Laminar forced convection to non-Newtonian fluids in ducts with prescribed wall heat flux

Heat transfer in laminar forced convection to non-Newtonian fluids in thermally developing flow inside circular tubes and parallel plate ducts with prescribed wall heat flux is solved exactly. The local and average Nusselt numbers are determined and accuracy of the existing approximate solutions is examined.     

Combined forced and free convection for laminar flow in horizontal tubes with uniform heat flux

This study considers the effects of free convection on laminar flow of water in horizontal circular tubes having essentially constant heat flux at the tube wall. A visual and quantitative study was performed utilizing electrically heated glass tubing. These data were combined with other data and correlations to obtain a general picture of the influence of free convection on the Nusselt number. The final correlation curves given in Fig. 11 are provisionally recommended for obtaining heat-transfer coefficients in practical situations. With reasonable heating rates, the heat-transfer coefficients can be three to four times the values predicted by traditional constant property solutions.     

Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow

An analytical solution is investigated for forced convection heat transfer from a laminar plane wall jet as conjugate case. For Re ? 1, boundary layer theory is used for the investigation. The problem has been solved for two classic cases such as Pr ? 1 and Pr ? 1. The conjugate model consists of considering the full Navier-Stokes equation in the fluid medium and coupling of energy equations in the fluid and the slab through the interface boundary conditions. Closed-form relations are found for Nusselt number (Nu), average Nusselt number and conjugate interface boundary temperature (θ_b). The effects of the Reynolds number (Re), the Prandtl number (Pr), the thermal conductivity ratio (k) between the slab and the fluid medium and the slab aspect ratio (λ) are investigated on the heat transfer characteristics. The analytical results are compared with the full numerical results.     

Forced turbulent heat convection in a square duct with non-uniform wall temperature

In the present work, the numerical simulation to calculate the problem of the turbulent convection with non-uniform wall temperature in a square cross-section duct was adopted. To solve this problem some assumptions for the flow, such as: the condition of fully developed turbulence and incompressible flow have been assumed. The methodology of the dimensionless energy equation was used to calculate the fluid temperature field in the square cross-section in function of the non-uniform wall temperatures prescribed. Numerical simulations were done using two different turbulent models to resolve the momentum equations and two more models to resolve the energy equation. The models of turbulence k-ε Nonlinear Eddy Viscosity Model (NLEVM) and the Reynolds Stress Model (RSM) were used to determine the turbulent intensities as well as the profiles of axial and secondary mean velocities. The turbulence model RSM was simulated using a commercial software. The thermal field was determined from other two models: Simple Eddy Diffusivity (SED), based in the hypothesis of the constant turbulent Prandtl number; and Generalized Gradient Diffusion Hypothesis (GGDH). In this last model, as the turbulent heat transfer depends on the shear tensions, the anisotropy is considered. These two last equation models of the energy equation of the fluid have been implemented in FORTRAN, a code of programming. The performances of the models were evaluated by validating them based in the experimental and numerical results published in the literature. Two important parameters of great interest in engineering are presented: the friction factor and the Nusselt number. The results of this investigation allow the evaluation of the behavior of the turbulent flow and convective heat fluxes for different square cross-sectional sections throughout the direction of the main flow, which is mainly influenced by the temperature distribution in the wall.     

Wall coupling effect in channel forced convection with streamwise periodic boundary heat flux variation

The present paper deals with the laminar forced convection in a parallel-plane channel, and is aimed to investigate the effect of conducting walls. On the external boundaries of the duct walls a thermal boundary condition is prescribed, such that the wall heat flux longitudinally varies with sinusoidal law. The local energy balance equation is written separately for the fluid and the solid regions, with reference to the fully developed regime, and then solved both analytically and numerically. Moreover, the local and average Nusselt numbers in a longitudinal period are evaluated. The average Nusselt number, if regarded as a function of the dimensionless pulsation, displays an interesting feature. In fact, for all the considered cases, it has a minimum, so that there exists a value of the dimensionless pulsation such that the heat exchange between the fluid and the solid wall is considerably inhibited.     

Exergy transfer characteristics of forced convective heat transfer through a duct with constant wall heat flux

The examination of exergy transfer characteristics caused by forced convective heat transfer through a duct with constant wall heat flux for thermally and hydrodynamic fully developed laminar and turbulent flows has been presented. The exergy transfer Nusselt number is put forward and the dependence relationships of the exergy transfer Nusselt number on the heat transfer Nusselt number, Reynolds number and Prandtl number are obtained. Expressions involving relevant variables for the local and mean convective exergy transfer coefficient, non-dimensional exergy flux and exergy transfer rate, etc. have been derived. By reference to a smooth duct, the numerical results of exergy transfer characteristics for fluids with different Prandtl number are obtained and the effect of the Reynolds number and non-dimensional cross-sectional position on exergy transfer characteristics is analyzed. In addition, the results corresponding to the exergy transfer and energy transfer are compared.     

Reduced-order modeling of turbulent forced convection with parametric conditions

Accurate reduced-order models of turbulent flows have been traditionally constructed with the proper orthogonal decomposition (POD), however the method has been limited to prototypical flows over a narrow parameter range. An orthogonal complement subspace method is developed here to treat inhomogeneous boundary conditions while implicitly coupling the velocity and temperature fields of turbulent convection. A new flux matching procedure is formulated as a state space residual series expansion to efficiently model parameter dependent convection, greatly extending the utility of the reduced-order modeling framework. An illustrative test case of turbulent channel flow over heated blocks shows flow and thermal models with 95% accuracy over the domain can be produced, while simultaneously reducing the number of degrees of freedom by a factor of 10³. Error bounds are formulated and provide a posteriori error estimates for the reduced-order model.     

Structure of turbulent heat flux in a flow over a heated wavy wall

A particle image thermometry technique is proposed to determine the turbulent heat flux in a water channel between a sinusoidal heated bottom and a flat top wall. Reynolds numbers between 2400 and 20,500 are considered. A proper orthogonal decomposition of combined velocity and temperature fields reveals a quantitative agreement between large-scale thermal and momentum structures. The distribution of budget terms of the streamwise and wall-normal heat fluxes are similar to those for the two Reynolds stress components. Co-spectra indicate that larger scale structures make a significant contribution to the streamwise heat flux and smaller scales are more important to the wall-normal heat flux.     

Near-wall velocity profile with adaptive shape functions for turbulent forced convection

This article applies Reichardt's velocity profile to turbulent convection analysis. In contrast to a conventional law-of-the-wall formulation with three regions, a single profile represents the entire region from the viscous sublayer to the fully turbulent region. Special shape functions are developed for this profile in a hybrid finite element/volume formulation, together with dissipation rate boundary conditions, which are consistent with the velocity profile modeling. Applications to turbulent channel flow are successfully predicted with a k−ɛ turbulence model.     

Evaporative mass transfer in turbulent forced convection duct flows

Experiments were performed to determine the mass transfer characteristics for evaporation from partially filled pans of distilled water recessed in the floor of a flat rectangular duct through which turbulent air flow was passed. During the course of the experiments, parametric variations were made of the Reynolds number of the air flow, the streamwise length of the pan, and the distance between the top of the pan and the water surface (hereafter referred to as the step height). For all of the operating conditions of the experiments, the measured Sherwood numbers were well correlated with the Reynolds number provided that the step height was used as the characteristic dimension. Guided by analytical considerations, a second correlation was constructed which provides Sherwood number predictions for operating conditions corresponding to pans longer than those used in the present experiments. By making use of the analogy between heat and mass transfer, it was shown how Nusselt numbers can be obtained from the Sherwood number correlations.     

Unsteady forced convection with sinusoidal duct wall generation: the conjugate heat transfer problem

Transient heat transfer solutions are found for a fluid flowing within a parallel plate duct when there is sinusoidal generation with axial position in the duct wall. Solutions are found for wall temperature, surface heat flux and fluid bulk mean temperature as a function of position and time in this conjugated problem. To develop this solution, finite difference methods are used as well as the quasi-steady method and another method which employs a two integral representation for the surface heat flux. Accuracy limitations of the quasi-steady results are identified. Transient local Nusselt number predictions show its dependence upon time.     

Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux

Upward mixed convection of air in a long, vertical tube with uniform wall heat flux has been studied numerically for Re=1000, Re=1500 and Gr?10⁸ using a low Reynolds number k-ε model. The results for the fully developed region identify two critical Grashof numbers for each Reynolds number, which correspond to laminar-turbulent transition and relaminarization of the flow. They also distinguish the Re-Gr combinations that result in a pressure decrease over the tube length from those resulting in a pressure increase. A correlation expressing the fully developed Nusselt number in terms of the Grashof and Reynolds numbers is proposed. It is valid for laminar and turbulent flows in the range 1000?Re?1500, Gr?5×10⁷.