Natural Convection Flow in Vertical Channel Due to Ramped Wall Temperature at One Boundary

2009 ◽  
Author(s):  
Narahari Marneni ◽  
Vijay R. Raghavan
Keyword(s):  
Natural Convection ◽  
Volume Flow Rate ◽  
Vertical Channel ◽  
The Other ◽  
Temperature Fields ◽  
Convection Flow ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Laplace Transform Technique ◽  
The Laplace Transform

An exact solution to the problem of unsteady natural convective flow of a viscous and incompressible fluid in a vertical parallel plate channel due to ramp heating at one boundary is presented. The temperature at one of the channel plates increases linearly over a certain time period and then remains constant while that at the other plate is maintained at the initial fluid temperature. The Laplace transform technique has been used to obtain the expressions for the velocity and temperature fields by solving the dimensionless governing partial differential equations under appropriate boundary conditions. The influence of the physical parameters on the velocity field, the temperature field, rate of heat transfer, skin-friction and volume flow rate of the fluid are analyzed systematically. The shear stress at the plate with ramped temperature boundary condition is significantly higher than that at the other plate because of the steeper velocity profiles in the vicinity. The Nusselt number at the plate with ramped temperature is much higher than that at the other plate indicating that much of the energy released from the plate because of its increasing temperature with time is convected out by the fluid before it reaches the second plate. The natural convection due to ramp heating has also been compared with the baseline case of flow with constant temperature.

scholarly journals Effect of Variable Viscosity on Natural Convection Flow Between Vertical Parallel Plates in the Presence of Heat Generation/Absorption

2019 ◽  
pp. 1-15
Author(s):  
Tada M. Kabir ◽  
Abiodun O. Ajibade
Keyword(s):  
Natural Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Variable Viscosity ◽  
Nonlinear Differential Equations ◽  
Convection Flow ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Parallel Plates ◽  
Natural Convection Flow

The present article was aimed at investigating the effects of variable viscosity on natural convection flow between vertical parallel plates in the presence of heat generation/absorption. The nonlinear differential equations governing the flow were solved using Homotopy perturbation method. The impacts of the several governing parameters on the velocity and temperature profiles are presented graphically and values of skin friction, rate of heat transfer, mass flux and mean temperature for various values of physical parameters are presented through tables. In the course of computation, it was revealed that viscosity  ontributes to decrease velocity and hence reduced resistance to flow. It was also discovered that as the heat generation increases, fluid temperature and velocity increase, while it decrease with the increase in heat absorption. Finally, it was concluded that the skin friction on both plates increase as viscosity increases.

scholarly journals Role of Induced Magnetic Field on Transient Natural Convection Flow in a Vertical Channel: The Riemann Sum Approximation Approach

2015 ◽  
Vol 20 (1) ◽  
pp. 65-85
Author(s):  
B.K. Jha ◽  
I. Sani
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Vertical Channel ◽  
Convection Flow ◽  
Induced Magnetic Field ◽  
Natural Convection Flow ◽  
Transient Natural Convection ◽  
Riemann Sum ◽  
Laplace Transform Technique

Abstract This paper investigates the role of induced magnetic field on a transient natural convection flow of an electrically conducting, incompressible and viscous fluid in a vertical channel formed by two infinite vertical parallel plates. The transient flow formation inside the channel is due to sudden asymmetric heating of channel walls. The time dependent momentum, energy and magnetic induction equations are solved semi-analytically using the Laplace transform technique along with the Riemann-sum approximation method. The solutions obtained are validated by comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical results for the temperature, velocity, induced magnetic field, current density, and skin-friction based on the semi-analytical solutions are presented and discussed.

Transient free convection flow due to the arbitrary motion of a vertical plate

1970 ◽  
Vol 67 (3) ◽  
pp. 677-688
Author(s):  
P. C. Sinha ◽  
Punyatma Singh
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Vertical Plate ◽  
Fluid Velocity ◽  
Temperature Fields ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Layer Flow

The paper deals with the free convection flow along a vertical plate moving arbitrarily in its own plane. The basic equations of the boundary-layer flow and heat transfer are linearized and the first two approximations are considered. The first approximation is the case of steady-state free convection flow while the second approximation is the response of the fluid velocity and temperature fields to the motion of the plate for which limiting solutions are obtained by the Laplace transform technique in two regions; namely, for large times and for small times. The particular case when the plate is given an impulsive start at t = 0 is investigated in detail. It is shown how the skin friction and the rate of heat transfer at the plate respond to the motion of the plate.

scholarly journals MHD heat and mass diffusion flow by natural convection past a surface embedded in a porous medium

2009 ◽  
Vol 36 (1) ◽  
pp. 1-27 ◽  
Author(s):  
R.C. Chaudhary ◽  
Arpita Jain
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Analytical Study ◽  
Mass Diffusion ◽  
Convection Flow ◽  
Governing Equations ◽  
Natural Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Flow Variables

This paper presents an analytical study of the transient hydromagnetic natural convection flow past a vertical plate embedded in a porous medium, taking account of the presence of mass diffusion and fluctuating temperature about time at the plate. The governing equations are solved in closed form by the Laplace-transform technique. The results are obtained for temperature, velocity, penetration distance, Nusselt number and skin-friction. The effects of various parameters are discussed on the flow variables and presented by graphs.

scholarly journals Thermo-diffusion effects on the magnetohydrodynamic natural convection flow of a chemically reactive Brinkman type nanofluid in a porous medium

2019 ◽  
Vol 51 (2) ◽  
pp. 168-179 ◽  
Author(s):  
G. S. Seth ◽  
R. Kumar ◽  
R. Tripathi
Keyword(s):  
Natural Convection ◽  
Skin Friction ◽  
Fluid Velocity ◽  
Surface Concentration ◽  
Convection Flow ◽  
Fluid Temperature ◽  
Species Concentration ◽  
Electrically Conducting ◽  
Laplace Transform Technique ◽  
Mass Transfers

An investigation on the unsteady MHD natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible, chemically reactive and heat-absorbing nanofluid of Brinkman type past an exponentially accelerated moving vertical plate with ramped wall temperature and ramped surface concentration is carried out. Governing equations are non-dimensionalized and Laplace Transform Technique is used to find the exact solutions for fluid velocity, fluid temperature and species concentration. The quantities of physical interest, i.e. skin friction, rates of heat and mass transfers at the plate are also calculated. Numerical results for the velocity, temperature and species concentration of the fluid are demonstrated with the help of graphs whereas those of skin friction, rate of heat and mass transfers at the plate are displayed in tables for various flow parameters.

scholarly journals Influence of thermal radiation on non-Darcian natural convection in a square cavity filled with fluid saturated porous medium of uniform porosity

2012 ◽  
Vol 17 (2) ◽  
pp. 223-237 ◽  
Author(s):  
Tapas Ray Mahapatra ◽  
Dulal Pal ◽  
Sabyasachi Mondal
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Thermal Radiation ◽  
Horizontal Plane ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Staggered Grid ◽  
Convection Flow ◽  
Physical Parameters ◽  
Square Cavity

Influence of thermal radiation on natural-convection flow in a square cavity filled with a porous medium of uniform porosity having isothermal vertical walls and adiabatic horizontal walls, has been studied numerically by using finite-difference method with staggered grid distribution. The simulation is performed by considering both Darcian and non-Darcian models. Governing momentum and energy equations are solved numerically to obtain velocity and temperature fields for various values of different physical parameters. It is seen that increasing the thermal radiation parameter enhances the local Nusselt number on the left vertical wall whereas the reverse effects are observed due to increase in the heat generating parameter when Ra = 109. The temperature at the mid-horizontal plane decreases with increase in the value of Rayleigh number up to a certain distance from the left vertical wall and beyond that distance the opposite trend is observed. The temperature at the mid-horizontal plane increases with increase in the value of heat generating parameter.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

scholarly journals Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

2016 ◽  
Vol 21 (3) ◽  
pp. 667-681 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Unsteady Mixed Convection ◽  
Phase Angles

Abstract An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., $T^* \left( {y^* ,z^* ,t^* } \right) = T_1 + \left( {T_2} - {T_ 1} \right)\cos \left( {{{\pi z^* } \over d} - \omega ^* t^* } \right)$ . A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

scholarly journals Heat Transfer Analysis for Viscous Fluid Flow with the Newtonian Heating and Effect of Magnetic Force in a Rotating Regime

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Rashid Ayub ◽  
Shahzad Ahmad ◽  
Muhammad Imran Asjad ◽  
Mushtaq Ahmad
Keyword(s):  
Viscous Fluid ◽  
Fluid Motion ◽  
Velocity Fields ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Newtonian Heating ◽  
Flow Parameters ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature And Velocity Fields

In this article, an unsteady free convection flow of MHD viscous fluid over a vertical rotating plate with Newtonian heating and heat generation is analyzed. The dimensionless governing equations for temperature and velocity fields are solved using the Laplace transform technique. Analytical solutions are obtained for the temperature and components of velocity fields. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are presented graphically.

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