Impact of Thermal Stratification on Unsteady Natural Convection Couette Flow Formation in a Vertical Channel Filled with Anisotropic Porous Material

2021 ◽  
Vol 408 ◽  
pp. 67-82
Author(s):  
Basant Kumar Jha ◽  
Muhammad Kabir Musa ◽  
Abiodun O. Ajibade
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Differential Equations ◽  
Porous Material ◽  
Couette Flow ◽  
Fluid Velocity ◽  
Vertical Channel ◽  
Stratified Fluid ◽  
Fluid Temperature ◽  
Riemann Sum

Recently, heat transfer problems where anisotropic porous medium or stably stratified fluid are taken into account have been separately studied. Developing a mathematical model that combines these physical quantities naturally results to complex coupled differential equations. In this paper, a fully developed time dependent natural convection Couette flow of stably stratified fluid between vertical parallel channels filled with anisotropic porous material is investigated. The governing partial differential equations are transformed into ordinary differential equations using Laplace transform techniques and then decoupled using D’Alembert method. Exact solutions in Laplace domain for the velocity and temperature equations are then obtained. A numerical method: Riemann-sum approximation is then used to invert the expressions for the velocity and temperature profiles, as well as the resulting skin friction, rate of heat transfer and volumetric mass flow rate into their corresponding time domain. The research establishes that both the anisotropic and the stratification parameters aid in regulating the fluid temperature and velocity. The research further reveals that the fluid velocity attains its maximum (or minimum) velocity when θ = 900 (or θ = 00) for k*<1 and when k*>1, the fluid velocity is least (or maximum) when θ = 900 (or θ = 00).

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.

Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Abiodun O. Ajibade ◽  
Tafida M. Kabir
Keyword(s):  
Boundary Condition ◽  
Natural Convection ◽  
Couette Flow ◽  
Viscous Dissipation ◽  
Fluid Velocity ◽  
Convective Boundary Condition ◽  
Heated Plate ◽  
Fluid Temperature ◽  
Convective Boundary ◽  
Energy And Momentum

Abstract The present article explores the effect of viscous dissipation on steady natural convection Couette flow subject to convective boundary condition. Due to the nonlinearity and coupling of the governing equations in the present situation, the homotopy perturbation method was employed to obtain the solutions of the energy and momentum equations. The impacts of the controlling parameters were investigated and discussed graphically. In the course of investigation, it was found that fluid temperature increases with an increase in viscous dissipation while the reverse trend was observed in fluid velocity. However, it was also discovered that heat generation leads to a decrease in the rate of heat transfer on the heated plate and it increases on the cold plate. Finally, it was concluded that the velocity boundary layer thickness increases with an increase in Biot number.

Heat Transfer Characteristics of One Side Heated Vertical Rectangular Channel Inserting Porous Material

2012 ◽  
Author(s):  
Tetsuaki Takeda ◽  
Akihiro Sato ◽  
Shumpei Funatani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Porous Material ◽  
Cooling System ◽  
Copper Wire ◽  
Rectangular Channel ◽  
Vertical Channel ◽  
High Porosity ◽  
The One ◽  
Passive Cooling System

The objective of this study is to not only investigate heat transfer characteristics of natural convection of a one-side heated vertical channel inserting the porous materials with high porosity but also develop the passive cooling system for the Very-High-Temperature Reactor (VHTR). An experiment and analysis was carried out using the one-side heated vertical rectangular channel. From the results obtained in the experiment and analysis, it was found that an amount of removed heat by forced convection using the copper wire (porosity>0.996) was about 15% higher than that without the wire. It was also found that the amount of transferred heat from the heated wall will be increased even if the heat removed by natural convection. Furthermore, the ratio between the amounts of heat removed of the rectangular channel with the porous material and without the porous material increases with increasing temperature of the channel wall. In order to obtain the heat transfer and fluid flow characteristics of the vertical channel inserting porous material, we have also carried out a numerical analysis using a commercial CFD code. This paper describes thermal performances of the one-side heated vertical rectangular channel inserting copper wire with high porosity. From a view point of economical and safety characteristics, the passive cooling system should be designed for the VHTR as the best way of the system. Therefore, the gas cooling system by natural convection is the one of candidate system.

scholarly journals DTM-PADE APPROACH TO MHD SLIP FLOW AND HEAT TRANSFER OVER A RADIALLY STRETCHING SHEET WITH THERMAL RADIATION

2020 ◽  
Vol 50 (3) ◽  
pp. 175-184
Author(s):  
Shoeb Rashid Sayyed ◽  
Brijbhan Singh ◽  
Oluwole Makinde ◽  
Nasreen Bano Muslim Shaikh
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Fluid Velocity ◽  
Slip Flow ◽  
Fluid Temperature ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Non Linear

The present paper deals with the boundary layer flow and heat transfer of an electrically conducting magnetohydrodynamic viscous fluid over a radially stretching power-law sheet with suction/injection within a porous medium by considering the effects of momentum and thermal slips and thermal radiation. The governing non-linear partial boundary layer differential equations are reduced to a  system of coupled non-linear ordinary differential equations (ODEs) with the aid of appropriate similarity transformations. These transformed ODEs are then solved by employing a semi-analytic technique known as differential transformation method (DTM) in combination with Pade approximation. The numerical values of skin friction and local Nusselt number are tabulated and validated by comparing them with the corresponding values available in the literature. Our results have been found in precise agreement  with the results published earlier. The effects of different governing parameters on velocity and temperature distributions are analyzed graphically. It has been found that with an increase in the velocity slip parameter the fluid velocity decreases whereas the temperature of the fluid increases. Also, the fluid temperature gets enhanced with an increase in the radiation parameter, but it decreases with an increase in thermal slip.

Magnetohydrodynamic Mixed Convective Flow Due to a Vertical Plate With Induced Magnetic Field

2018 ◽  
Vol 10 (6) ◽  
Author(s):  
R. Nandkeolyar ◽  
M. Narayana ◽  
S. S. Motsa ◽  
P. Sibanda
Keyword(s):  
Magnetic Field ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Linearization Method ◽  
Fluid Temperature ◽  
Magnetic Field Effects ◽  
Induced Magnetic Field ◽  
Partial Differential

The steady hydromagnetic flow of a viscous, incompressible, perfectly conducting, and heat absorbing fluid past a vertical flat plate under the influence of an aligned magnetic field is studied. The flow is subject to mixed convective heat transfer. The fluid is assumed to have a reasonably high magnetic Prandtl number which causes significant-induced magnetic field effects. Such fluid flows find application in many magnetohydrodynamic devices including MHD power-generation. The effects of viscous dissipation and heat absorption by the fluid are investigated. The governing nonlinear partial differential equations are converted into a set of nonsimilar partial differential equations which are then solved using a spectral quasi-linearization method (SQLM). The effects of the important parameters on the fluid velocity, induced magnetic field, fluid temperature and as well as on the coefficient of skin-friction and the Nusselt number are discussed qualitatively.

Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

2015 ◽  
Vol 7 (3) ◽  
pp. 369-386 ◽  
Author(s):  
K. Vajravelu ◽  
K. V. Prasad ◽  
S. R. Santhi
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Dust Particle ◽  
Maxwell Fluid ◽  
Fluid Temperature ◽  
Heat Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Ucm Fluid ◽  
Flow Phenomena

AbstractAn analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena.

A Natural Convection Fin with a Solution-Determined Nonmonotonically Varying Heat Transfer Coefficient

1981 ◽  
Vol 103 (2) ◽  
pp. 218-225 ◽  
Author(s):  
E. M. Sparrow ◽  
S. Acharya
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Transfer Coefficient ◽  
First Principles ◽  
Numerical Solutions ◽  
Flow Direction ◽  
Operating Conditions ◽  
Fluid Temperature ◽  
Wide Range

A conjugate conduction-convection analysis has been made for a vertical plate fin which exchanges heat with its fluid environment by natural convection. The analysis is based on a first-principles approach whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, and energy in the fluid boundary layer adjacent to the fin. The natural convection heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. For a wide range of operating conditions, the local heat transfer coefficients were found not to decrease monotonically in the flow direction, as is usual. Rather, the coefficient decreased at first, attained a minimum, and then increased with increasing downstream distance. This behavior was attributed to an enhanced buoyancy resulting from an increase in the wall-to-fluid temperature difference along the streamwise direction. To supplement the first-principles analysis, results were also obtained from a simple adaptation of the conventional fin model.

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