Constant Heat Flux Case Research Articles

Forced Convective Heat Transfer in a Channel Filled With a Functionally Graded Metal Foam Matrix

Fully developed forced convective heat transfer within a channel filled with a functionally graded metal foam matrix was investigated analytically for the case of constant wall heat flux. A series of functionally graded metal foam matrices of the same mass (i.e., the same solidity) were examined in views of their heat transfer performances. The porosity either increases or decreases toward the heated wall following a parabolic function. Among the metal foam matrices of the same mass, the maximum heat transfer coefficient exists for the case in which the porosity decreases toward the heated wall (i.e., more metal near the wall). The heat transfer coefficients in such channels filled with a functionally graded metal foam matrix are found 20–50% higher than that expected from the increase in the effective thermal conductivity. Hence, functionally graded metal foam matrices are quite effective to achieve substantially high heat transfer coefficient with an acceptable increase in pressure drop.

Estimating Heat Transfer Coefficients and Friction Factors in Non-Newtonian Flows between Parallel Plates

ABSTRACTA simplified method, successfully tested previously for flow in circular pipes, is used in this work to estimate the friction factor and Nusselt number in fully-developed laminar flow between parallel plates of non-Newtonian fluids. Both constant wall temperature and constant wall heat flux cases are considered. The methodology was tested using several constitutive equations, including generalized Newtonian fluids, such as the Herschel–Bulkley, Bingham, Casson, and Carreau–Yasuda models, and also the simplified Phan-Thien–Tanner viscoelastic model. The error of the approximate methodology was found to be small, below 3.4%, except for the fluids with yield stress for which the maximum error increased to 8.4% for the cases analyzed, which cover a wide range of shear viscosity curves.

Mixed convection boundary layer flow of viscoelastic nanofluid past a horizontal circular cylinder: Case of constant heat flux

The steady of two-dimensional convection boundary layer flow of a viscoelastic nanofluid over a circular cylinder is investigated in this paper. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as a nanoparticle with the Prandtl number Pr = 6.2. The governing boundary layer partial differential equations are transformed into dimensionless forms. Then they are solved numerically by using the Keller-Box method. This paper focus on the effects of selected parameter on the flow and heat transfer characteristics and be presented in graphs. The results show that, the velocity profiles and the temperature profiles are increased by increasing the values of nanoparticles volume fraction. While velocity profile decreases when viscoelastic parameter is increase. The reverse trend is observed for the temperature profiles. Also, the values of reduced skin friction are increased by increasing mixed convection parameter, but the values of heat transfer coefficient produce an opposite behaviour with an increasing in mixed convection parameter.

Conjugated Conduction-Free Convection Heat Transfer in an Annulus Heated at Either Constant Wall Temperature or Constant Heat Flux

In this paper, we investigate numerically the effect of thermal boundary conditions on conjugated conduction-free convection heat transfer in an annulus between two concentric cylinders using Fourier Spectral method. The inner wall of the annulus is heated and maintained at either CWT (Constant Wall Temperature) or CHF (Constant Heat Flux), while the outer wall is maintained at constant temperature. CHF case is relatively more significant for high pressure industrial applications, but it has not received much attention. This study particularly focuses the latter case (CHF). The main influencing parameters on flow and thermal fields within the annulus are: Rayleigh number Ra; thickness of inner wall Rs; radius ratio Rr and inner wall-fluid thermal conductivity ratio Kr. The study has shown that the increase in Kr increases the heat transfer rate through the annulus for heating at CWT and decreases the inner wall dimensionless temperature for heating at CHF and vice versa. It has also been proved that as the Rs increases at fixed Ra and Rr, the heat transfer rate decreases for heating at CWT and the inner wall dimensionless temperature increases for heating at CHF at Kr ＜1. The study has also discussed that the effect of increase in Rs for both cases of heating at Kr＞1 depends on Rr. It has been shown that for certain combinations of controlling parameters there will be a value of Rr at which heat transfer rate will be minimum in the annulus in case of heating at CWT, while there will be a value of Rr at which inner wall dimensionless temperature will be maximum in case of heating at CHF.

Figure of merit for optimization of nanofluid flow in circular microchannel by adapting nanoparticle migration

In this paper, the laminar fully developed flow of alumina/water nanofluid inside circular microchannels subjected to a constant wall temperature (CWT) is theoretically investigated. The effect of nanoparticles migration originating from thermophoretic diffusion (temperature-gradient driven force) and Brownian diffusion (concentration-gradient driven force) on the thermophysical characteristics of nanofluids has been considered. A Navier's slip condition is considered at the wall to model the non-equilibrium region at the fluid-solid interface. In order to assume a hydrodynamically and thermally fully developed flow, the governing equations are reduced to a system of ordinary differential equation and solved using the appropriate reciprocal algorithm. The effects of pertinent parameters including the ratio of Brownian motion to thermophoresis (NBT), slip parameter (λ) and bulk mean nanoparticle volume fraction (ϕB) on the flow and thermal fields are investigated. In addition, the results are compared with the case of constant heat flux (CHF) at the wall. The figure of merit (FoM) is used to measure the thermal performance of equipment and finding the optimum thermal condition. It is shown that the anomalous heat transfer enhancement depends on the thermal boundary condition as well as the nanoparticles diameter. Furthermore, the optimum value of NBT for the case of constant wall temperature (approximately 1) is found to be greater than that of the constant wall heat flux (approximately 0.5). Thus, it can be concluded that the optimum diameter of nanoparticles for the case of constant wall temperature should be smaller than that of constant wall heat flux.

Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption

This paper presents an exact solution of a fully developed natural convection flow in a vertical concentric annulus in the presence of transverse magnetic field and heat absorption. The non-dimensional form of the equation governing the flow is first obtained and then the unified analytical solutions for the temperature field, velocity field, and skin-frictions as well as rate of heat transfer are obtained for both isothermal and constant heat flux case on the outer surface of the inner cylinder. The effect of various identified governing parameters on the flow was illustrated with the aid of line graphs. It is found that the magnitude of maximum fluid velocity is greater in the case of isothermal heating compared with the constant heat flux case when the gap between the cylinders is less or equal to radius of the inner cylinder. More also, the various values of the non-dimensional heat absorption parameter (H) and the corresponding values of annular gap where these fields are almost the same are presented in table 1.

Performance optimization of a channel flow problem using shape functions

This study explores the use of shape functions on the boundary condition optimization of a forced convection channel flow subjected to an axial heat flux distribution. The goal is to determine the heat flux distribution that minimizes the coolant overheating and simultaneously reduces the computational optimization efforts. The calculations are implemented in a 2-D homemade code, which solved the conservation equations of mass, momentum and energy, while coupling the optimization variables, here represented by the multiple coefficients of the shape functions, with a genetic algorithm. Generally speaking, two types of shape functions were used: unbiased and biased. In the former, the optimization procedure is responsible for obtaining the optimal coefficients for Legendre shape functions, while in the latter, scaling-based power laws are used to construct shape functions. The results computed for both biased and unbiased shape functions show that not only higher performance levels (i.e., less overheating) can be obtained with the present formulation when compared with the techniques employed so far in the available literature (e.g., constant discrete heat flux heaters along the channel), but it also significantly reduced computation efforts. More specifically, the biased shape functions outperform the unbiased formulation by lowering the maximum plate temperature as much as 20% with respect to the standard constant heat flux case, while simultaneously reducing the computational time by a factor of over 4.

Three-dimensional flow with heat transfer of a viscoelastic fluid over a stretching surface with a magnetic field

ABSTRACTThe present research study deals with the steady flow and heat transfer of a viscoelastic fluid over a stretching surface in two lateral directions with a magnetic field applied normal to the surface. The fluid far away from the surface is ambient and the motion in the flow field is caused by stretching surface in two directions. This result is a three-dimensional flow instead of two-dimensional as considered by many authors. Self-similar solutions are obtained numerically. For some particular cases, closed form analytical solutions are also obtained. The numerical calculations show that the skin friction coefficients in x- and y-directions and the heat transfer coefficient decrease with the increasing elastic parameter, but they increase with the stretching parameter. The heat transfer coefficient for the constant heat flux case is higher than that of the constant wall temperature case.

Conjugate Heat Transfer Study of Turbulent Slot Impinging Jet

Conjugate heat transfer in a two-dimensional, steady, incompressible, confined, turbulent slot jet impinging normally on a flat plate of finite thickness is one of the important problems as it mimics closely with industrial applications. The standard high Reynolds number two-equation k–ε eddy viscosity model has been used as the turbulence model. The turbulence intensity and the Reynolds number considered at the inlet are 2% and 15,000, respectively. The bottom face of the impingement plate is maintained at a constant temperature higher than the jet exit temperature and subjected with constant heat flux for the two cases considered in the study. The confinement plate is considered to be adiabatic. A parametric study has been done by analyzing the effect of nozzle-to-plate distance (4–8), Prandtl number of the fluid (0.1–100), thermal conductivity ratio of solid to fluid (1–1000), and impingement plate thickness (1–10) on distribution of solid–fluid interface temperature, bottom surface temperature (for constant heat flux case), local Nusselt number, and local heat flux. Effort has been given to relate the heat transfer behavior with the flow field. The crossover of distribution of local Nusselt number and local heat flux in a specified region when plotted for different nozzle-to-plate distances has been discussed. It is found that the Nusselt number distribution for different thermal conductivity ratios of solid-to-fluid and impingement plate thicknesses superimposed with each other indicating that the Nusselt number as a fluid flow property remains independent of solid plate properties.

Simulation of Thermal Characteristics of Turbulent Dual Jets

The thermal characteristic study of a dual jets comprising of combined wall jet and offset jet, with different bottom wall boundary conditions (i.e.; adiabatic, constant wall heat flux) is formulated. The flow is two-dimensional, steady, incompressible, and turbulent at high Reynolds number with negligible body forces. Initially the code developed for single off set jet with bottom wall adiabatic and constant heat flux boundary condition of different offset ratios. The simulated results are validated with the benchmark results, and the simulated results are found in good agreement with the experimental results. Dual jets case is also studied with adiabatic bottom wall, temperature distribution in the heated jets and the temperature decay in the normal direction due the entrainment characteristics are observed. For constant heat flux case, variation of local Nusselt number with the separation ratio is observed.

An analytical solution for the temperature field around a cylindrical surface subjected to a time dependent heat flux

The analytical solution for the temperature field in an infinite solid medium which surrounds a cylindrical surface, determined by Carlslaw and Jaeger for the case of constant heat flux, is extended to the case of any time dependent heat flux. Then, with reference to a sinusoidally varying heat flux, the analytical solution is employed to determine benchmark results for the time evolution of the dimensionless temperature of the surface. These results are used to check the accuracy of the numerical solutions obtained by two different commercial codes: the finite-element code COMSOL Multiphysics and the finite-volume code FLUENT.

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli. The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening tendency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.

Similarity solutions for flows and heat transfer in microchannels between two parallel plates

In this paper we give analytical similarity solutions of the Navier–Stokes equations coupled with energy equation of Newtonian fluid in a microchannel between two parallel plates taking into account the effects of viscous dissipation, the velocity slip and the temperature jump at the wall. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). We provide new similarity transformations for the governing equations and derive the expressions of Poiseuille number ( Po) and Nusselt number ( Nu). Then, the homotopy analysis method (HAM) is employed to solve the nonlinear differential equations with related boundary conditions. Both the dimensionless analytical expressions of velocity and temperature are obtained. The rarefaction effects on velocity distribution and flow friction are exhibited. The interactive effects of the Brinkman number ( Br) and the Knudsen number ( Kn) on Nu are analytically studied for both the CHF and CWT cases.

Entropy analysis of laminar-forced convection in a pipe with wall roughness

Momentum and heat transfer rates, as well as entropy generation have been numerically investigated for fully developed, forced convection, laminar flow in a micro-pipe. Compressible and variable fluid property continuity, Navier-Stokes and energy equations are solved for various Reynolds number, constant heat flux and surface roughness cases; entropy generation is discussed in conjunction with the velocity and temperature profiles, boundary layer parameters and heat transfer-frictional characteristics of the pipe flow. Simulations concentrated on the impact of wall roughness based viscous dissipation on the heat transfer behaviour and so occurring heating/cooling activity and the resulting overall and radial entropy generation.

Unsteady heat transfer in impulsive Falkner–Skan flows: constant wall heat flux case

A theoretical study of the heat transfer in the unsteady thermal boundary layer associated with the forced convection flow past a sharp, semi-infinite wedge that is started impulsively from rest and for which the constant heat flux at the walls is suddenly changed is presented in this paper. The velocity far from the wedge is given by ue (x) = xm, where x is the coordinate measured along the wedge and m is a constant. Using appropriate non-dimensional transformations, the number of independent variables in the governing boundary-layer equations is reduced from three to two. These equations are then solved numerically for both small (initial) and large (steady-state) times. It is found that for the steady-state flow the Blasius-like solutions exist for each value of m in the range m* ≤ m < ∞, where m* is the value of the power law exponent m that corresponds to a self-similar solution profile with vanishing skin friction.

The Relationship Between the Distributions of Slot-Jet-Impingement Convective Heat Transfer and the Temperature in the Cooled Solid Cylinder

A conjugate heat transfer investigation was conducted to better understand the effects of an impinging radial slot jet cooling device on both the heat transfer rates and temperature fields in the fluid, and especially in the cylindrical solid cooled by this device. The study used numerical methods to model a configuration in which a set of four radially positioned slot jets cooled a cylindrical steel target using air with a jet Reynolds number of 20,000. A steady-state v 2 f Reynolds averaged Navier-Stokes model was used with a representative two-dimensional section of the axisymmetric target and flow domain. Boundary conditions, heat intensity, target wall thickness, and thermal conductivity were varied to study the effects of the impingement cooling on the temperature distribution in the solid. For Biot (Bi) numbers between 0.0025 and 0.073, temperatures in the solid were clearly affected by lateral conduction, and temperature variation in the solid was an order of magnitude smaller than the variation in the surface heat transfer coefficient. For the case of constant heat flux, the area-weighted standard deviation in the solid temperature was found to correlate well with the dimensionless parameter Z ≡ Bi(d/t eq)2, where d is the cylinder diameter and t eq is the equivalent wall thickness, and a correlation equation was developed.

A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux

We numerically investigate turbulent thermal convection driven by a horizontal surface of constant heat flux and compare the results with those of constant temperature. Below Ra ≈ 109, where Ra is the Rayleigh number, when the flow is smooth and regular, the heat transport in the two cases is essentially the same. For Ra &gt; 109 the heat transport for imposed heat flux is smaller than that for constant temperature, and is close to experimental data. We provide a simple dimensional argument to indicate that the unsteady emission of thermal plumes renders typical experimental conditions closer to the constant heat flux case.

Mixed Convection of a Viscous Dissipative Fluid about a Vertical Flat Plate Embedded in a Porous Medium: Constant Heat Flux Case

Mixed Convection of a Viscous Dissipative Fluid about a Vertical Flat Plate Embedded in a Porous Medium: Constant Heat Flux Case

Numerical Simulation of Electrokinetic Flow and Heat Transfer in Microchannels with a Finite-Volume Method

ABSTRACT In this article, electrokinetic flow in rectangular microchannels is studied numerically with a finite-volume method. An externally applied electric field generates varying electromagnetic forces on the fluid, which can be manipulated to control heat exchange and fluid acceleration within the microchannel. Convective heat transfer is predicted on a staggered grid with a finite-volume formulation. The electromagnetic force is modeled as a linearized source term in a segregated solution of the axial momentum equation. Predictions of fluid velocity are compared successfully against past data. Constant wall temperature and constant wall heat flux cases are analyzed. The predicted results suggest that near-wall velocity and temperature gradients (constant wall temperature case) increase at larger Hartmann numbers, thereby leading to larger wall friction and convective heat transfer.

Effect of Hydraulic Jump on Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk Analyzed by Integral Method

Flow and heat transfer in a liquid film flowing over the surface of a rotating disk was analyzed by integral technique. The integral analysis includes the prediction of the hydraulic jump and its effects on heat transfer. The results of this analysis are compared to the earlier results that did not include this effect. At low inlet Reynolds numbers and high Rossby numbers, corresponding to low film inertia and low rotation rates, respectively, a hydraulic jump appears on the disk surface. The location of the jump and the liquid film height at this location are predicted. A scaling analysis of the equations governing the film thickness provided a semi-empirical expression for these quantities that was found to be in very good agreement with numerical results. Heat transfer analysis shows that the Nusselt numbers for both constant disk surface temperature and constant disk surface heat flux boundary conditions are lowered in the vicinity of the hydraulic jump due to the thickened liquid film. This effect can be more pronounced for the constant heat flux case depending on the location of the hydraulic jump. The Nusselt number exhibits a turning point at the jump location and can have higher values downstream of the hydraulic jump compared to those obtained from the analysis that does not include the gravitational effects.