Control volume finite element simulation of MHD forced and natural convection in a vertical channel with a heat-generating pipe

Using the Galerkin weighted residual control volume finite element method, the effects of magnetic field and Joule heating on combined convection flow and heat transfer characteristics inside an octagonal vertical channel containing a heat-generating hollow circular pipe at the centre is performed. The flow enters at the bottom and exits from the top surface. All solid walls of the octagon are considered to be adiabatic. Graphical representation of streamlines, isotherms, average Nusselt number and maximum temperature of fluid for different combinations of Hartmann number (Ha), Joule heating parameter (J) and Richardson number (Ri) are displayed. The results indicate that the flow and thermal fields in the vertical channel depend markedly on the above mentioned parameters. In addition rate of heat transfer is obtained optimum in the absence of both MHD and Joule heating effects.     

A study on the thermal resistance over solid–liquid–vapor interfaces in a finite-space by a molecular dynamics method

Molecular dynamics of argon atoms in a nano-triangular channel which consists of (111) platinum walls were studied. The molecular dynamics simulations aim to gain understanding in the heat transfer through the channel including the influence of the contact resistances which become important in small-scale systems. The heat transfer properties of the finite-space system were measured at a quasi-steady non-equilibrium state achieved by imposing a longitudinal temperature gradient to the channel. The results indicate that the total thermal resistance is characterized not only by the thermal boundary resistances of the solid–liquid interfaces but also by the thermal resistance in the interior region of the channel. The overall thermal resistance is determined by the balance of the thermal boundary resistances at the solid–liquid interfaces and the thermal resistance attributed to argon adsorption on the lateral walls. As a consequence, the overall thermal resistance was found to take a minimum value for a certain surface potential energy. A rich solid–liquid interface potential results in a reverse flow along the wall which gives rise to a stationary internal flow circulation. In this regime, the nanoscale-channel functions as a heat-pipe with a real steady state.     

Eddy diffusivity of heat transfer in the radial direction for turbulent flow of mercury in annuli

A basic experimental study of the fluid dynamics and heat-transfer characteristics of mercury, in fully developed turbulent flow through annuli, was carried out. This paper, the third in a series on this project, presents the results on the eddy diffusivity of heat transfer. Velocity and temperature profiles were measured in vertical annuli with heat transfer from the inner wall only, and experiments were conducted where the mercury either did not wet at all, or did thoroughly wet, the channel walls.The shapes of the ε_H profiles were found to be similar to those of the ε_M profiles, with the maxima and minima often occurring at or near the same radial locations, for the same experimental conditions. All minima occurred at the radius of maximum velocity, but the valleys in ε_H profiles were relatively more shallow than those in the ε_M profiles. The effect of wetting on the relative shape of the ε_H profile, as in the case of the ε_m profile, was found to be appreciable. When both walls were unwetted, the hydrodynamic behavior of the mercury was found [1] to be very similar to that of ordinary fluids. Although the present results obtained with unwetted walls do not agree with predictions based on existing theory, they do lend appreciable support to the method of Ramm and Johannsen [7].     

Joule heating in magnetohydrodynamic flows in channels with thin conducting walls

Joule heating in liquid metal magnetohydrodynamic flows is investigated with reference to self-cooled liquid metal blankets for tokamaks. Pressure-driven flow of an electrically conducting fluid confined between two parallel, infinite walls with a transverse magnetic field is studied. The walls are electrically conducting, which implies strong currents flowing within the thin conducting walls. The problem is solved both analytically and numerically.It is shown that the Joule heat cannot be neglected in certain range of parameters relevant to fusion blanket applications. The magnitude of the Joule heat released inside the channel and the walls depends on the thermal conductivity of the outside surface of the channel walls. For thermally conducting outside surface of the walls the Joule heat can become significant for high values of the Hartmann number and moderate average velocity. The effect is even more pronounced for thermally insulating outside surface of the walls. For example, for lead–lithium flow with stainless steel walls the temperature increase along the flow exceeds 200 °C over the length of the blanket, which is almost three times higher than that for thermally conducting outside surface of the walls.The main reason for such a strong rise in temperature is the heat released inside the walls. The heat produced in the fluid region is quickly convected towards the exit from the channel. The heat released inside the walls can only leave the domain by diffusion into the fluid region and thus is accumulated along the channel length.     

Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium

The classical Graetz methodology is applied to investigate the effect of local thermal non-equilibrium on the thermal development of forced convection in a parallel-plate channel filled by a saturated porous medium, with walls held at constant temperature. The Brinkman model is employed. The analysis leads to an expression for the local Nusselt number, as a function of the dimensionless longitudinal coordinate, the Péclet number, the Darcy number, the solid-fluid heat exchange parameter, the solid/fluid thermal conductivity ratio, and the porosity.     

Forced convection in porous microchannels with viscous dissipation in local thermal non-equilibrium conditions

Fully developed, steady-state forced convection, in parallel-plate microchannels, filled with a porous medium saturated with rarefied gases at high temperatures, in local thermal non-equilibrium (LTNE) condition, is investigated for the first-order slip-flow regime (0 ≤ Kn ≤ 0.1). Both velocity and temperature jumps at the walls are accounted for. An analytic solution is proposed for the Darcy–extended Brinkman flow model with assigned uniform heat flux at the microchannel walls and viscous heat dissipation in the fluid phase. The solution for NTLE includes the shear work done by the slipping effects. A closed-form expression of the Nusselt number is derived. A validation analysis with respect to the case of channels filled with saturated porous medium is accomplished. The results show that the internal dissipation increases as the velocity slip increases. In addition, the heat dissipation strongly affects the fluid temperature profiles. The increases in velocity slip and temperature jump lead to decreases of temperature gradients in the fluid and solid along the sections. The heat transfer at channel walls is enhanced due to an increase in the bulk heat transfer.     

Influence of conjugate heat transfer on the minimization of entropy generation for forced convective flow through parallel plate channel filled with porous material

A fluid–solid conjugate heat transfer model is developed to analyze the characteristics of entropy generation for forced convective steady hydrodynamically fully developed laminar flow of a Newtonian fluid through a parallel plate channel filled with porous material by modulating the following parameters: substrate thickness, the ratio of thermal conductivity of wall to fluid, Biot number, the axial temperature gradient in the fluid, and Peclet number. The exteriors of both the walls are subjected to the thermal boundary conditions of the third kind. The mass and Brinkman momentum conservation equations in the fluidic domain and the coupled energy conservation in both the solid and fluidic domain are solved analytically using the local thermodynamic equilibrium model, so as to derive closed-form expressions for the velocity in the fluid and the temperature both in the fluid and solid walls in terms of relevant parameters. Suitable combinations of influencing factors, namely the geometric parameters of the system, fluid, flow, and substrate properties are identified for which global entropy generation rate is minimized. The findings may be helpful in the design of thermal systems frequently used in diverse engineering applications having heat transfer in the solid wall being a crucial parameter.     

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio (α_s), inertial force parameter (Γ), porosity (ε), and the effective thermal conductivity ratio (k_r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α_s and ε, while it decreases with increasing k_r.     

Forced Convective Heat Transfer in a Plate Channel Filled with Solid Particles

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Laminar conjugate mixed convection in a vertical channel with heat generating components

Conjugate mixed convection arising from protruding heat generating ribs attached to substrates (printed circuit boards) forming channel walls is numerically studied. The substrates with ribs form a series of vertical parallel plate channels. Assuming identical disposition and heat generation of the ribs on each board, a channel with periodic boundary conditions in the transverse direction is considered for analysis. The governing equations are discretised using a control volume approach on a staggered mesh and a pressure correction method is employed for the pressure–velocity coupling. The solid regions are considered as fluid regions with infinite viscosity and the thermal coupling between the solid and fluid regions is taken into account by the harmonic thermal conductivity method. Parametric studies are performed by varying the heat generation based Grashof number in the range 10⁴–10⁷ and the fan velocity based Reynolds number in the range 0–1500, with air as the working medium. Results are obtained for the velocity and temperature distributions, natural convection induced mass flow rate through the channel, the maximum temperatures in the heat sources and the local Nusselt numbers. The natural convection induced mass flow rate in mixed convection is correlated in terms of the Grashof and Reynolds numbers. In pure natural convection the induced mass flow rate varies as 0.44 power of Grashof number. The maximum dimensionless temperature is correlated in terms of pure natural convection and forced convection inlet velocity asymptotes. For the parameter values considered, the heat transferred to the working fluid via substrate heat conduction is found to account for 41–47% of the heat removal from the ribs.     

Analysis of temperature gradient bifurcation in porous media – An exact solution

The phenomenon of temperature gradient bifurcation in a porous medium is analyzed by studying the convective heat transfer process within a channel filled with a porous medium, with internal heat generation. A local thermal non-equilibrium (LTNE) model is used to represent the energy transport within the porous medium. Exact solutions are derived for both the fluid and solid temperature distributions for two primary approaches (Models A and B) for the constant wall heat flux boundary condition. The Nusselt number for the fluid at the channel wall is also obtained. The effects of the pertinent parameters such as fluid and solid internal heat generations, Biot number and fluid to solid thermal conductivity ratio are discussed. It is shown that the internal heat generation in the solid phase is significant for the heat transfer characteristics. The validity of the one equation model is investigated by comparing the Nusselt number obtained from the LTNE model with that from the local thermal equilibrium (LTE) model. The results demonstrate the importance of utilizing the LTNE model in the present study. The phenomenon of temperature gradient bifurcation for the fluid and solid phases at the wall for Model A is established and demonstrated. In addition, the temperature distributions for Models A and B are compared. A numerical study for the constant temperature boundary condition was also carried out. It was established that the phenomenon of temperature gradient bifurcation for the fluid and solid phases for the constant temperature boundary condition can occur over a given axial region.     

Transient temperature field in a parallel-flow three-fluid heat exchanger with the thermal capacitance of the walls and the longitudinal walls conduction

Transient temperature response of a parallel-flow three-fluid heat exchanger with the thermal capacitance of the walls and the longitudinal heat conduction through the walls is investigated numerically, by the implicit MacCormack method, for a step change in flow rate of one fluid. The impact of thermal properties of the walls on temperature field is examined. The results of calculations show that as the thermal diffusivity of the walls decreases, the effect of the walls increases.     

Uni-directional heat flux through the horizontal fluid layer with sinusoidal wall temperature at the top or bottom boundaries

Infinite horizontal fluid layer is considered between the top and bottom walls. Either top or bottom wall temperature is sinusoidally oscillated in terms of the constant average temperature in an opposing horizontal wall. This is the system with no temperature difference between the top and bottom walls in time-averaged sense, as studied by Kalabin et al. for a square channel. The fluid is Newtonian and Boussinesq approximation is made. The fluid layer of height 1 versus the horizontal width 1 or 4 is adopted and numerical computations are carried out for Pr = 1. The time-averaged Nusselt numbers computed both at top and bottom walls give the upward time-averaged heat flux without depending on the temperature oscillation either at the upper or lower walls. This is because the time-dependent convection plumes occur at the almost largest temperature of the bottom wall in comparison to the top wall. The time-averaged heat flux is always positive, i.e., upward, even if the time-averaged temperature difference is zero between the top and bottom walls.     

Computational Conjugate Heat Transfer Analysis of a Hybrid Electric Vehicle Inverter

ABSTRACT

A physics-based computational simulation of the heat transfer characteristics of an insulated gate bipolar transistor (IGBT) developmental inverter is reported. The simulation considers the fluid/thermal multiphysics interactions via a conjugate heat transfer analysis. The fluid phase includes air and liquid coolant; the solid phase, where the heat is conducted, includes various solid materials. Numerical solutions of the heat conduction and convection phenomena in and around the IGBT modules and the inverter, built as a three-dimensional computational model, are sought for by using parallel computing. Comparisons with the available experimental data show a satisfactory agreement of the inverter temperature at three power levels under two different coolant flow rates. Detailed examination of the flow field reveals that the design features of the rectangular coolant flow chamber in the heat sink and the small clearance between the tips of the pin fin and the walls lead to an evenly distributed coolant flow around most of the pin fins. The temperature distributions of the pin fins depend highly on their locations relative to the IGBT modules. The findings from the current study can be useful in future efforts to optimize the thermal performance of IGBT inverters.     

Calculation of turbulent flow and heat transfer in a porous-baffled channel

This study presents the numerical predictions on the turbulent fluid flow and heat transfer characteristics for rectangular channel with porous baffles which are arranged on the bottom and top channel walls in a periodically staggered way. The turbulent governing equations are solved by a control volume-based finite difference method with power-law scheme and the k-ε turbulence model associated with wall function to describe the turbulent structure. The velocity and pressure terms of momentum equations are solved by SIMPLE (semi-implicit method for pressure-linked equation) method.The parameters studied include the entrance Reynolds number Re (1×10⁴-5×10⁴), the baffle height (h=10, 20 and 30 mm) and kind of baffles (solid and porous); whereas the baffle spacing S/H are fixed at 1.0 and the working medium is air. The numerical calculations of the flow field indicate that the flow patterns around the porous- and solid-type baffles are entirely different due to different transport phenomena and it significantly influences the local heat transfer coefficient distributions. Relative to the solid-type baffle channel, the porous-type baffle channel has a lower friction factor due to less channel blockage.Concerning the heat transfer effect, both the solid-type and porous-type baffles walls enhanced the heat transfer relative to the smooth channel. It is further found that at the higher baffle height, the level of heat transfer augmentation is nearly the same for the porous-type baffle, the only difference being the Reynolds number dependence. As expected, the centerline-averaged Nusselt number ratio increases with increasing the baffle height because of the flow acceleration.     

Numerical investigation of the MHD forced convection and entropy generation in a straight duct with sinusoidal walls containing water–Al2O3 nanofluid

This paper examines forced convection heat transfer and entropy generation of a nanofluid laminar flow through a horizontal channel with wavy walls in the presence of magnetic field, numerically. The Newtonian nanofluid is composed of water as base fluid and Al₂O₃ as nanoparticle which is exposed to a transverse magnetic field with uniform strength. The inlet nanofluid with higher temperature enters the cool duct and heat is exchanged along the walls of a wavy channel. The effects of the dominant parameters including Reynolds number, solid volume fraction, Hartmann number, and different states of amplitude sine waves are studied on the local and average Nusselt number, skin friction, and total entropy generation. Computations show excellent agreement of the present study with the previous literature. The computations indicate that with the increasing strength of a magnetic field, Nusselt number, skin friction, and total entropy generation are increased. It is found that increasing the solid volume fraction of nanoparticles will increase the Nusselt number and total entropy generation, but its effect on the skin friction is negligible. Also, results imply that increasing amplitude sine waves of the geometry has incremental effect on both Nusselt number and skin friction, but its effect on the total entropy generation is not so tangible.     

Anisotropy Effects on Heat and Fluid Flow by Unsteady Natural Convection and Radiation in Saturated Porous Media

ABSTRACT

This article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with anisotropic, in both thermal conductivity and permeability, fluid-saturated porous medium. The bounding walls of the channel are gray and kept at a constant hot temperature.

In the present study we suppose the validity of the Darcy law for motion and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The numerical results allow us to represent the time–space variations of the different state variables. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely, the single scattering albedo ω, the temperature ratio R, the anisotropic thermal conductivity ratio R_c, and the anisotropic permeability ratio R_k, are addressed. Numerical results indicate that the controlling parameters of the problem, namely, ω, R, R_c, and R_k, have significant effects on the flow and thermal field behavior and also on the transient process of heating or cooling of the medium. Effects of such parameters on time variations of the volumetric flow rate q_v and the convected heat flux Q at the channel's outlet are also studied.     

Laminar heat transfer in a porous channel simulated with a two-energy equation model

Laminar heat transfer in a porous channel is numerically simulated with a two-energy equation model for conduction and convection. Macroscopic equations for continuity, momentum and energy transport for the fluid and solid phases are presented. The numerical methodology employed is based on the control volume approach with a boundary-fitted non-orthogonal coordinate system. Fully developed forced convection in a porous channel bounded by parallel plates is considered. Solutions for Nusselt numbers along the channel are presented for laminar flows. Results simulate the effects Reynolds number Re, porosity, particle size and solid-to-fluid thermal conductivity ratio on Nusselt sumber, Nu, which is defined for both the solid and fluid phases. High Re, low porosities, low particle diameters and low thermal conductivity ratios promote thermal equilibrium between phases leading to higher values of Nu.     

Numerical Investigation of Forced Convection Conjugate Heat Transfer from Offset Square Cylinders Placed in a Confined Channel Covered by Solid Wall

Flow over two isothermal offset square cylinders in a confined channel is simulated for different Reynolds numbers to disclose the forced convection heat transfer from the heated square cylinders to the ambient fluid. The spacing between the cylinder in the normal direction and the blockage ratio are fixed. The channel walls are covered by solid walls of thickness equal to the size of the cylinder and conjugate heat transfer is considered by including these walls. Heat transfer from the cylinders to the ambient fluid as well as that conducted within the solid wall through the conjugate interface boundary are investigated in connection with Reynolds number and are reported for both steady and periodic flows. Simulation is carried out for Reynolds number varying from 10 to 100 with air as the fluid. The onset of the vortex begins when the Reynolds number equals 48. The conjugate interface temperature declines when the Reynolds number grows. The isotherms in the solid wall show two dimensionality near the cylinder region.     

Oscillatory slip flow of Fe3O4 and Al2O3 nanoparticles in a vertical porous channel using Darcy's law with thermal radiation

The heat transfer phenomena and oscillatory flow of an electrically conducting viscous nanofluid (NF) in a channel with porous walls and saturated porous media exposed to the thermal radiation are studied. The nanoparticles (NPs) Fe₃O₄ and Al₂O₃ are taken with water as base fluid along with nonuniform temperature and velocity slip at the wall of channel (y′ = 0). The basic laws of momentum and energy conservation are converted into the dimensionless system of the partial differential equations (PDEs) using similarity variables. Closed‐form solutions of these coupled PDEs are constructed for all values of time by taking the oscillatory pressure gradient. The physical insight of involved parameters on the fluid velocity, temperature profile, heat transfer rate, and surface friction is studied and analyzed graphically. It is noted from this study that the fluid velocity shows a decreasing behavior with the volume fraction of NPs. Furthermore, the amplitude of the oscillatory motion in case of skin friction decreases for a large magnetic field.