Interfacial instabilities in plane Poiseuille flow of two stratified viscoelastic fluids with heat transfer. Part 1. Evolution equation and stability analysis

1995 ◽  
Vol 299 ◽  
pp. 241-265 ◽  
Author(s):  
Sang W. Joo
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Stability Analysis ◽  
Evolution Equation ◽  
Vertical Channel ◽  
Viscoelastic Fluids ◽  
Lubrication Approximation ◽  
Plane Poiseuille Flow ◽  
Interfacial Instabilities ◽  
Different Temperatures

An evolution equation is derived that describes the nonlinear development of the interface between two viscoelastic fluids flowing, under the action of imposed pressure gradient and gravity, in a vertical channel. The channel walls are kept at different temperatures, resulting in heat transfer across the layers. The equation, based on the lubrication approximation, models the effects of stratifications in density, viscosity, elasticity, shear thinning, and thermal conductivity. It also describes the capillary and thermocapillary effects, as well as the sensitivity of viscosities to temperature. Linear-stability analysis is performed based on the evolution equation to understand the competing effects of viscous, elastic, and Marangoni instabilities. Particular attention is paid to the active control of the interfacial instabilities through the thermocapillarity.

Onset of Natural Convection from a Suddenly Heated Horizontal Cylinder

1980 ◽  
Vol 102 (4) ◽  
pp. 636-639 ◽  
Author(s):  
J. R. Parsons ◽  
J. C. Mulligan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Stability ◽  
Heat Capacity ◽  
Natural Convection ◽  
Stability Analysis ◽  
Horizontal Cylinder ◽  
Finite Cylinder ◽  
Global Motion ◽  
Experimental Apparatus

A study of the onset of transient natural convection from a suddenly heated, horizontal cylinder of finite diameter is presented. The termination of the initial conductive and “locally” conuectiue heat transfer regime which precedes the onset of global natural convection is treated as a thermal stability phenomenon. An analysis is presented wherein the effects of finite cylinder diameter, cylinder heat capacity, and cylinder thermal conductivity are included in calculations of the convective delay time. A simple experimental apparatus is described and data presented. The thermal stability analysis is confirmed experimentally and data is presented which indicates localized natural convection prior to global motion.

Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid

2016 ◽  
Vol 26 (5) ◽  
pp. 1460-1485 ◽  
Author(s):  
B Mahanthesh ◽  
B J Gireesha ◽  
R S R Gorla
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Mixed Convection ◽  
Three Dimensional ◽  
Vertical Channel ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow ◽  
Rotating Channel

Purpose – The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid. Design/methodology/approach – Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed. Findings – Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer. Originality/value – Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated.

scholarly journals Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. M. Hamza ◽  
I. G. Usman ◽  
A. Sule
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Approximate Solutions ◽  
Variable Thermal Conductivity ◽  
Convection Flow

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

scholarly journals Study of Thermal Performance of Closed Loop Pulsating Heat Pipe using Computational Fluid Dynamics

2021 ◽  
Vol 9 (9) ◽  
pp. 1384-1388
Author(s):  
K. C. Giri
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Heat Pipe ◽  
Closed Loop ◽  
Filling Ratio ◽  
Pulsating Heat Pipe ◽  
Heat Transfer Characteristics ◽  
Different Temperatures

Abstract: Pulsating heat pipe is a heat transfer device which works on two principles that is phase transition and thermal conductivity which transfer heat effectively at different temperatures. Different factors affect the thermal performance of pulsating heat pipe. So, various researchers tried to enhance thermal conductivity by changing parameters such as working fluids, filling ratio, etc. Analysis of heat transfer characteristics of closed loop pulsating heat pipe (CLPHP) is to be carried out by using Computational Fluid Dynamics. The CLPHP is to be modelled on ANSYS Workbench, the flow of CLPHP is to be observed under specific boundary conditions by using ANSYS Fluent software. Acetone and Water are taken as the working fluid with 70% filling ratio at ambient temperature 30° C and the heat flux of 200 W is supplied at evaporator. Also, the analysis has been done to know the behaviour of PHPs under varying supply of heat flux at evaporator (inlet), the output heat flux is obtained at condenser (outlet) and find out how the heat flux is varying at different temperatures. CFD results shows the heat transfer characteristics observing the performance of CLPHP is a numerical manner. The obtained CFD results are compared with the experimental. The outputs of the simulations are plotted in graphs and outlines. Keywords: Closed Loop Pulsating Heat Pipe, CFD, Heat Transfer, ANSYS.

Effect of thickness and thermal conductivity of metal foams filled in a vertical channel – a numerical study

2019 ◽  
Vol 29 (1) ◽  
pp. 184-203 ◽  
Author(s):  
Banjara Kotresha ◽  
N. Gnanasekaran
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Metal Foam ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Vertical Channel ◽  
Metal Foams ◽  
Heat Transfer Analysis ◽  
Transfer Model ◽  
Content Type

PurposeThis paper aims to discuss about the two-dimensional numerical simulations of fluid flow and heat transfer through high thermal conductivity metal foams filled in a vertical channel using the commercial software ANSYS FLUENT.Design/methodology/approachThe Darcy Extended Forchheirmer model is considered for the metal foam region to evaluate the flow characteristics and the local thermal non-equilibrium heat transfer model is considered for the heat transfer analysis; thus the resulting problem becomes conjugate heat transfer.FindingsResults obtained based on the present simulations are validated with the experimental results available in literature and the agreement was found to be good. Parametric studies reveal that the Nusselt number increases in the presence of porous medium with increasing thickness but the effect because of the change in thermal conductivity was found to be insignificant. The results of heat transfer for the metal foams filled in the vertical channel are compared with the clear channel in terms of Colburn j factor and performance factor.Practical implicationsThis paper serves as the current relevance in electronic cooling so as to open up more parametric and optimization studies to develop new class of materials for the enhancement of heat transfer.Originality/valueThe novelty of the present study is to quantify the effect of metal foam thermal conductivity and thickness on the performance of heat transfer and hydrodynamics of the vertical channel for an inlet velocity range of 0.03-3 m/s.

Instability of Variable Thermal Conductivity Magnetohydrodynamic Nanofluid Flow in a Vertical Porous Channel of Varying Width

2017 ◽  
Vol 378 ◽  
pp. 85-101
Author(s):  
Md. Sarwar Alam ◽  
Oluwole Daniel Makinde ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Porous Wall ◽  
Variable Thermal Conductivity ◽  
Physical Parameters

A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al2O3-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

scholarly journals Nonlinear thermal conductivity in gases

2016 ◽  
Vol 57 ◽  
Author(s):  
Arvydas Juozapas Janavičius ◽  
Sigita Turskienė
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nonlinear Equation ◽  
Diffusion Processes ◽  
Finite Velocity ◽  
Practical Applications ◽  
Different Temperatures ◽  
Gas Molecules ◽  
Diffusivity Equation ◽  
Nonlinear Thermal Conductivity

The nonlinear diffusion equation corresponds to the diffusion processes which can occur with a finite velocity. A.J. Janavičius proposed nonlinear equation which describes more exactly the diffusion of impurities in Si crystals in many interesting practical applications. The heat transfer in gases is also based on diffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. In this case the heat transfer can be considered using similar nonlinear thermal diffusivity equation. The approximate analytical solution of this nonlinear equation can be used for the experimental analysis of thermal conductivity coefficients using temperature profiles dependence on different temperatures and pressures in gases.  

Heat Flow Calorimetry

2008 ◽  
Author(s):  
José A. Martinho Simões ◽  
Manuel Minas da Piedade
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Heat Flow ◽  
Heat Sink ◽  
Reaction Vessel ◽  
Heat Output ◽  
Large Numbers ◽  
Different Temperatures

Heat flow calorimeters, also known as “heat flux,” “heat conduction,” or “heat leakage” calorimeters, are instruments where the heat output or input associated with a given phenomenon is transferred between a reaction vessel and a heat sink. This heat transfer can be monitored with high thermal conductivity thermopiles containing large numbers of identical thermocouple junctions regularly arranged around the reaction vessel (the cell) and connecting its outside wall to the heat sink (the thermostat). The determination of the heat flow relies on the so-called Seebeck effect. An electric potential, known as thermoelectric force and represented by E, is observed when two wires of different metals are joined at both ends and these junctions are subjected to different temperatures, T1 and T2. Several thermocouples can be associated, forming a thermopile. For small temperature differences, the thermoelectric force generated by the thermopile is proportional to T1 − T2 and to the number of thermocouples of the pile (n): E = nε ′ (T1 − T2) (9.1) where ε′ is the thermoelectric power of a single thermocouple (ε′ = dE/dT).

Combined effect of variable viscosity and thermal conductivity on free convection flow of a viscous fluid in a vertical channel

2016 ◽  
Vol 26 (1) ◽  
pp. 18-39 ◽  
Author(s):  
Jawali C Umavathi ◽  
A J Chamkha ◽  
Syed Mohiuddin
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Variable Viscosity ◽  
Vertical Channel ◽  
Variable Thermal Conductivity ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Temperature Relation ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose – The purpose of this paper is to investigate the effect of exponential viscosity-temperature relation, exponential thermal conductivity-temperature relation and the combined effects of variable viscosity and variable thermal conductivity on steady free convection flow of viscous incompressible fluid in a vertical channel. Design/methodology/approach – The governing equations are solved analytically using regular perturbation method. The analytical solutions are valid for small variations of buoyancy parameter and the solutions are found up to first order for variable viscosity. Since the analytical solutions have a restriction on the values of perturbation parameter and also on the higher order solutions, the authors resort to numerical method which is Runge-Kutta fourth order method. Findings – The skin friction coefficient and the Nusselt number at both the plates are derived, discussed and their numerical values for various values of physical parameters are presented in tables. It is found that an increase in the variable viscosity enhances the flow and heat transfer, whereas an increase in the variable thermal conductivity suppresses the flow and heat transfer for variable viscosity, variable thermal conductivity and their combined effect. Originality/value – This research is relatively original as, to the best of the authors’ knowledge, not much work is done on the considered problem with variable properties.

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