Laminar forced convection inside ducts with periodic variation of inlet temperature

Laminar forced convection with periodic variations of inlet temperature is studied in both parallel-plate channels and circular ducts. The generalized integral transform technique is employed to reduce the original problem to a system of linear first-order differential equations, which is then solved utilizing the related complex matrix eigenvalue problem. Amplitudes and phase lags with respect to the inlet condition are determined for fluid bulk temperature and wall heat flux, and the results are presented in graphical form as a function of the dimensionless axial distance along the channels for different values of the dimensionless frequency of inlet oscillations.     

Transient conjugated forced convection in ducts with periodically varying inlet temperature

Transient forced convection for slug flow inside parallel-plate channels and circular ducts including conjugation to the walls is solved analytically and exactly for periodic variation of the inlet temperature. The periodic solution to the problem involved eigenfunctions and eigenvalues of a complex eigenvalue problem. The complex eigenvalue problem is solved by modifying the recently advanced Count Method, and benchmark results are presented for the eigenvalues in tabular form. The amplitude and phase lag of oscillations with respect to the conditions at the inlet are determined for the wall temperature, fluid bulk temperature and heat flux. The results for the cases of both parallel-plate channels and circular ducts are presented in the graphical form as a function of the axial position for different values of the parameters signifying the rate of energy storage in the walls. The effects of walls on damping the amplitude and altering the phase of temperature and heat flux oscillations along the duct are investigated.     

Exact solution of the transient forced convection energy equation for timewise variation of inlet temperature

An exact solution to the equation of transient forced convection for time varying inlet temperature with a general, space dependent boundary condition of an incompressible laminar forced convection heat transfer with fully developed flow between two parallel plates is given. The finite integral transform technique has been used as the method of analysis. Analytical results for laminar and turbulent flow are presented. The results are confirmed experimentally by the frequency response method.     

Natural convection in porous cavity with sinusoidal bottom wall temperature variation

Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20–500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment.     

Turbulent forced convection flow inside inward-outward rib corrugated tubes with different rib-shapes

The thermal and hydrodynamic behaviors of forced convection turbulent flow inside the corrugated tube are investigated numerically. The ribs of corrugated tube are distributed in inward-outward arrangement simultaneously and alternately (referred as IOCT). Three roughness shapes of the corrugated tube are examined; rectangular, semicircular, and trapezoidal ribs. The computational model is validated through comparison with the predicted results with correlated and experimental ones of related works. The performance of IOCT is compared thermally and hydrodynamically with that of the inward-rib corrugated tube (ICT), outward-rib corrugated tube (OCT) and smooth tubes. The results reveal that the heat is exchanged effectively by employing IOCT than utilizing OCT but with extra pumping power losses. At the maximum Re, it is found that the heat transfer of IOCT is 17.7% higher than that of OCT, and utilizing IOCT instead of ICT results in a reduction of friction factor by about 27.2%. Also, IOCT exhibits a lower friction factor and pressure drop penalty than that imposed by ICT. Also, roughness shapes have an insignificant effect on the thermal and hydrodynamic performances of IOCT for the same rib geometrical parameters. Furthermore, the influence of variation pitch-to-diameter ratio is also examined for various rib shapes of IOCT.     

Turbulent heat transfer of natural convection between two vertical parallel plates

We measure heat transfer coefficients of natural convection between two vertical smooth parallel plates heated uniformly in the laminar, transition, and turbulent regions. The heat transfer characteristics are experimentally investigated with changing width, δ, between the vertical parallel plates, wall heat flux, q_w, overall watercourse length, L,of the vertical parallel plate and heating conditions. For natural convection between the vertical parallel plates, in the turbulent region of , the heat transfer is strongly suppressed owing to the effect of combined convection. On the contrary, the heat transfer in the laminar region is enhanced due to the tunnel effect. These tendencies become pronounced with decreasing δ and increasing L.The location of the heat transfer reduction shifts downstream with increasing q_w under a fixed δ. Furthermore, under smaller δ, we cannot clearly distinguish the transition process in accordance with both the heat transfer enhancement in the laminar region and the heat transfer reduction in the turbulent region. © 2001 Scripta Technica, Heat Trans Asian Res, 31(1): 56–67, 2002     

Natural convection laminar flow between two vertical walls with a nonlinear variation of density and viscosity with temperature

Under the combined influence of buoyancy force and constant pressure gradient, the free convection flow and heat transmission inside a channel placed vertically and consisting of two parallel walls are examined. Through the application of the Runge–Kutta fourth-order approach and the shooting procedure, the modeled equations of the problem including nonlinear density–temperature and quadratic viscosity–temperature change at constant but different wall temperatures are numerically solved. For distinct values of the embedded parameters, the fluctuations in fluid's velocity and temperature are examined. For various situations of linear, quadratic, and nonlinear dependence of density on temperature, numerical values for heat transmission rate, volume flow rate and skin friction are determined and tabulated. The fluctuations of the Nusselt number with the Grashof number corresponding to thermal expansion coefficients are depicted through graphical interpretations. It was found that the combined effect of thermal expansion coefficients raises the values of the physical entities, Nusselt number, volume flow rate, and heat transmission rate. For the lower Reynolds number values, the Nusselt number value stays around one, indicating the same impact of conduction and convection on heat transmission.     

Laminar forced convection slip-flow in a micro-annulus between two concentric cylinders

Forced convection heat transfer in hydrodynamically and thermally fully developed flows of viscous dissipating gases in annular microducts between two concentric micro cylinders is analyzed analytically. The viscous dissipation effect, the velocity slip and the temperature jump at the wall are taken into consideration. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio, the Knudsen number and the Brinkman number. The analytical results obtained are compared with those available in the literature and an excellent agreement is observed.     

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.     

Field synergy analysis of laminar forced convection between two parallel penetrable walls

In this paper, some exact solutions for 2-D convective heat transfer between two parallel penetrable walls were derived and analyzed based on field synergy theory. They are valuable to further develop the field synergy principle and understand how to improve or to weaken field synergy in practice. In addition, these solutions can be used as benchmarks to verify numerical solutions and to develop numerical schemes, grid generation methods and so forth. All solutions given in this paper can be proven easily by substituting them into the governing equations.     

Magnetohydrodynamic natural convection in a vertical cylindrical cavity with sinusoidal upper wall temperature

A series of numerical simulations were performed in order to study liquid metal MHD natural convection in a vertical cylindrical container with a sinusoidal temperature distribution at the upper wall and the other surfaces being adiabatic. Starting from the basic hydrodynamic case, the effect of vertical (axial) and horizontal magnetic fields is assessed. Depending on the magnitude of the Rayleigh and Hartmann numbers, both turbulent and laminar (azimuthally symmetric or not) flows are observed. The results show that the increase of Rayleigh number promotes heat transfer by convection while the increase of Hartmann number favors heat conduction. The vertical magnetic field reduces the Nusselt number more than the horizontal. The circulation patterns for the most convective cases are confined close to the top corner of the container with the simultaneous formation of a secondary flow pattern at the bottom corner, while for the more conductive cases only one circulation pattern exists covering the entire domain.     

Entropy generation through combined non-grey gas radiation and forced convection between two parallel plates

The current study presents a numerical computation of combined gas radiation and forced convection through two parallel plates. A laminar flow of a temperature-dependent and non-grey gas in the entrance region of the channel was investigated. Over-heated water vapor was chosen as a gas because of its large absorption bands. Some special attention was given to entropy generation and its dependence on geometrical and thermodynamic parameters. The radiative part of the study was solved using the “Ray Tracing” method through S₄ directions, associated with the “statistical narrow band correlated-k” (SNBCK) model. The temperature fields were used to calculate the distributions of local and global entropy generation.     

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.     

Analytical solution of Graetz problem in pipe flow with periodic inlet temperature variation

The paper reports an analytical solution for the temperature field in a fully developed pipe flow subject to periodic (of any shape) inlet temperature variation. The solution is given in term of a series of Kummer functions for the cases of uniform and constant wall temperature and wall heat flux, thus comprising also the adiabatic wall case. A “fully developed” region for the fluctuating component of the fluid temperature is also evidenced and closed-form solutions are given. An interpretation of the temperature field as superposition of travelling thermal waves is presented and discussed.     

Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side

A numerical study has been carried out in rectangular enclosures, which have a vertical active wall with all the other walls insulated. The equally divided active sidewall is heated and cooled with sinusoidal temperature profiles. Two cases have been considered: the first is the lower part is heated while the upper part is cooled and the second, the upper part is heated and lower part is cooled. Steady state heat transfer by laminar natural convection has been studied by numerically solving equations of mass, momentum and energy, to determine the thermal penetration in the enclosures and heat transfer as a function of Rayleigh number, the aspect ratio and the position of side heating with respect to side cooling. Rayleigh number was varied from 10³ to 10⁶ and the aspect ratio from 0.2 to 5, and the results are presented in the form of streamlines and isotherms, local and average Nusselt number, and heat penetration length. It is found that the penetration approaches to 100% at high Rayleigh numbers when the lower part is heated while the higher part is cooled. In the case of the higher part is heated and the lower part is cooled, the penetration is limited to 70% passing through maxima at Rayleigh number below 10⁶.     

Fully developed forced convection of the Phan-Thien-Tanner fluid in ducts with a constant wall temperature

Two problems of laminar-forced convection in pipes and channels, under fully developed conditions, are solved for an imposed constant temperature at the wall, with fluids obeying the simplified Phan-Thien-Tanner (SPTT) model. The fluid properties are taken as constants and axial conduction is negligible. The first case represents the asymptotic behaviour of the Graetz problem for the SPTT fluid, i.e., equilibrium between axial convection and radial conduction of thermal energy with negligible viscous dissipation. The solution is given by an analytical expression but it is only approximate (within 0.3%) as it was obtained with an algebraic method based on successive approximations. The second problem has an exact analytical solution representing the equilibrium between viscous dissipation and radial heat conduction, with negligible axial convection and a constant wall temperature.     

Laminar forced convection heat transfer around two rotating side-by-side circular cylinder

The present study numerically investigates two-dimensional laminar force convection heat transfer past two rotating circular cylinders in a side-by-side arrangement at a various range of absolute rotational speeds (|α| ? 2) for four different gap spacings (g1) of 3, 1.5, 0.7 and 0.2 at Reynolds number of 100, and a fixed Prandtl numbers of 0.7 (air). As |α| increases, the thermal field became stabilized and eventually steady beyond the critical rotational speed depending on the gap spacing. In general, as |α| increases, because the vertical motion of flow in the region of gap is strongly inhibited, the inner isotherms are early merged and shorter than the outer isotherms in the free-stream sides elongating further downstream. As |α| increases, because the rotating fluid near the cylinders surrounded much space where the steady conduction mode is predominant to the heat transfer, the behavior of the time- and surface-averaged Nusselt number has the decaying pattern with increasing |α| for all gap spacings considered in this study.