scholarly journals Unsteady Radiative Natural Convective MHD Nanofluid Flow Past a Porous Moving Vertical Plate with Heat Source/Sink

Molecules ◽  
2020 ◽  
Vol 25 (4) ◽  
pp. 854 ◽  
Author(s):  
Talha Anwar ◽  
Poom Kumam ◽  
Zahir Shah ◽  
Wiboonsak Watthayu ◽  
Phatiphat Thounthong
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Sink ◽  
Vertical Plate ◽  
Flow Direction ◽  
Transverse Magnetic ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Partial Differential ◽  
Source Sink

In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and TiO 2 ) past a moving porous vertical plate. A uniform transverse magnetic field is imposed perpendicular to the flow direction. Thermal radiation and heat sink terms are included in the energy equation. The governing equations of this flow consist of partial differential equations along with some initial and boundary conditions. The solution method of these flow interpreting equations comprised of two parts. Firstly, principal equations of flow are symmetrically transformed to a set of nonlinear coupled dimensionless partial differential equations using convenient dimensionless parameters. Secondly, the Laplace transformation technique is applied to those non-dimensional equations to get the close form exact solutions. The control of momentum and heat profile with respect to different associated parameters is analyzed thoroughly with the help of graphs. Fluid accelerates with increasing Grashof number (Gr) and porosity parameter (K), while increasing values of heat sink parameter (Q) and Prandtl number (Pr) drop the thermal profile. Moreover, velocity and thermal profile comparison for Cu and TiO 2 -based nanofluids is graphed.

scholarly journals Effects of Hall current on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate with Newtonian heating

2016 ◽  
Vol 21 (1) ◽  
pp. 187-203 ◽  
Author(s):  
G.S. Seth ◽  
S. Sarkar ◽  
R. Sharma
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Convection ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Hall Current ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Partial Differential ◽  
Present Solution

Abstract An investigation of unsteady hydromagnetic free convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively moving vertical plate with Newtonian surface heating embedded in a porous medium taking into account the effects of Hall current is carried out. The governing partial differential equations are first subjected to the Laplace transformation and then inverted numerically using INVLAP routine of Matlab. The governing partial differential equations are also solved numerically by the Crank-Nicolson implicit finite difference scheme and a comparison has been provided between the two solutions. The numerical solutions for velocity and temperature are plotted graphically whereas the numerical results of skin friction and the Nusselt number are presented in tabular form for various parameters of interest. The present solution in special case is compared with a previously obtained solution and is found to be in excellent agreement.

scholarly journals Numerical Solutions of Hybrid Nanofluids Flow Via Free Convection Over a Solid Sphere

2021 ◽  
Vol 83 (1) ◽  
pp. 34-45
Author(s):  
Mohammed Zaki Swalmeh
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Convection ◽  
Numerical Solutions ◽  
Solid Sphere ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Partial Differential ◽  
Hybrid Nanofluids

The purpose of the existing study is to examine how heat transfer enables consolidated by variations in the basic advantages of fluids in the existence of free convection with the assistance of suspended hybrid nanofluids. Iron-graphene oxide suspended in water as a hybrid nanofluid flow on a solid sphere is also considered in this work. The partial differential equations are gotten, for this problem, by transforming the mathematical governing equations using similarity equations (stream function). These partial differential equations are solved numerically by Keller-Box method and programmed by MATLAB program. the acquired numerical results are in excellent agreement with the preceding literature results. Graphical results of the influence of the hybrid nanofluid parameters on some physical quantities regarded to examine the behavior of hybrid nanofluid flow were attained, and they proved that hybrid nanofluid flow represents a more essential role in the operation of heat transfer than a regular nanofluid flow.

Diffusion in Heterogeneous Media

1982 ◽  
Vol 104 (4) ◽  
pp. 781-787 ◽  
Author(s):  
M. D. Mikhailov ◽  
M. N. O¨¸zisik ◽  
B. K. Shishedjiev
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Heterogeneous Media ◽  
Integral Transform ◽  
Three Dimensional ◽  
Solid Cylinder ◽  
Partial Differential ◽  
Source Sink ◽  
General Linear Boundary Conditions ◽  
Mass Concentrations

Heat or mass diffusion problems of finite heterogeneous media are characterized by a set of partial differential equations for temperatures or mass concentrations, Tk (x, t), (k = 1, 2, . . . , n), in every point in space, which are coupled through source-sink terms in the equations. In the present analysis, appropriate integral transform pairs are developed for the solution of the n-coupled partial differential equations subject to general linear boundary conditions. Three-dimensional, time-dependent solutions are presented for the distributions of the potentials (i.e., temperatures or mass concentrations), Tk (x, t), (k = 1, 2, . . . , n), as a function of time and position for each of the n-components in the medium. The results of the general analysis are utilized to develop solutions for the specific cases of one-dimensional slab, long solid cylinder, and sphere. Numerical results are presented for the dimensionless potentials (i.e., temperature or mass concentration), Tk (x, t), (k = 1, 2, 3), at the center of the slab, long solid cylinder, or sphere for each of the three components of a three-component system.

scholarly journals Heat Dissipation Performance of Micro-channel Heat Sink with Various Protrusion Designs

2021 ◽  
Vol 20 ◽  
pp. 240-249
Author(s):  
Siyuan Bai ◽  
Khalil Guy ◽  
Yuxiang Jia ◽  
Weiyi Li ◽  
Qingxia Li ◽  
...  
Keyword(s):  
Porous Medium ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Sink ◽  
Heat Dissipation ◽  
Volume Averaging ◽  
Micro Channel ◽  
Partial Differential ◽  
Micro Channels ◽  
Pin Fins

This research will focus on studying the effect of aperture size and shape of the micro-channel heat sink on heat dissipation performance for chip cooling. The micro-channel heat sink is considered to be a porous medium with fluid subject inter-facial convection. Derivation based on energy equation gives a set of governing partial differential equations describing the heat transfer through the micro-channels. Numerical simulation, including steady-state thermal analysis based on CFD software, is used to create a finite element solver to tackle the derived partial differential equations with properly defined boundary conditions related to temperature. After simulating three types of heat sinks with various protrusion designs including micro-channels fins, curly micro-channels fins, and Micro-pin fins, the result shows that the heat sink with the maximum contact area per unit volume will have the best heat dissipation performance, we will interpret the result by using the volume averaging theorem on the porous medium model of the heat sink.

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