MIXED CONVECTION ANALYSIS IN TRAPEZOIDAL CAVITY WITH A MOVING LID (original) (raw)
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Mixed convection heat transfer in a two-dimensional trapezoidal cavity has been investigated with a locally heated lower wall and moving cold top lid. The enclosure represents a practical system where the space requirement is very important factor for efficient electronic cooling system. The numerical study is conducted for several values of aspect angle of the cavity and a range of Richardson numbers with constant Reynolds and Prandtl numbers. The influence of Richardson number on average Nusselt number is investigated for various aspect angles. Results are represented in the form of isotherms and streamlines under different conditions. The solution procedure is conducted using the Galerkin finite element method.
Mixed Convection in Lid Driven Trapezoidal Cavities with Aiding or Opposing Side Wall
Mixed convection heat transfer and fluid flow fields inside a lid-driven trapezoidal cavity were studied numerically. The cavity horizontal walls were thermally insulated while the inclined side walls were maintained isothermally at different temperatures. Forced convec-tion was induced by moving the hotter right inclined side wall. The problem is formulated using the stream function–vorticity procedure. Together with the established boundary conditions on the right moving wall, the problem is solved by the finite difference method. The Richardson number Ri (0.01–10) and inclination angle of the side walls U (66–80) were considered as pertinent parameters and investigated in two lid-driven cases: aiding and opposing directions. The results show that the behavior of Nusselt number is different from Richardson number depending on the direction of the lid. The inclination angle of the side walls was found to have a significant effect on Nusselt number when Ri was relatively low (1); otherwise, a negligible effect of U on Nusselt number was recorded.
Effect of Driven Sidewalls on Mixed Convection in an Open Trapezoidal Cavity With a Channel
Journal of Heat Transfer, 2020
The mixed convection in an open trapezoidal lid-driven cavity connected with a channel is investigated in the present paper. Four different cases were considered depending on the movement of the cavity sidewalls. For case I, the left sidewall moves downward; for case II, the left sidewall moves downward and the right one moves upward; while for case III, only the right sidewall moves upward. A comparative case (case 0) is accounted when both sidewalls are assumed stationary. The base of the cavity is subjected to a localized heat source of constant temperature T h. The effects of Richardson number Ri and Reynolds number ratio Re r on the flow and thermal fields have been investigated. The results indicated that for cases I and II, the average Nusselt number increases with the increase of the Richardson number and Reynolds number ratio. Moreover, it was found that the maximum average Nusselt number occurs with case I. When the lid-driven speed is three times that of the inlet airflow velocity, the augmentations of the average Nusselt number compared with stationary walls are 163%, 158%, and 96% for cases I, II, and III, respectively.
Mixed Convection Flow and Heat Transfer in a Two Sided Lid Driven Cavity Using SIMPLE Algorithm
IRJET, 2023
In this paper mixed convection flow and heat transfer in steady 2-D incompressible flow through a two sided lid driven cavity is studied. The upper and lower walls of cavity are moving with uniform velocity. The upper wall is at higher temperature and the lower wall is kept at lower temperature. SIMPLE algorithm is employed for solution of governing equations of the model. A staggered grid system is employed for numerical computations for velocity, pressure and temperature. Various values of under relaxation factors for velocity, pressure and temperature are used to obtain the stability of the numerical solutions. Bernoulli equation has been taken up to check the accuracy of the computed solutions. The significant findings from this study have been given under conclusion.
Mixed convection from a uniform and non uniform sinusoidal heat source on the bottom of a rectangular cavity is studied numerically. Two-dimensional forms of non-dimensional Navier-Stokes equations are solved by using control volume based finite volume technique with staggered grid . Three typical values of the Reynolds numbers are chosen as Re = 10, 100, and 2000 and steady, laminar results are obtained in the values of Richardson number as Ri = 0, 1 and 10, 100 and the values of Prandtl numbers is taken as Pr = 0.71, 7 and 10. The parametric studies for a wide range of governing parameters show consistent performance of the present numerical approach to obtain as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented based on the value of Re and Pr. The computational results indicate that the heat transfer is strongly affected by Reynolds number and Richardson number. In the present investigation, bottom wall is(a) uniformly heated & (b) non –uniformly heated while the two vertical walls are maintained at constant cold temperature and the top wall is well insulated. A complete study on the effect of Ri shows that the strength of circulation increases with the increase in the value of Ri irrespective of Re and Pr. As the value of Ri increases, there occurs a transition from conduction to convection dominated flow at Ri =1. A detailed analysis of flow pattern shows that the natural or forced convection is based on both the parameters Ri and Pr.
Mixed Convection Flow And Heat Transfer In A Lid Driven Cavity Using SIMPLE Algorithm
IRJET, 2023
In the present study mixed convection flow and heat transfer in steady 2-D incompressible flow through a lid driven cavity is investigated. The upper wall of cavity is moving with uniform velocity and is at higher temperature. The stationary lower wall is kept at lower temperature. The governing equations of the model are solved numerically using SIMPLE algorithm. A staggered grid system is employed for numerical computations for velocity, pressure and temperature. Under relaxation factors for velocity, pressure and temperature are used for the stability of the numerical solutions. Bernoulli equation has been taken up to check the accuracy of the computed solutions. The significant findings from this study have been given under conclusion.
Mixed Convection of Heat Transfer in a Square Lid-Driven Cavity
International Letters of Chemistry, Physics and Astronomy, 2015
Three dimensional steady state mixed convection in a lid driven cubical cavity heating from below has been investigated numerically. Two sided walls are maintained at a constant ambient temperature Ttop > Tbottom, while the vertical walls are thermally insulated. Governing equations expressing in a dimensionless form are solved by using finite element method. The Reynolds number is fixed at Re=100, while the Richardson number is varied from 0.001 to 10. Parametric studies focusing on the effect of the Richardson number on the fluid flow and heat transfer have been performed. The flow and heat transfer characteristics, expressed in terms of streamlines, isotherms and average wall Nusselt number are presented for the entire range of Richardson number considered. Multiple correlations in terms of the heat transfer rate and Richardson number has been established.
Heliyon, 2021
A two dimensional flow analysis in a cavity shaped isosceles trapezium is carried out. Non-parallel sides of a trapezium are adiabatic. A varying sinusoidal temperature is applied to the lower wall while the upper wall is at constant temperature. Upper wall of the cavity moves with a velocity 0 in the positive x-direction. Also, 0 is constant magnetic field of strength aligned in the same x-direction and Newtonian fluid is considered. The values of magnetic field parameter used are = 0, 50, the Richardson number is = 0.1, 1, 10, = 100 is Reynolds number used for the analysis, the amplitude of sinusoidal temperature is = 0.25, 0.5, 1. The impacts of different leading parameters are analyzed by plotting streamlines for flow fields and isotherm contours for temperature of the flow dynamics. The graphs that signify the variation of average Nusselt number and local Nusselt number are sketched for both lower and upper walls of the cavity. Result indicated that with constant temperature the top wall of the boundary layer thickness decreases as Richardson number Ri increases and for bottom wall with variable temperature. The Nusselt number gets higher with an increment in the amplitude of the oscillation of temperature function. Furthermore, the study revealed that the average Nusselt number gets reduced as the intensity of magnetic field is enhanced. The variation in transit of heat at the bottom wall is similar but the maximum value of heat transfer at the bottom wall shows a variation from 3.8 to 20 when = 0 and from 3 to 18 when = 50. The accuracy of the present numerical algorithms is also established.
The problem of steady, laminar and incompressible mixed convection flow in a symmetrical trapezoidal enclosure is formulated in the present study. In this investigation, the top wall of the enclosure is considered adiabatic and moving in its own plane at a constant speed, while both inclined sidewalls are maintained at a constant cold temperature, and an isoflux heat source is provided at the bottom surface. The enclosure is assumed to be filled with a Bousinessq fluid having a Prandtl number of 0.71. Investigations have been carried out for various geometric configurations of the enclosure as well as for various flow conditions inside the enclosure. The sidewall inclination angle of the enclosure is varied from 0° to 45°. For the fluid flow inside the enclosure, the Reynolds number is considered to be 100, while the Richardson number is varied from 0.1 to 10. A combined finite element method with triangular mesh elements has been adopted to solve the corresponding pressure-velocity form of the Navier-Stokes equations and energy equations. The obtained results are presented in terms of streamlines and isotherms as well as average Nusselt number over the hot bottom surface.