Transient Free Convection Heat Research Articles

A transient free convection heat transfer study in an oil tank with vertical and horizontal arrangements of heating coils

A transient free convection heat transfer study in an oil tank with vertical and horizontal arrangements of heating coils

MHD influence on convective heat transfer in a semi-circular cavity using nonhomogeneous nanofluid model

A transient free convective heat transfer in a semicircular vicinity occupied with distinct nanofluids has been examined numerically with a periodic magnetic field. The bottom surface of the cavity is heated non-uniformly as parabolic shape whereas the circular surface is kept at constant cold temperature. In the numerical simulation, ZnO, Fe 3 O 4 , Co, Al 2 O 3 , and Ag have been used as nanoparticles and water and kerosene as the base fluid to investigate the flow regimes and thermal fields developed inside the computed vicinity. Effects of various governing parameters are revealed with depictions of isotherms, streamlines and iso-concentrations. The results show that there is found less computational time to reach a steady-state solution for a higher Rayleigh number and the effects of the periodic magnetic field magnifies the strength of the vortices turning in the cavity. The average heat transfer rate at the bottom surface is uppermost for cobalt-kerosene nanofluid compared to other nine sorts of nanofluids. The results also reveal that the periodic magnetic field as well as the Brownian motion have substantial impacts on the heat transfer rate.

Hall effect on MHD transient free convection flow of chemically reactive Casson fluid with heat source/sink past an infinite vertical cylinder

This article presents an analytical investigation of the effect of Hall current, magnetic field, and chemical reaction on an unsteady MHD transient free convection heat and mass transfer flow of viscous incompressible, electrically conducting Casson fluid past an infinite vertical cylinder subject to heat source and sink. Closed-form solutions are obtained by employing Laplace transform and inverted using Mellin-Fourier integral and presented them in terms of Bessel functions and modified Bessel functions. To get an insight into the model, we have depicted the graphs of velocity, temperature and concentration profiles for various values of the pertinent flow parameters. The values of Sherwood number, Nusselt number, and skin friction are calculated and presented in the tabular form. Further, we have also considered a special case and investigate the velocity profiles of the Newtonian fluid for both heat source and sink as the Casson parameter α → ∞. From the investigation, it is perceived that with an increase in the values of chemical reaction parameters the species concentration and the velocity of the Casson fluid get reduced while its reverse trend has been observed on Sherwood number and skin friction. With an increase in the Prandtl number the fluid temperature decreases whereas, the Nusselt number increases. A crossing over point is observed in velocity distribution for the Hall current parameter. This fluid flow model will be applicable in geophysics, mining industry, chemical and biomedical engineering such as underground energy system, electromagnetic material production, and automotive fuel level indication, etc.

Transient free convection heat and mass transfer of Casson nanofluid over a vertical porous plate subjected to magnetic field and thermal radiation

In this present study, the transient magnetohydrodynamics free convection heat and mass transfer of Casson nanofluid past an isothermal vertical flat plate embedded in a porous media under the influence of thermal radiation is studied. The governing systems of nonlinear partial differential equations of the flow, heat and mass transfer processes are solved using implicit finite difference scheme of Crank-Nicolson type. The numerical solutions are used to carry out parametric studies. The temperature as well as the concentration of the fluid increase as the Casson fluid and radiation parameters as well as Prandtl and Schmidt numbers increase. The increase in the Grashof number, radiation, buoyancy ratio and flow medium porosity parameters causes the velocity of the fluid to increase. However, the Casson fluid parameter, buoyancy ratio parameter, the Hartmann (magnetic field parameter), Schmidt and Prandtl numbers decrease as the velocity of the flow increases. The time to reach the steady state concentration, the transient velocity, Nusselt number and the local skin-friction decrease as the buoyancy ratio parameter and Schmidt number increase. Also, the steady-state temperature and velocity decrease as the buoyancy ratio parameter and Schmidt number increase. Also, the local skin friction, Nusselt and Sherwood numbers decrease as the Schmidt number increases. However, the local Nusselt number increases as the buoyancy ratio parameter increases. It was established that near the leading edge of the plate), the local Nusselt number is not affected by both buoyancy ratio parameter and Schmidt number. It could be stated that the present study will enhance the understanding of transient free convection flow problems under the influence of thermal radiation and mass transfer as applied in various engineering processes.

Transient free convection heat transfer in a section-triangular prismatic enclosure with different aspect ratios

Free convection studies in a section-triangular prismatic enclosure with different aspect ratios (depth-width ratios, A) is conducted using three-dimensional numerical modeling approach. The Rayleigh number (Ra) covers a broad range from 100 to 107. Transient free convection is characterized under top cooled and bottom heated boundary conditions. The flow structure of transverse rolls and longitudinal rolls is described. The critical Rayleigh numbers for the transition of the flow from driven by the baroclinic to Rayleigh-Bénard instability and from a steady to an unsteady state have been obtained for different aspect ratios. Free convection in the section-triangular prismatic enclosure could be divided into three regimes, which are presented in a Ra-A space. The quantitative relationship between heat transfer and the aspect ratio as well as the Rayleigh number has been obtained numerically.

Effects of Radiation and Viscous Dissipation on Transient Free Convection Heat Transfer Flow Past a Hot Vertical Surface in Porous Media

The radiation effects on unsteady transient free convection flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity taking viscous dissipation onto account has been carried out. Thermal radiation effects are simulated via a radiation-conduction parameter (),rK based on the Rossseland diffusion approximation. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalzed using appropriate transformations and then solved subject to physically realistic boundary conditions using the Ritz finite element method. The computed numerical results for velocity(),u temperature(),θ shear stress function()τ and wall temperature gradient function()Nu are presented through the graphs and tables for air (0.71)rP= and water (7.00).rP= It has been found that increasing thermal radiation parameter ()rKcauses a considerable increase in the flow velocity .u Temperature θ is significantly increased within the boundary layer with a rise in.rK The velocity is found to decrease with an increase in inverse permeability parameter ()pK and increases with increase in the Grashof number ()rG and Eckert number ().

Transient free convective heat transfer in nanoliquid-saturated porous square cavity with a concentric solid insert and sinusoidal boundary condition

In this study, we use the finite-difference method to numerically investigate the problem of transient free convective heat transfer in a nanoliquid-saturated porous square cavity with a sinusoidal boundary condition. The left vertical wall of the cavity is maintained at a constant temperature and the right wall is heated sinusoidally. The horizontal insulated walls allow no heat transfer to the surrounding. To regulate the heat transfer, we insert a solid square at the centre of the cavity in such a way that there is symmetry in the flow configuration. We use the Darcy law along with the Boussinesq approximation for the flow, and for the investigation, we employ water-based nanoliquids with Cu, Al2O3 or TiO2 nanoparticles. We obtain the results of this study for various parameters such as Rayleigh number, periodicity parameter, nanoparticle volume fraction, thermal conductivity ratio, length of the inner solid, modified conductivity ratio, and dimensionless time. We explain the different influences on the parameter contours of streamlines, isotherms, local Nusselt number and weighted-average heat transfer in unsteady and steady regimes based on the thermal conductivities of nanoparticles, water and porous media. The results show that the overall heat transfer is significantly increased with the relatively non-uniform heating. Further, we show that convective heat transfer is inhibited by the presence of the solid insert. The results have the potential for application in heat-removal and heat-storage liquid-saturated porous systems.

New benchmark solutions for transient natural convection in partially porous annuli

Purpose – The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro-ri. Moreover, several Darcy numbers have been considered. Design/methodology/approach – A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement. Findings – For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number. Research limitations/implications – A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems. Practical implications – The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility. Originality/value – This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

Conjugate Transient Free Convective Heat Transfer from a Vertical Slender Hollow Cylinder with Heat Generation Effect

Numerical analysis is performed to study the conjugate heat transfer and heat generation effects on the tran- sient free convective boundary layer flow over a vertical slender hollow circular cylinder with the inner surface at a con- stant temperature. A set of non-dimensional governing equations namely, the continuity, momentum and energy equations is derived and these equations are unsteady non-linear and coupled. As there is no analytical or direct numerical method available to solve these equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The dis- cretized equations are solved using the tridiagonal algorithm. Numerical results for the transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is ob- served that the time required to reach the steady-state increases as the conjugate-conduction parameter or heat generation parameter increases.

Diffusion-Thermo Effects on Free Convective Heat and Mass Transfer Flow in a Vertical Channel With Symmetric Boundary Conditions

This article investigates the influence of diffusion-thermo effect on transient free convective heat and mass transfer flow in a channel bounded by two infinite vertical parallel plates. Fully developed laminar flow is considered when the boundaries are subjected to symmetric concentration and thermal input. The Dufour effect is taken into consideration. The velocity, temperature, and concentration profiles are obtained analytically using the Laplace transforms technique and used to compute the shear stress, Nusselt number, and mass flux. During the course of computation, it was found that transient solution at large time coincides with steady-state solution derived separately. Diffusion-thermo (Dufour effect) is observed to create an anomalous situation in temperature and velocity profiles for small Prandtl numbers. There is also flow reversal for a small Dufour number and negative values of the sustentation parameter (N). At steady-state, there is neither heat nor mass transfer between the fluid and the plates.

Theoretical Analysis of Radiative Effects on Transient Free Convection Heat Transfer past a Hot Vertical Surface in Porous Media

The purpose of the present investigation deals with the unsteady free convective flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalized using appropriate transformations and then solved subject to physically realistic boundary conditions using the Laplace transform technique. Thermal radiation effects are simulated via a radiation-conduction parameter, Kr, based on the Rosseland diffusion approximation. The influence of Grashof (free convection) number, radiation-conduction parameter (Kr), inverse permeability parameter (Kp) and dimensionless time (t) are studied graphically. We observe that increasing thermal radiation parameter causes a noticeable increase in the flow velocity, u. Temperature, θ, is significantly increased within the boundary layer with a rise in Kr since the latter represents the relative contribution of thermal radiation heat transfer to thermal conduction heat transfer. Increased radiation therefore augments heat transfer, heats the fluid and increases the thickness of the momentum and thermal boundary layers. Velocity is found to decrease with an increase in Kp (inverse permeability parameter) as are shear stress function ( ∂u/∂y | y=0) magnitudes owing to greater resistance of the porous medium for lower permeabilities, which decelerate the flow. An increase in Kr however boosts the shear stress function magnitudes i.e. serves to accelerate the flow. Temperature gradient, ∂θ/∂y | y=0 is also positively affected by an increase in thermal radiation (Kr) and with time. The present study has applications in geological convection, forest fire propagation, glass heat treatment processes at high temperature, metallurgical processing etc.

Experimental estimation of the transient free convection heat transfer coefficient on a vertical flat plate in air

Transient heat convection on a vertical plate has been interpreted both theoretically and experimentally, in terms of a variable heat transfer coefficient, by several authors. Few results concern the case were air is the fluid. Joule heating of a very thin vertical graphite foil has been tested experimentally here. Two different methods of inversion have been studied for estimating the local or global transfer coefficient, starting from infrared camera measurements. The second method has been able to provide the convective contribution to the measured global transfer coefficient. Experimental results with different levels of heating show that the early transfer coefficient decrease proportionally (in time t) to t −1, and not to t −1/2 as the early times conduction theory would anticipate. Other effects than those already presented in the literature remain to be investigated, in order to explain the discrepancy of this theory for air. Relaxation experiments show that enhancement of the wall/air exchange by a mastering of the transient heating of the whole wall seems to be quite difficult to obtain

Parametric study of transient free convection heat transfer

In several situationss the control of a surface temperature is ensured by convective exchange; for examples for steel metallurgy or electronic components. And among the three types of convective exchanges, forced convection is often used because of its efficiency. A contrario natural convection has the advantage to be free in terms of energy expense but generates low heat transfer coefficient. Thus it will be interesting to improve free convection heat transfer in order to substitute for the expensive forced convection. Laminar free convection problem on a vertical wall has been plentifully investigated considering a wall heat flux density constant [1–3] or varying sinusoidally [4]. But only two studies deal with the influence of the different parameters of the problem. Thereby Yang et al. [4] evaluated the influence of the amplitude and of the frequencies of the sinusoid whereas the Vargas and Bejan [5] study is based on the optimisation of heat transfer. This last investigation considers a fluid (water) initially at rest before being suddenly put in motion thanks to a periodical heat flux density applied to the wall. Scale analysis, numerical and experimental studies have been carried out and show that the heat transfer is optimised when the heating and cooling (wall adiabatic) periods are equal. In this paper the wall is subjected to a uniform heat flux density until the steady states (thermal and dynamical) are reached. Then a periodical heat flux density which varies from qw to 0 (adiabatic wall) is applied to the surface in order to improve the free convection heat transfer. A parametric study is then carried out in order to optimise the heat transfer. 2. Modelling

BEM SOLUTION TO TRANSIENT FREE CONVECTIVE HEAT TRANSFER IN A VISCOUS, ELECTRICALLY CONDUCTING, AND HEAT GENERATING FLUID

The nonlinear partial differential equations for the transient free convective heat transfer in a viscous, electrically conducting, and heat-generating fluid past a vertical porous plate in the presence of free stream oscillations are solved by the boundary element method (BEM). Time-dependent fundamental solutions are employed in a time marching scheme to resolve the field variables. Numerical results are compared with previously reported analytical solutions in order to validate the developed BEM algorithm. These previous studies reported results for simpler versions of our problem, in which the convective effects in the momentum and energy equations were neglected in order to obtain analytical numerical solutions. Our BEM results are shown to be in close agreement with the reported data. The effects of convection currents, the temperature-dependent heat sources (or sinks), the magnetic currents, and the viscous dissipation on the flow and heat transfer characteristics are assessed in a parametric study...

Transient free convective heat transfer from co-rotating concentric disks

Experimental investigations are carried out for the determination of transient heat transfer coefficients between parallel co-rotating and concentrically stationary disks with internal heat generation. The experimental model simulates a typical induction motor with unequal losses in the stator and rotor at the start-up condition. The data collected cover a range of Taylor numbers for various heat inputs. Quantitative assessment is made for the increase in heat transfer with speed of rotation under free convective ambient conditions. Temperatures along the axial, radial and tangential directions are measured. Unsteady heat transfer coefficients to the ambient air are evaluated in the radially diverging section. The results of the corresponding R-C network are obtained on a digital computer. The predicted values of temperatures at the corresponding nodal points are compared with the measured values and found to be in good agreement. The results are potentially very useful in the thermal design of electrical machines, more specifically, radially ventilated induction motors.

On Free Transient Convective Heat Transfer Between Cable and its Surrounding Pipe or Duct Wall

The transient free convection heat transfer problem between cable and its enclosure is solved using the method of finite difference. As the transient time is found to be very small compared with a typical operation time, the steady state Nusselt number Can be used in lieu of the transient Nusselt number. Our numerical results are summarized in Fig. 9 which consists of three Nusselt number vs. Grashof number plots with diameter ratio as parameter and serves as a design chart for practical free convective heat transfer calculations.

Transient Free Convection from a Suddenly Heated Horizontal Wire

Experimental data are presented for the transient free convective heat transfer from a horizontal wire in air subjected to a step change in heat rate. An unbalanced Wheatstone bridge is described which allows simultaneous observation of wire temperature and heat rate, under transient as well as steady-state conditions. An “overshoot” of the steady-state is shown to occur in the transient decay of the Nusselt number, and the occurrence, magnitude, and duration of this phenomenon is shown to depend upon the Rayleigh number. Simple stability theory is shown to explain the delay in the convective process which is associated with the overshoot in heat transfer. Steady-state data are also presented and are shown to agree well with proposed low Rayleigh number correlations.

An experimental study of transient free-convection heat transfer with mercury in a vertical rectangular channel

An experimental study is presented of the transient and steady-state natural convection heat transfer in mercury following a step change in uniform heat flux of the vertical rectangular channel wall. The fluid was initially stagnant and at a uniform temperature. Temperature distributions were measured during the transient and at steady-state conditions. Heat transfer characteristics of the system were determined from these measurements.