Constant Axial Heat Flux Research Articles

Numerical Analysis of Non-Fourier Heat Transfer in a Solid Cylinder with Dual-Phase-Lag Phenomenon

In this study, transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition. Governing equations for the model are expressed in two-dimensional cylindrical coordinates; the equations are nondimensionalized and exact solution for the equations is presented by using the separation of variable method. Results showed that the dual-phase-lag model requires less time to meet the steady temperature compared with single-phase-lag model. On the contrary, thermal wave diffusion speed for the dual-phase-lag model is greater than the single-phase-lag model. Also the effect of relaxation time in dual-phase-lag model has been taken on consideration.

Fully developed forced convection through semi-elliptic ducts

An exact solution of the problem of fully developed forced convection through semi-elliptic ducts is obtained under constant axial heat flux and peripherally uniform temperature. The solution is validated by comparing the local and average Nusselt numbers with the published approximate and asymptotic values.

Laminar Flow Forced Convection Heat Transfer Behavior of a Phase Change Material Fluid in Microchannels

In this paper, a phase change material (PCM) fluid (N-eicosane) is compared with pure water as heat transfer fluid. The heat transfer behavior of PCM fluid under laminar flow conditions (Reynolds number of 700) in circular and rectangular microchannels was studied numerically. In the numerical study, an effective specific heat model was used to take into account the phase change process. Heat transfer results for circular and rectangular microchannels with PCM fluid were obtained under hydrodynamically and thermally fully developed conditions. A PCM fluid in microchannels with aspect ratios of 1 to 2, 1 to 4, and 1 to 8 was found to enhance the thermal behavior of microchannels which can be beneficial in a host of cooling applications. The flow was assumed to be hydrodynamically fully developed at the inlet and thermally developing inside the microchannel. Heat transfer characteristics of PCM slurry flow in microchannels have been studied under three types of wall boundary conditions including constant axial heat flux with constant peripheral temperature (H1), constant heat flux with variable peripheral temperature (H2), and constant wall temperature (T) boundary condition. The fully developed Nusselt number was found to be higher for H1 than for H2 and T boundary conditions for all the geometries. Moreover, Nusselt number also increased with aspect ratio and was sensitive to the variations in effective specific heat.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross Section with Constant Axial Heat Flux

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly connected cross sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully developed, laminar flow in microchannels of arbitrary cross sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross sections with a maximum difference on the order of 9%.

Laminar flow and heat transfer in a periodic trapezoidal channel with semi-circular cross-section

Computational fluid dynamics (CFD) has been used to study fully developed laminar flow and heat transfer behaviour in periodic trapezoidal channels with a semi-circular cross-section. The trapezoidal elements are characterised by their wavelength (2 L), channel diameter ( d), radius of curvature of bends ( R c), the amplitude (2 A) and the length of the straight section ( B) with results reported for Reynolds numbers ( Re) up to 400, as well as for a range of geometric configurations ( 0.525 ⩽ R c d ⩽ 1.3 , 3.6 ⩽ L d ⩽ 12 , 0.17 ⩽ B L ⩽ 1 , 0.125 ⩽ A L ⩽ 1 ) at Re = 200. This generic geometry takes a variety of shapes with limiting forms of a regular square serpentine ( B = 2 A = L) and a zig-zag or saw-tooth ( B → 0). The flow in these channels is characterised by the formation of Dean vortices following each bend. As the Reynolds number is increased, stronger vortical flow patterns emerge and these vortices lead to efficient fluid mixing and high rates of heat transfer. Constant wall heat flux (H2), constant axial heat flux with peripherally constant temperature (H1) and constant wall temperature (T) boundary conditions are examined for a fluid with a Prandtl number of 6.13. Higher rates of heat transfer with relatively small pressure loss penalty are found relative to fully developed flow in a straight pipe, with heat transfer enhancements of up to four at the highest Reynolds number. In addition to presenting channel enhancements the stackability of channels on a plate is considered. The concepts of area enhancement (based solely on geometric factors) and heat transfer intensification, the product of the heat transfer enhancement and the area enhancement, are introduced and used to compare different geometrical configurations. The swept zig-zag pathway provided the greatest intensification of heat transfer in a multi-channel plate structure.

A general implementation of the H1 boundary condition in CFD simulations of heat transfer in swept passages

A methodology has been developed to study laminar flow and heat transfer behaviour in periodic non-straight passages with a heat transfer boundary condition of constant axial heat flux and constant peripheral temperature ( H1). The technique uses Newton iteration to determine the wall temperature distribution required to satisfy the H1 boundary condition. The methodology is validated for hydrodynamically developed and thermally developing flow, as well as for hydrodynamically and thermally developed flow in straight ducts with various cross-sections. The methodology is extended to study fully developed flow in a periodic serpentine channel, consisting of a number of bends and straight sections, with a semi-circular cross-section. The results show the existence of a non-monotonic temperature distribution along the serpentine channels which exists because increased rates of heat transfer at bends lead to reductions in the local wall temperature in order to maintain a constant axial heat flux. Hot spots within the passage cross-section, typical of the H2 boundary condition, are removed in the H1 case.

Analysis of the heat transfer in unsymmetrically heated triangular microchannels in slip flow regime

A theoretical analysis of heat transfer characteristics is presented for the fully developed laminar flow of the incompressible gas in the triangular microchannels heated unsymmetrically with constant axial heat flux. Through solving the energy equation with temperature jump boundary conditions in slip flow regime by virtue of a computation- oriented method of the orthonormal function analysis, the dimensionless temperature profiles and the average Nusselt number for various thermal boundary conditions are obtained. The effects of Knudsen number, aspect ratio, and thermal boundary conditions on the heat transfer are discussed. The calculated results show that the orthonormal function method can be used to study the heat transfer characteristics of the unsymmetrically heated triangular microchannels. The average Nusselt number in triangular microchannels is lower for slip flow than for no-slip flow, and decreases with increasing Knudsen number. The aspect ratios and thermal boundary conditions of triangular microchannels have significant influences on the change of average Nusselt numbers with the increase in the Knudsen number. For the equilateral triangular microchannels, the decrease of the Nusselt number ratio due to temperature jump is smaller at large Knudsen number and larger at small Knudsen number on the boundary condition of bottom wall heated alone as compared with the one on the boundary condition of two heated hypotenuse walls. The correlations of the average Nusselt number with the Knudsen number for equilateral triangular microchannels are obtained.

Analytical determination of the temperature distribution and Nusselt numbers in rectangular ducts with constant axial heat flux

A rigorous solution is obtained for the temperature field and the Nusselt numbers in the fully developed thermal region of rectangular ducts, wherein a laminar fully developed velocity profile occurs. The H1 thermal boundary condition, constant axial wall heat flux with a constant peripheral wall temperature, has been examined. The two dimensional (2D) temperature distribution and the Nusselt numbers are calculated as functions of the aspect ratio. The results, in terms of 2D-temperature profiles and Nusselt numbers, are presented and discussed in tables and graphs, considering all the possible combinations of heated and adiabatic walls of the rectangular cross section. A comparison with the numerically evaluated H1 Nusselt numbers found in literature is presented. The present analytical results are a powerful tool to test the commercial or self-produced thermal fluid-dynamic codes which permit the investigation of the internal forced convection of incompressible flows.

Finite element analysis of laminar convective heat transfer in vertical ducts with arbitrary cross-sections

The problem of combined free and forced convection, in a fully developed laminar steady flow through vertical ducts under the conditions of constant axial heat flux and uniform peripheral wall temperature, is considered. Finite element solution algorithm with triangular elements and piecewise linear interpolation polynomials for temperature and velocity profiles are derived for ducts with arbitrary shape. Numerical values for Nusselt numbers at selected Rayleigh numbers are obtained for the special cases of square and triangular ducts.