Unsteady Natural Convection Heat Transfer Research Articles

Statistical and numerical analysis of magnetic field effects on laminar natural convection heat transfer of nanofluid in a hexagonal cavity

This paper presents a statistical and numerical investigation that examines the optimization and sensitivity analysis of the unsteady laminar natural convective heat transfer flow of Fe3O4-water nanofluid in a hexagonal cavity considering the impacts of a sloping magnetic field in one-component nanofluid model. The inclined walls of the cavity are maintained at a constantly low temperature, while the bottom wall is uniformly heated. The upper wall, however, is regarded as adiabatic. The nanofluid thermal conductivity model incorporates the impact of Brownian motion. The Galerkin weighted residual finite element method has been employed to solve the governing dimensionless equations. The results are provided regarding the average Nu, streamlines, and isotherms. The study uses response surface methodology to analyze the sensitivity of parameters such as the Ha, Ra, and nanoparticle volume percentage. Using a response surface policy allows for optimizing the process and identifying the most favorable circumstances to achieve the maximum thermal transfer rate. The flow pattern of the nanofluid is significantly affected by the magnetic field and its alignment. The numerical results indicate a significant rise in the average Nu as the nanoparticle volume percentage, magnetic field inclination angle, nanoparticle type factor, and Ra increase. Conversely, the Hartmann number and the nanoparticle's diameter have contrasting effects. When considering Brownian motion, the average Nu grows by 225.89 % for Ra = 106 with ϕ = 0.03 and 25.28 % for the other case. The optimal condition for heat transfer occurs when Ra = 106, Ha = 4, and ϕ =0.03 while keeping the other parameters constant.

Time-periodic natural convection in a pentagonal house with pitched roof during one day

A numerical investigation of unsteady natural convective flow and heat transfer in a pentagonal house is performed. We set a sinusoidal periodic heat flux boundary condition for the pitched roof. Local radial basis function method and Fourier spectral method are adopted to solve the governing equations. The Rayleigh number varies from 103 to 105, the period of the roof heat flux ranges from 10 to 1,000, and the amplitude is set as 0.1, 0.3, and 0.5, respectively. It is found that all the control parameters significantly impact the fluid flow and heat transfer. The temperature and flow fields exhibit periodic behavior due to the sinusoidal heat source. The increasing Rayleigh number leads to a larger periodic average Nusselt number of the top and right walls and a smaller value of the bottom wall. Moreover, an obvious hysteresis phenomenon of heat transfer occurs especially for high Rayleigh number and large period.

Natural convection flow and heat transfer of generalized Maxwell fluid with distributed order time fractional derivatives embedded in the porous medium

<p>Numerical simulation was performed for unsteady natural convection flow and heat transfer in a porous medium using the generalized Maxwell model and fractional Darcy's law with distributed order time fractional derivatives. The finite volume method combined with the fractional <italic>L1</italic> scheme was used to solve strongly coupled governing equations with nonlinear fractional convection terms. Numerical solutions were validated via grid independence tests and comparisons with special exact solutions. The effects of porosity, Darcy number, and relaxation time parameters on transport fields are presented. The results illustrate that porosity and permeability have opposite influences on temperature and velocity profiles. Moreover, the relaxation time parameters have remarkable effects on velocity profiles, and the variations possess significant differences.</p>

Study on unsteady natural convection heat transfer of crude oil storage tank based on fractional-order Maxwell model

When considering the natural flow processes in crude oil in static storage tanks, researchers usually treat the nonlinear heat and mass transfer and flow using integer-order models. However, this ignores the nonlinear convection and heat-transfer phenomena that occur; these are dependent on time and space due to the viscoelasticity of crude oil, which is a non-Newtonian fluid. In this work, we examined the time and space dependence of the nonlinear natural convective heat-transfer processes in crude-oil storage tanks. Fractional-order Maxwell and Cattaneo–Vernotte models were applied to the traditional momentum and temperature equations considering the Boussinesq approximation. Based on the L1 discrete format, the fractional-order pressure-correction equation was derived, and an associated solver, CaputoTemporalFractionalFoam (CTfracFoam), was developed to simulate the convection processes in static crude-oil storage tanks. The results show that when α equals 0.1, the maximum velocity in monitoring area 2 is 0.1404 m/s, and the velocity gradually increases as α increases with a maximum value of 1.1468 m/s at 0.9. When the β is 0.1 and 0.2, the temperature changes in the transition region are −5.204 and −0.165 °C, respectively, while when β is greater than 0.2, the temperature changes are all positive values with a maximum value of 1.924 °C at 0.9. Compared with integer-order Fourier heat-transfer and Newtonian fluid-flow models, the developed fractional-order model can describe the natural convection phenomena of non-Newtonian fluids such as crude oil more flexible and accurately.

Natural Convection in a Circular Enclosure with Four Cylinders under Magnetic Field: Application to Heat Exchanger

This paper documents the 2D numerical study of magnetohydrodynamic unsteady natural convective heat transfer in a circular enclosure with four heating cylinders in both the horizontal and the vertical mid-plane. The fluid is an incompressible Newtonian fluid. The main transport equations based on the conservation of mass, momentum, and energy are calculated and solved using a finite element numerical solver with the following parameter ranges: dimensionless distance between cylinders S = 0.05–0.29, Rayleigh number Ra=103–106, and Hartmann number for Ha = 0–120. COMSOL Multiphysics, a numerical simulation program, was used to solve the governing equations. It was demonstrated that for lower Ra values, heat transfer through an applied magnetic field is unaffected for a specific S value because the mechanism of transport is diffusion, whereas for larger Ra, there is a complex interaction among magnetic field and physical thermal properties. The features of the heat transfer rate are determined by the interaction. The Nusselt number virtually stays constant as Ha rises at smaller Ra. However, at high Ra, the Nusselt number initially declines with Ha and thereafter essentially stays constant, and at high Ra values, the switch from conduction to convective heat transfer takes place. Additionally, Nu rises slightly with S at increasing Ra.

Numerical investigation of mixed convection from rectangular cylinders subjected to upper cross flow

Unsteady combined natural and forced convection heat transfer from a rectangular cylinder subjected to upward cross flow is investigated numerically. The working fluids are air (Pr = 0.7) and water (Pr = 7), and the flow is laminar. The governing flow and energy equations are solved using a fractional step finite-difference scheme. The effects of the cylinder aspect ratio (a = L/D), Reynolds and Richardson numbers on the flow and heat transfer characteristics are investigated. Numerical simulations were carried out for the cylinders with aspect ratios of a = 0.5, 1, and 2, while the Richardson and Reynolds numbers varied between 0 to 10, and 100 to 200, respectively. The mean drag, mean rms lift coefficients, as well as the Strouhal number and the mean Nusselt number were computed for each simulation to determine the quantitative effects on flow and heat transfer. Steady flow is observed for Pr = 0.7, Ri = 0.5, and a = 0.5 or for Re ≥ 150 and Ri ≥ 1. For Ri = 10 and Re = 200, the flow becomes unsteady in the downstream region and trigger vortex street formation for a = 0.5, 1, and 2. Decreasing the aspect ratio, as well as increasing Reynolds number, increases the heat transfer from the cylinder. The rms lift coefficient decreases sharply at Ri < 1 for Pr = 0.7, Ri < 2 for Pr = 7 due to vortex breakdown. Further increase in the Richardson leads to a slight increase in rms lift coefficient except for Re = 200 where the sharp increase is observed due to triggered vortex formation again. For air, the increase in the mean Nusselt number in Ri = 10 case with respect to the forced convection case (Ri = 0) was 54–65% and 80–98%, respectively, for a = 0.5 and 2, while these values for water were realized as 50–68% and 53–63%, respectively. Using the computed data and nonlinear regression, the mean Nusselt number and the drag coefficients were developed.

Natural convection in an enclosure with a pair of cylinders under magnetic field

This two-dimensional numerical study investigates magnetohydrodynamic unsteady natural convection heat transfer inside an enclosure with two heated circular cylinders within it in the horizontal mid-plane. The fluid is incompressible and Newtonian. The governing transport equations based on the conservations of mass, momentum and energy are computationally solved using a finite element based numerical solver for the following range of parameters: dimensionless spacing between the cylinders S = 0.1–0.5, Rayleigh number Ra = 103–106 and Hartmann number Ha = 0–120. The results show that for lower values of Ra the heat transfer remains unaltered by the imposed magnetic field for a specific value of S as the transport mechanism is diffusion, while, for higher Ra, there is a complex interaction between the magnetic field and the physico-thermal properties that determines the heat transfer rate. For lower Ra the time-averaged Nusselt number (Nut) remains almost unaltered with Ha. However, at higher Ra, Nut initially decreases with Ha and then remains approximately constant and the transition between conductive and convective heat transfer occurs at higher Ra values. Moreover, for higher Ra, Nut decreases somewhat initially with the increase of S from 0.1 to 0.2 and thereafter, Nut slightly increases with S.

Natural convection heat transfer within a square porous enclosure with four heated cylinders

The present numerical study investigates unsteady natural convection heat transfer within a square-shaped porous confinement with four heated cylinders. Simulations are performed for different cylinder spacings by arranging the cylinders along the enclosure diagonals in a rectangular array for different Darcy numbers (Da) and Rayleigh numbers (Ra). The positions of cylinders within the enclosure are limited to 0.3 ≤ S (= sH /L = sV /L) ≤ 0.6 and for each rectangular array computations were performed for 103 ≤ Ra ≤ 106 and 10−4 ≤ Da ≤ 10−2. Results reveal that conduction mode heat transfer dominates within the enclosure at Ra ≤ 104 irrespective of Da, whereas for Da = 10−3, 10−2, convective heat transfer prevails for high Ra (105, 106) values. With the increase in Ra up to Ra ≥ 105, the temperature and flow fields lose symmetry about the vertical centerline of the enclosure. For Ra = 106 and Da = 10−2 the change in time-averaged Nusselt number Nut with cylinder spacing is insignificant for all cylinders, whereas for Da = 10−3Nut at the lower cylinders decreases slightly between S = 0.3 and 0.4 and then increases slightly up to S = 0.6.

Effect of Fin Number and Position on Non-linear Characteristics of Natural Convection Heat Transfer in Internally Finned Horizontal Annulus

Detailed numerical calculations are performed for investigating the effect of fin number and position on unsteady natural convection heat transfer in internally finned horizontal annulus. The SIMPLER algorithm with Quick scheme is applied for solving the Navier Stokes equations of flow and heat transfer. The results show that the heat transfer rate in annulus with fins increases with the increasing numbers of fin and Rayleigh numbers. For Ra = 2 × 105, the effect of numbers of fins and fins position at the bottom part on the unsteady solutions can be neglected, because the self-oscillation phenomenon is mainly affected by natural convection at the upper part of annulus. Although the fin positions cannot increase heat transfer rate significantly in the case of four fins, the self-oscillated solutions can be suppressed by altering fins position.

Unsteady natural convection boundary layer flow and heat transfer past a vertical flat plate with novel constitution models

Seeking proper and reasonable constitutive relations to study the characteristics of flow and heat transfer of viscoelastic fluid is a hot topic in recent years. In this work, a new distributed order time fractional constitution model is put forward to analyse the unsteady natural convection boundary layer flow and heat transfer, in which the magnetic field effect is considered. The mid-point quadrature method is applied to approach the distributed order integrals and the L1-formula is employed to discrete the time fractional derivatives. The influences of different involved parameters on the velocity and temperature distributions and the comparisons of the distributions with different constitution models are presented by graphical illustrations and discussed in detail.

Periodic unsteady natural convection in square enclosure induced by inner circular cylinder with different vertical locations

The periodic unsteady natural convection flow and heat transfer in a square enclosure containing a heated circular cylinder with different vertical locations is numerically studied. The temperature of the enclosure keeps lower constant while the temperature of the inner circular cylinder oscillates periodically with time at higher averaged value, the natural convection in the enclosure is driven by the temperature difference. The two-dimensional natural convection is simulated with high accuracy temporal spectral method and local radial basis functions method at Rayleigh number Ra = 105. The location of inner circular cylinder varies from −0.25 to 0.25 vertically, the temperature pulsating amplitudes are a = 0.5, 1.0 and 1.5 and the temperature pulsating period ranges from 0.01 to 100. Numerical results show that the heat transfer is strongly dependent on the vertical location and the pulsating temperature of inner cylinder. The heat transfer is enhanced generally for the time-periodic unsteady natural convection comparing with its steady state natural convection, and the local maximum heat transfer rate is observed for some locations. Moreover, the phenomenon of backward heat transfer is discussed and the quantity of back heat transfer rate is presented. Finally, the influence of the vertical locations and pulsating temperature on the unsteady fluid flow and heat transfer are discussed and analyzed.

SORET AND MEMORY EFFECTS ON UNSTEADY MHD NATURAL CONVECTION HEAT AND MASS TRANSFER FLOW IN A POROUS MEDIUM WITH NEWTONIAN HEATING

SORET AND MEMORY EFFECTS ON UNSTEADY MHD NATURAL CONVECTION HEAT AND MASS TRANSFER FLOW IN A POROUS MEDIUM WITH NEWTONIAN HEATING

Soret and Dufour Effects on Unsteady Free Convection Fluid Flow in the Presence of Hall Current and Heat Flux

Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.

Numerical modeling of fractional viscoelastic non-Newtonian fluids over a backward facing step – Buoyancy driven flow and heat transfer

The unsteady flow and natural convection heat transfer of fractional Maxwell viscoelastic fluid over sudden expansion geometry such as vertical backward facing step is studied. The time–space fractional derivatives are calculated based on Caputo fractional derivative. The nonlinear governing equations are solved using finite difference method mixed with a L-1 algorithm. The step, upstream and downstream walls were set at a constant temperature. The range of step length is 0≤S≤0.5 and dimensionless temperature is 0.25≤θw≤1. The effects of velocity and temperature fractional derivatives (αand β) and various physical parameters, such as step length, dimensionless temperature, on Nusselt number, friction coefficient, profile of velocity and temperature, are investigated numerically. The results reveal that the fractional derivative parameters, the variation of wall temperature and step length have significant effects on the rate of heat transfer, the friction coefficient, the velocity and temperature of backward facing step. The average of Nusselt number variation increases with increasing of β and decreases of α parameters. The results show that the velocity and thermal boundary layer of the non-Newtonian fluid (ordinary Maxwell) is higher than Newtonian fluid. Also, the Nusselt number for the ordinary Maxwell fluid flow is greater than the Newtonian fluid flow. With the increase of the step length of backward facing step, the average Nusselt number, friction coefficient, velocity boundary layer, and temperature boundary layer increases. The obtained results can improve significantly the performance of the systems design that operate with the non-Newtonian fluids.

Numerical Analysis of Unsteady Natural Convection Flow and Heat Transfer in the Existence of Lorentz Force in Suddenly Expanded Cavity Using Open FOAM

The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity. The Lorentz force based magnetohydrodynamics (MHD) solver using electric potential formulation coupled with the energy equation by the means of Boussinesq approximation is developed in the open-source CFD tool OpenFOAM. The unsteady flow is generated by the buoyancy force keeping the Rayleigh number (Ra) at 109, at the fixed Prandtl number (Pr) of 0.71. The effects of the magnetic field on the flow and heat transfer are explained for various orientations of magnetic field (Bx, B45, and By) in terms of Hartmann number (Ha=0, 50, 100, 300 and 500). The increase in the magnetic field increases the strength of the Lorentz force, which regulates the flow pattern and suppresses down the unsteady nature of flow and heat transfer into the steady-state. It is perceived that the average Nusselt number decreases as the intensity of Bx and B45 magnetic field increases. However, for By magnetic field the average Nusselt number increases up to Ha of 100 as compared to the non-MHD case (Ha=0). The distribution of Lorentz force in the domain plays a significant role in the governing of the fluid flow and heat transfer.

Heat transfer augmentation in a diamond shaped enclosure utilizing CNT-water Nanofluid

A numerical analysis has been investigated for unsteady natural convection heat transfer problem in diamond shaped cavity. Carbon nanotube (CNT)-water nanofluid is used to analyze the heat transfer and compared with the pure water as working fluid. The lower right wall is kept at heated surface with constant heat flux and upper left wall is kept cold. Both the bottom left and upper right wall are kept adiabatic. The considered physical problem is characterized mathematically by a set of governing equations along with the corresponding boundary conditions. Galerkin weighted residual method of finite element analysis is used to solve the governing equations. Calculations are done for pertinent parameters such as the solid volume fraction (ϕ = 0.0–0.12) and Rayleigh number (Ra = 104–108) at dimensionless times (τ = 0.01 and 1.0) and fixed Pr = 6.2. Obtained results are presented in terms of average Nusselt number and maximum fluid temperature, streamlines and isotherms in graphs, charts and related contours. It has been observed that increase of Rayleigh number and solid volume fraction enhance the heat transfer rate and reduce the maximum fluid temperature. In this investigation the highest amount of overall heat transfer reaches up to 115%.

Effects of Some Flow Parameters on Unsteady MHD Fluid Flow Past a Moving Vertical Plate Embedded in Porous Medium in the Presence of Hall Current and Rotating System

This paper is on the numerical study of the effects of some flow parameters like Hall current, rotation, thermal diffusion (Soret) and diffusion thermo (Dufour) on unsteady magnetohydrodynamic natural convective heat and mass transfer of a viscous, rotating, electrically conducting and incompressible fluid flow past an impulsively moving vertical plate embedded in porous medium. The fundamental governing dimensionless coupled boundary layer partial differential equations are solved by the method of lines (MOL). Computations are then performed to determine the effects of the governing flow parameters. The results show that an increase in Soret number, Dufour number and Hall current parameter, causes an increase in the primary and secondary velocities of the fluid flow. As rotating parameter increases, the primary velocity of the flow decreases. Similarly, as Dufour and Soret numbers increase, the temperature and concentration profiles of the fluid flow increase. The effects of the flow parameters on primary and secondary velocity, temperature and concentration fields for externally cooling of the plate are shown graphically.

Unsteady MHD natural convective boundary layer flow and heat transfer over a truncated cone in the presence of pressure work

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Influence of conjugate convective heat transfer on temperature fields in thin walls that organize liquid layers of various orientations

Numerical studies of unsteady conjugate natural convective heat transfer in the model of a thin-walled fuel tank are carried out in the conjugate formulation. The fields of temperature in liquid and in solid walls of the tank are calculated. The evolution of convective flows and temperature fields after a sudden supply of heat to the base of the tank is investigated. Flat layers of liquid enclosed between flat walls of different orientations with inclination angles of 0, 30, 45, 60 and 90 degrees are considered. With the angle of inclination of 0 degrees the outer surface of the side walls is insulated. The outer surface of the lower wall heats up suddenly, the outer surface of the upper wall is isothermally cold. The system of equations of thermogravitation convection in the Boussinesq approximation in dimensionless form, written in terms of temperature, vector potential of the velocity field and velocity vortex, is solved. It is shown that an inhomogeneous temperature field is formed inside the solid walls of the finite thermal conductivity. The thermal conductivity of walls and conditions at the upper boundary of the liquid layer affect significantly the spatial form of convective fuel flows in fuel tanks and laws of conjugated natural convective heat exchange.

Unsteady MHD Natural Convection Flow of Nanofluid in a Cavity Containing Adiabatic Obstacle with Heat Corners

Unsteady natural convection heat transfer of nanofluid within cavities with local heaters occurs in several engineering applications. Therefore, investigation of nanofluid flow and heat transfer processes in such systems has a considerable value for evolution of industry. In the current investigation, unsteady MHD natural convection flow of Cu-water nanofluid and heat transfer behavior in square cavity containing a centered adiabatic square block. The mathematical formulation part for present problem is presented in succeeding section. It has been found the size of the adiabatic obstacle influences the behavior of the nanofluid and conduction becomes dominant when size aspect ratio increases to 0.5. It is also noticed that angle of the applied magnetic field can maximize(minimum)the rate of heat transfer if applied in the stream-wise (normal) direction. The novelty of the present work is to consider cavity containing a centered adiabatic square block as well as unsteady effects in the natural convection of nanofluids.