Laminar heat transfer to power law fluids in flat gaps with various thermal wall conditions

Summary This paper deals with laminar, steady heat transfer in flat gaps formed by two wide parallel plates to power law fluids with temperature dependent rheological properties. Basic equations governing the problem to be discussed here are derived including the effects of viscous dissipation but neglecting the internal heat generation. The derived equations of motion, energy and continuity (the last in integral form) have been solved numerically by means of Dufort-Frankel scheme for various thermal wall conditions (constant and variable wall temperature as well as constant and variable wall heat flux). The results of numerical computations are presented in form of graphs illustrating the changes in temperature and velocity profiles as well as in local and mean Nusselt numbers and pressure drops with increasing distance from the inlet cross section. A special attention has been paid to the effects of viscous dissipation and temperature dependent rheological fluid properties on the changes mentioned above. The present work is intended to be an extension of the classical Graetz-Nusselt problem on non-Newtonian power law fluids with temperature dependent rheological properties flowing through a narrow gap formed by two wide parallel plates.With 8 Figures     

Some peculiarities of the asymmetric Graetz problem

A numerical simulation and an analysis of the steady state forced convection heat transfer with plane laminar flow confined by two parallel plates that are kept at constant but different temperatures are presented. We name this heat transfer configuration shortly the asymmetric Graetz problem. The essential features of the asymmetric in comparison to the symmetric Graetz problem are the reversal of the heat flux and the jump of the Nusselt number from positive to negative region at the plate having the temperature closer to the fluid inlet temperature. These phenomena occur at different axial positions, which depend on the thermal asymmetry and the fluid inlet conditions. The numerical results agree excellently with an analytical solution obtained in terms of Kummer confluent hypergeometric function and Hermite polynomials.     

Pressure-driven plug flows between superhydrophobic surfaces of closely spaced circular bubbles

Fully developed convective flow in a tube filled with an anisotropic porous material with viscous dissipation due to an internal heat source is considered. An analytical solution is obtained subject to constant heat flux at the wall of the tube. The effect of the anisotropy parameters (anisotropic permeability ratio \(\lambda \) and inclination angle of principal axes \(\varphi \)) of the porous medium on the hydrodynamic and convective heat transfer inside the tube is shown. The singular behavior of the Nusselt number is discussed. Asymptotic analysis for high and low Darcy numbers is shown to support the validity of the present study. Detailed analysis showing the effect of anisotropy on the convective heat transfer is performed.     

Heat transfer characteristics of oscillating flow regenerator filled with circular tubes or parallel plates

Under assumption of small perturbation, linear thermoacoustic theory was applied to analyze heat transfer characteristics of compressible oscillating flow in two kinds of simple regenerators filled with circular tubes or parallel plates. Based on the cross-sectional oscillating velocity and temperature distributions, the exact expressions of Nusselt number were derived in complex notation. The Nusselt number is the function of Prandtl number, kinetic Reynolds number Re_ω and the third dimensionless variable, D. Here, the D is defined as the ratio of heat transfer capability aroused by mean temperature gradient and gas compressibility. Both the gas compressibility and mean temperature gradient effects were discussed and two corresponding Nusselt numbers were given. In particular, simpler expressions for these two Nusselt numbers were deduced for extreme values of Re_ω and D. Finally, combined effect of gas compressibility and non-zero mean temperature gradient on heat transfer characteristics were analyzed via D. The analysis shows that the mean temperature gradient gives predominant contribution to the heat transfer performance of oscillating flow regenerator.     

Numerical study of an unsteady free convective magnetohydrodynamic flow of a dissipative fluid along a vertical plate subject to a constant heat flux

A new method is presented to solve the transient free convection MHD flow of a dissipative fluid along a semi-infinite vertical plate with mass transfer, the surface of which is exposed to a constant heat flux. The non-linear system of partial differential equations is numerically solved by means of the network simulation method, based on the thermo–electric analogy. This method permits the direct visualisation and evolution of the local and/or integrated transport variables (temperatures, velocities, concentrations and fluxes) at any point or section of the medium. At the same time, the solution for both transient and steady-state problems is obtained, the only requirement being finite-difference schemes for the spatial variable, while its programming does not involve manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The technique is always stable and convergent. Velocity, temperature and concentration profiles, local skin-friction, local Nusselt and local Sherwood numbers are plotted for air. The influence of the viscous dissipation, buoyancy ratio parameter, Schmidt number and magnetic parameter on heat and mass transfer and on the time needed to reach the steady-state are discussed.     

Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration

Summary. An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.     

Numerical study on heat transfer and entropy generation of developing laminar nanofluid flow in helical tube using two-phase mixture model

Nanofluids and helical tubes are among the best methods for heat transfer enhancement. In the present study, laminar, developing nanofluid flow in helical tube at constant wall temperature is investigated. The numerical simulation of Al₂O₃-water nanofluid with temperature dependent properties is performed using the two-phase mixture model by control volume method in order to study convective heat transfer and entropy generation. The numerical results is compared with three test cases including nanofluid forced convection in straight tube, velocity profile in curved tube and Nusselt number in helical tubes that good agreement for all cases is observed. Heat transfer coefficient in developing region inside a straight tube using mixture model shows a better prediction compared to the homogenous model. The effect of Reynolds number and nanoparticle volume fraction on flow and temperature fields, local and overall heat transfer coefficient, local entropy generation due to viscous dissipation and heat transfer, and the Bejan number is discussed in detail and compared with the base fluid. The results show that the nanofluid and the base fluid have almost the same axial velocity profile, but their temperature profile has significant difference in developing and fully developed region. Entropy generation ratio by nanofluid to the base fluid in each axial location along the coil length showed that the entropy generation is reduced by using nanofluid in at most length of the helical tube. Also, better heat transfer enhancement and entropy generation reduction can be achieved at low Reynolds number.     

Thermal boundary layers over a shrinking sheet: an analytical solution

In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.     

Numerical simulation of laminar flow of oil and heat transfer near a circular cylinder with arched guide plates

We have investigated the intensification of the heat transfer from a cylinder in an oil medium due to the setting of arched guide plates on the basis of the numerical solution of the Navier-Stokes and energy equations with the help of multiblock computer-aided technologies realized in the VP2/3 package. Calculations have been made for the laminar nonstationary cross flow around a heated cylinder in a viscous medium with a strong temperature dependence of its thermophysical characteristics. Comparison has been made between the numerical forecasts of the drag, local heat transfer, thermohydraulic efficiency, and total Nusselt number for a cylinder with plates and for a single cylinder. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 4, pp. 705–711, July–August, 2008.     

Heat transfer characteristics of oscillating flow regenerators in cryogenic temperature range below 20 K

Linearized thermoacoustic model considering temperature oscillation in the solid wall is applied to analyze the heat transfer characteristics of compressible oscillating flow in parallel-plate and circular-tube regenerators. In particular, the study focus results of heat transfer analysis are applicable in lower cryogenic temperature ranges (<20 K). Complete expression for Nusselt number is derived and it is shown to be the function of six nondimensional parameters when the shape of the regenerator is fixed. These parameters are discussed, respectively. Simplified expressions of the Nusselt numbers for both parallel plates and circular tubes structured regenerators are derived. Heat transfer characteristics can be evaluated via these simple expressions. Possible approaches of enhancing heat transfer in a thermoacoustic regenerator are discussed.     

Conjugated Effect of Joule Heating and Magnetohydrodynamic on Laminar Convective Heat Transfer of Nanofluids Inside a Concentric Annulus in the Presence of Slip Condition

In the current study, the conjugated effect of Joule heating and magnetohydrodynamics (MHD) on the forced convective heat transfer of fully developed laminar nanofluid flows inside annular pipes, under the influence of MHD field, has been investigated. The temperature and nanoparticle distributions at both the inner and outer walls are assumed to vary in the direction of the fluid. Furthermore, owing to the nanoparticle migrations in the fluid, a slip condition becomes far more important than the no-slip condition of the fluid–solid interface, which appropriately represents the non-equilibrium region near the interface. The governing equations—obtained by employing the Buongiorno’s model for nanofluid in cylindrical coordinates—are converted into two-point ordinary boundary value differential equations and solved numerically. The effects of various controlling parameters on the flow characteristics, the average Nusselt number and the average Sherwood number have been assessed in detail. Additionally, the effect of the inner to outer diameter ratio on the heat and mass transfer rate has been studied. The results obtained indicate that, in the presence of a magnetic field when the fluid is electrically conductive, heat transfer will be reduced significantly due to the influences of Joule heating, while the average mass transfer rate experiences an opposite trend. Moreover, the increase in the slip velocity on both the walls causes the average heat transfer to rise and the average mass transfer to decrease.     

三个关键几何参数对人字形波纹钎焊板式换热器换热性能影响的分析

以水-水热交换器为例,以CFD模拟软件为手段,以κ-ε模型为基础构建人字形波纹板式换热器模型,并系统分析波纹倾角、波纹深度、波纹间距这3个重要几何参数对换热器内部温度场、压力场、流场及平均努塞尔数和流动阻力的影响。研究结果表明,触点是板间换热效果最好的点,触点的扰流作用使流体在触点周围湍流程度最高,传热得到强化,这也是板式换热器内流体在雷诺数较低时发生湍流的主要原因;另一方面,流体经过触点后压力损失较大,是产生阻力损失的主要原因。波纹倾角是最重要的一个影响参数,最优波纹倾角在60°附近,此时换热效果较好而阻力尚未达到最大;波纹深度增加,平均努塞尔数增大,换热效果趋于好转,板间压力降也逐渐降低。但随着波纹深度的增加,结垢的倾向也会增加,因此较为合理的波纹深度应该在4～5mm之间;在给定的边界条件下,通过计算所得的波纹间距与波纹深度之比在3～4范围内时换热器性能较好。     

Thermal analysis of airflow inside a refrigerated container

A numerical study of conjugated heat transfer in ceiling-slot refrigerated containers is carried out to analyze the temperature distribution effectiveness and to determine the ventilation characteristics. The effect of slot size on thermal characteristics is studied by considering half-span and full-span injection. The container walls are defined as conductive opaque and are interacting with outside environment. The outer surface heat transfer coefficients of conductive walls are computed by studying the flow around the refrigerated truck. The Reynolds number at the slot exit varied between 2 × 10⁴ ≤ Re ≤ 2 × 10⁵. The gravity effect is taken into account, and the coupled mass, momentum, and energy equations are discretized in finite volumes. The heat transfer coefficients of inner flow are presented as plots of the mean Nusselt number versus the modified Reynolds number. The maximum dispersion in the numerical data being at 14.54-percent, the mean Nusselt number, the modified Reynolds number, and the aspect ratio of the container are correlated.     

Heat transfer in turbulent nanofluids: Separation flow studies and development of novel correlations

Convective heat transfer plays a significant role in numerous industrial cooling and heating applications. This method of heat transfer can be passively improved by reconfiguring flow passage, fluid thermophysical properties, or boundary conditions. The broader scope of nanotechnology introduced several studies of thermal engineering and heat transfer. Nano-fluids are one of such technology which can be thought of engineered colloidal fluids with nano-sized particles. In the present study, turbulent forced convection heat transfer to nanofluids in an axisymmetric abrupt expansion heat exchanger was investigated experimentally. During heat transfer investigation, the functionalized multiwalled carbon nanotubes (MWCNT-COOH), polycarboxylate functionalized graphene nanoplatelets (F-GNP), SiO₂ and ZnO water-based nanofluids were used. The convective heat transfer coefficient of fully developed turbulent flow of nanofluids flowing through an abrupt enlargement with the expansion ratio (ER) of 2 was experimentally determined at a constant wall heat flux of 12,128.56 W/m². The experiments were conducted at the Re ranges of 4000–16,000. The observed Nusselt numbers were higher than in the case of fully developed pipe flow indicating the level of the turbulent transport is high even though the recirculating velocities were a few percentages of the bulk mean velocity. The effect of Reynolds number and nanofluid’s volume concentration on heat transfer and friction losses were studied, where all the results reveal that with the increase of weight concentration and Reynolds number, the local Nusselt number enhanced at the increment of axial ratios in all the cases showing greater heat transfer rates than those of the base fluids. Comparison between the examined four types of nanofluids, show that the carbon-based nanofluids have a greater effect on enhancing heat transfer (33.7% and 16.7% heat transfer performance improvement for F-GNP and MWCNT nanofluids respectively at 0.1 wt% concentration) at the downstream of the sudden expansion pipe. There is no reported work dealing with the prediction of the local Nusselt number at the distance equivalent to the axial ratio and flow through sudden expansion. So far, two excellent correlations for the Local Nusselt number are proposed with reasonably good accuracy. Furthermore, a new correlation is developed for the average Nusselt number.     

Mass transfer effects on impulsively with variable surface heat flux

Numerical Solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with variable surface heat flux and mass transfer is presented here. The governing equations are solved using implicit finite-difference scheme of Crank-Nicolson type. The velocity profiles are compared with exact Solution and are found to be in good agreement. The transient and steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that there is a rise in the velocity due to the presence of a mass diffusion. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.     

Forced convection of low temperature nitrogen gas in rectangular channels with small aspect ratio

Forced convection of low temperature (80-150 K) nitrogen gas flowing through rectangular channels with hydraulic diameters of 0.513-1.814 mm and aspect ratios of 0.013-0.048 has been investigated experimentally. Close attention was focused on the effects of channel depth and heat addition on the heat transfer and flow characteristics, the transition from laminar to turbulent flow and the existence of an optimum channel depth. A dimensionless heating number was adopted to characterize the heating effect. The experimental correlation developed for the Nusselt number shows that the heat addition is the most important effect, followed by the channel aspect ratio, Reynolds number and Prandtl number.     

Combined heat and mass transfer in MHD free convection from a vertical surface with Ohmic heating and viscous dissipation

The problem of combined heat and mass transfer of an electrically conducting fluid in MHD natural convection adjacent to a vertical surface is analyzed, taking into account the effects of Ohmic heating and viscous dissipation. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference technique. The solution is found to be dependent on the governing parameters including the magnetic field parameter, the buoyancy ratio between species and thermal diffusion, the Eckert number, the Prandtl number, and the Schmidt number. Effects of these major parameters on the transport behaviors are investigated methodically and typical results are illustrated to reveal the tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number.     

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.     

Estimation of magnetohydrodynamic radiative nanofluid flow over a porous non‐linear stretching surface: application in biomedical research

The present study investigates the effects of thermal radiation and chemical reaction on magnetohydrodynamic flow, heat, and mass transfer characteristics of nanofluids such as Cu–water and Ag–water over a non‐linear porous stretching surface in the presence of viscous dissipation and heat generation. Using similarity transformation, the governing boundary layer equations of the problem are transformed into non‐linear ordinary differential equations and solved numerically by the shooting method along with the Runge–Kutta–Fehlberg fourth–fifth‐order integration scheme. The influences of various parameters on velocity, temperature, and concentration profiles of the flow field are analysed and the results are plotted graphically. A backpropagation neural network is applied to predict the skin friction coefficient, Nusselt number, and Sherwood number and these results are presented through graphs. The present numerical results are compared with the existing results and are found to be in good agreement. The results of artificial neural network and the obtained numerical values agree well with an error <5%.Inspec keywords: silver, copper, transforms, nanofluidics, friction, backpropagation, heat radiation, water, external flows, partial differential equations, nonlinear differential equations, boundary layers, Runge‐Kutta methods, mass transfer, flow through porous media, magnetohydrodynamicsOther keywords: magnetohydrodynamic radiative nanofluid flow, nonlinear stretching surface, biomedical research, thermal radiation, chemical reaction, magnetohydrodynamic flow, nonlinear porous stretching surface, viscous dissipation, similarity transformation, governing boundary layer equations, nonlinear ordinary differential equations, shooting method, Runge–Kutta–Fehlberg fourth–fifth‐order integration scheme, flow field, backpropagation neural network, Cu–water nanofluid, Ag–water nanofluid, skin friction coefficient, Nusselt number, Sherwood number, artificial neural network, Ag‐H₂ O, Cu‐H₂ O     

Effect of initial aqueous solution concentration and heating conditions on heat transfer characteristics of ice slurry

In this study, parameters affecting the heat transfer characteristics of ice slurry were investigated experimentally. The initial concentration of the ethanol solution from which the ice slurry was produced was varied as experimental parameter. Moreover, the heat flux at the test tube surface was varied as the experimental parameters, and the heat transfer coefficients measured. The effect of initial ethanol solution concentration and heating conditions on the heat transfer characteristics was not significant, and the Nusselt number can be expressed as a function of apparent Reynolds number, ice packing factor and ratio of average ice particle diameter to test tube diameter.