence of axial heat conduction within the flow on the heat transfer for hydrodynamically fully developed flow. The calculations have been carried out for a semi-infinite heated section as well as for a heated section of finite length. Additionally, by considering different models for calculating the turbulent heat flux, the normally used assumption that the eddy diffusivity in axial and normal direction are the same was investigated.

Analysis of the transpiration cooling of a thin porous plate in a hot laminar convective flow

This paper deals with the asymptotic and numerical analysis for the steady-state transpiration cooling of a thin porous flat plate in a laminar hot convective flow, taking into account the streamwise heat conduction through the plate. For high conductivity plates, a regular perturbation analysis has been carried out, yielding a three-term asymptotic solution for the distribution of plate temperature. In the limit of a very poorly conducting plate, a singular perturbation technique, based on matched asymptotic expansions, is employed to solve the governing equations. We also solved the equations numerically using a quasilinearization technique. The numerical results are in good agreement with the asymptotic solution close to the asymptotic limits studied.

Higher-Order Approximations for Darcian Free Convective Flow About a Semi-Infinite Vertical Flat Plate

Higher-order effects of Darcian free convection boundary-layer flow adjacent to a semi-infinite vertical flat plate with a power law variation of wall temperature (i.e., Tˆw αxˆλ for xˆ≥0) are examined theoretically in this paper. The method of matched asymptotic expansions is used to construct inner and outer expansions. The small parameter of the perturbation series is the inverse of the square root of the Rayleigh number. The leading term in the inner expansions is taken to be the boundary layer theory with the second-order term due to the entrainment effect, and the third-order term due to the transverse pressure gradient and the streamwise heat conduction. The ordering of the term due to the leading edge effect depends on the wall temperature distribution; this term is determinate within a multiplicative constant owing to the appearance of an eigenfunction in the inner expansion. Thus, the perturbation solutions are carried out up to this term. For the case of an isothermal vertical plate (λ = 0), the second-order corrections for both the Nusselt number and the vertical velocity are zero, with the leading edge effect appearing in the third-order term. For λ>0, both the second- and third-order corrections in the Nusselt number are positive. The increase in surface heat flux is due to the fact that the higher-order effects increase the velocity parallel to the heated surface. The boundary layer theory for the prediction of the Nusselt number is shown to be quite accurate even at small Rayleigh number for 0≤λ≤1/3. The higher order effects tend to have a stronger influence on the velocity distribution than the temperature distribution. These effects become more pronounced as λ is increased from λ=1/3, or as the Rayleigh number is decreased.

Matched asymptotic expansions for free convection about an impermeable horizontal surface in a porous medium

The problem of steady free convection in a porous medium adjacent to a horizontal impermeable heated surface, with wall temperature distribution w= ∞+ A λ(0≤λ<2), for ≥0 and = ∞ for <0, is investigated by the method of matched asymptotic expansions. The small parameter in the perturbation series is found to be the inverse one-third power of the Rayleigh number. For the first-order inner problem the governing equations reduced to the boundary layer approximations which have been solved previously. The effects of fluid entrainment, streamwise heat conduction and upward-drift induced friction are taken into consideration in the second and third-order theory for which similarity solutions are obtained. Numerical results for temperature and streamwise velocity profiles as well as the local Nusselt number at different local Rayleigh numbers and different prescribed wall temperature distributions are presented. It was found that the local Nusselt numbers as obtained from the boundary layer theory for λ=0.5 are accurate to the third-order, while those for λ=0 are accurate to the second-order. For other values of λ, the boundary layer theory underestimates the local Nusselt number slightly; the accuracy of the boundary layer theory decreases as the Rayleigh numbers decrease and as λ increases from λ=0.5.

Influence of Streamwise Molecular Heat Conduction on the Heat Transfer Coefficient for Liquid Metals in Turbulent Flow between Parallel Plates

The energy equation for mechanically fully developed turbulent flow between parallel plates is numerically solved taking into account the term of streamwise heat conduction. Solutions are presented for Re = 7060 and 73620, and for Pr ranging from 0.001 to 0.1. Generally the influence of the streamwise molecular conduction results in a remarkable decrease of the Nusselt number in the thermal inlet.

The steady state ice layer profile on a constant temperature plate in a forced convection flow—I. Laminar regime

The shape of the steady state ice layer that forms on a constant temperature horizontal plate in a parallel forced convection flow was analyzed. This paper, part I of a two part series, will examine phenomena that effect the shape of the ice layer in the laminar flow regime. Of particular interest are the effects of curvature of the ice surface on the free stream flow and of streamwise heat conduction in the ice layer. A two-dimensional theory developed to account for these effects suggests that a modified Reynolds number of the form Re x / θ 2 c where θ c is a temperature ratio parameter should be used to correlate the ice profiles. It was found that measurements could be correlated over a wide range of plate temperatures, free stream temperatures and free stream velocities using this parameter. Also in the laminar regime thermal instabilities of the boundary layer were observed which produced longitudinal grooves in the ice surface.

Effect of Streamwise Heat Conduction on Heat Transfer from a Nonisothermal Flat Plate at Low Prandtl Numbers

The effect of streamwise heat conduction on heat transfer from a flat plate is studied at low Prandtl numbers. The surface temperature of the plate is assumed to vary according to a power law with the longitudinal distance. The analysis is performed as a perturbation of the classical boundary-layer theory. The resulting similar energy equations are solved for small Prandtl number by using the method of matched asymptotic expansions.

Streamwise Heat Conduction Effects in Forced-Convection Boundary Layers Without and With Superposed Free Convection

An analytical study is performed to determine the threshold value of the Peclet number below which conventional Nusselt number relations are invalidated by the effect of streamwise heat conduction. The investigation encompasses the Prandtl number range of liquid metals. Consideration is given to pure forced-convection boundary layer flow on a flat plate and to the forced-convection boundary layer on a vertical plate with superposed free convection. If Pex, Rex, and Grx, respectively, denote the Peclet, Reynolds, and Grashof numbers, all based on the streamwise coordinate x, then the threshold value of Pex is found to range from 12 to 7 as Grx/Rex2 ranges from 0 (pure forced convection) to 1.0. The present analysis does not provide Nusselt number results for very low Peclet numbers, where streamwise conduction effects play a decisive role.

Heat Transfer From a Small Isothermal Spanwise Strip on an Insulated Boundary

Detailed analysis of heat transfer of an isothermal spanwise strip in a uniform shear field is presented. Solutions for the leading edge and the trailing edge are obtained by method of relaxation. These solutions are exact in that the streamwise heat conduction term, in the differential equation of energy, is not neglected. The results are compared with the Le´veˆque similarity solution, and the ranges where the solution is valid are defined. A similarity solution for the trailing wake is also presented.