Mixed Convection over a Horizontal Plate with Streamwise Non-uniform Surface Temperature Distribution (original) (raw)
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Mixed convection of a two-dimensional laminar incompressible flow along a horizontal flat plate with streamwise sinusoidal surface temperature has been numerically investigated for different values of Rayleigh number and Reynolds number for constant values of Prandtl number, amplitude and frequency of periodic temperature. The numerical scheme is based on the finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm. The fluid considered in this study is air. The results are obtained for the Rayleigh number and Reynolds number ranging from 102 to 104 and 1 to 100, respectively, with constant physical properties for the fluid medium considered. Velocity and temperature profiles, streamlines, isotherms, and average Nusselt numbers are presented to observe the effect of the investigating parameters on fluid flow and heat transfer characteristics. The present results show that the convective phenomena are greatly influenced by the variation of Rayleigh numbers and Reynolds number.
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi, 2021
In this paper, the numerical results of mixed convection flow over a flat plate with the imposed heat and different angles of inclination are established by applying the finite difference method of Crank-Nicolson. We further compare these numerical results with the case of non-mixed convection flow. The velocity and temperature profiles are decreased when the different values of the Prandtl number (Pr) are increased. Meanwhile, the velocity profiles are increased, when the different values of angle of inclination (alfa) and mixed convection parameter (lambda) are increased. The mixed convection flow case (lambda=1.5) is affected by the external force, so the velocity of convection flow is higher than the non-mixed case (lambda=0).
Laminar Forced Convection Over An Inclined Flat Plate With Unheated Starting Length
Journal of Polytechnic
Two-dimensional laminar forced convection over an inclined flat plate with an unheated starting length was investigated numerically for both constant surface temperature and constant heat flux boundary conditions. The numerical study was implemented using the commercial software ANSYS Fluent 15.0. Air is used as working fluid. The influence of Reynolds number, inclination angle and the length of unheated plate on velocity and temperature distributions, surface temperature, surface heat flux and local Nusselt number was investigated. The results show that Reynolds number, inclination angle and the length of unheated region of plate play important role on heat transfer from the plate. It is seen that Nusselt number increases with increasing Reynolds number and inclination angle of inclined flat plate but decreases with increasing the length of unheated region of plate.
Closed-form analytical solutions for laminar natural convection on horizontal plates
Journal of Heat Transfer, 2013
A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T w ð xÞ À T 1 ¼ a x n whereas the heat flux is assumed to vary according to q w ð xÞ ¼ b x m . Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr 1 or Pr % 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate. plate temperature T w varies with x in the following prescribed manner: T T Cx w n 1 where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically. Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in literature with good agreement.
The simultaneously developing of steady laminar mixed convection flow of incompressible Newtonian fluid in vertical double passage parallel plates channel has been analyzed numerically using marching technique in the axial direction. Axial conduction, axial mass diffusion, and viscous dissipation within the fluid were assumed negligible. A numerical, finite control volume approach following the SIMPLER algorithm was adopted in solving the governing equations subjected to the Boussinesq approximation. Numerical analysis has been conducted for the case of uniform wall temperature (T boundary condition) using two values of Prandtl number Pr=0.7 and Pr=7.0 which are corresponding to air and water respectively for a wide range of ratio Gr/Re. Results were limited to the case of heating (hot walls and cold fluid) in the following range of baffle positions: Y * =0.25, Y * =0.50, and Y * =0.75. These results included developing axial velocity fields, developing temperature fields, local Nus...
Laminar Forced Convection in Horizontal Channel with Heat Generation Plates Cooled by Water
Proceedings of the 23rd ABCM International Congress of Mechanical Engineering, 2015
Blank line)single line spacing-Times New Roman 10 This paper describes the study of the behavior of two-dimensional and parallel horizontal flat plates with uniform internal heat generation subjected to laminar forced convection of water. The governing equations are solved numerically using the finite volume technique with Power-Law interpolating scheme and the SIMPLE algorithm. After the simulations the temperature and velocity fields were obtained for various plates spacing and fluid inlet velocities, as well as the Nusselt number values.
Scientific reports, 2017
This scientific report investigates the heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate with constant wall temperature. The problem is modelled in terms of coupled partial differential equations with initial and boundary conditions. Some suitable non-dimensional variables are introduced in order to transform the governing problem into dimensionless form. The resulting problem is solved via Laplace transform method and exact solutions for velocity, shear stress and temperature are obtained. These solutions are greatly influenced with the variation of embedded parameters which include the Prandtl number and Grashof number for various times. In the absence of free convection, the corresponding solutions representing the mechanical part of velocity reduced to the well known solutions in the literature. The total velocity is presented as a sum of both cosine and sine velocities. The unsteady velocity in each case is arranged in the form...
Computational Fluid Dynamics Analysis of Horizontal Heated Plate for Natural Convection
Free or natural convection heat transfer is predominant in many engineering applications such as cooling of electronic equipment, pollution, materials processing, energy systems, and safety in thermal processes and geophysical flows. The present work discusses about the result of a computational fluid dynamics study of Steady, Laminar, Free convection heat transfer in a horizontal plate facing upwards in which two walls are adiabatic and other two ends are open to the ambient .The aim is to simulate the flow using appropriate CFD tools and compare the results with available experimental data. The CFD tool used here is ANSYS-FLUENT.
A Numerical Study of Unsteady Natural Convection from Two-Sided Thin Horizontal Isothermal Plates
Proceedings of the 10th International Conference on Fluid Flow, Heat and Mass Transfer (FFHMT 2023)
Unsteady natural convective heat transfer following sudden heating of two-sided, thin isothermal horizontal plates with complex shapes has been numerically studied. The plates were isothermal and exposed to air at ambient conditions. Three different plate shapes were considered. Variations of the heat transfer rates, expressed in terms of the Nusselt number with dimensionless time for various Rayleigh numbers were first obtained with the square root of the plates' surface area being used as the length scale. Then, the heat transfer rates for steady state were obtained with the same length scale being used. The transient heat transfer rate results showed that depending on the value of the Rayleigh number, the Nusselt number either gradually decreased to a steady state value or first decreased to a minimum and then increased to the steady state value. Similar Nusselt number variation with time were obtained for all plate shapes considered. Now, in studies of steady state natural convective heat transfer rates from horizontal plates with different shapes, it has been found that if 4*Area/Perimeter is used as the length scale in presenting the results, the variation of Nusselt number with Rayleigh number were essentially the same for all shapes considered. Therefore, the unsteady state results obtained in the present study were re-expressed using 4*Area/Perimeter as the length scale and it was found that the variations of Nusselt number with dimensionless time for various Rayleigh numbers for the plate shapes considered, were much closer to each other when 4*area/perimeter was used as the length scale than when the square root of the plate area was used as the length scale.