Browse
Submit Data
Databases
API
Help

Dataset Information

16 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Closed form solutions for unsteady free convection flow of a second grade fluid over an oscillating vertical plate.

ABSTRACT: Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter ?, phase angle ?? and time ?. Numerical values of skin friction ? 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.

SUBMITTER: Ali F

PROVIDER: S-EPMC3925078 | biostudies-other | 2014

REPOSITORIES: biostudies-other

ACCESS DATA

Json Xml

Publications

Closed form solutions for unsteady free convection flow of a second grade fluid over an oscillating vertical plate.

Ali Farhad F Khan Ilyas I Shafie Sharidan S

PloS one 20140214 2

Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solut ...[more]

PMID: 24551033

Similar Datasets

Natural convection flow of a second grade fluid in an infinite vertical cylinder.

Project description:In current study natural convection flow of second grade fluid in an oscillating infinite vertical cylinder is investigated. The dimensionless governing equations for temperature and velocity are obtained by introducing the non-dimensional variables. Exact solutions for temperature and velocity field are computed by means of integral transformation. Solutions for cosine and sine oscillations of velocity field are introduced in the form of transient and post-transient arrangements. A special case for Newtonian fluid is obtained from general results and transients solutions are computed in terms of tables. In the end, the impact of dimensionless numbers (Grashof and Prandtl numbers) at different values of time is presented in graphical form and found that velocity for Newtonian fluid has greater values than the second grade fluid. Furthermore, there are some comparisons of calculated solutions with existing solutions in literature.

| S-EPMC7239940 | biostudies-literature

A scientific report on heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate.

Project description: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 of transient and post transient parts. It is found that the post transient parts are independent of time. The solutions corresponding to Newtonian fluids are recovered as a special case and comparison between Newtonian fluid and Maxwell fluid is shown graphically.

| S-EPMC5353556 | biostudies-literature

Unsteady MHD free convection flow of an exothermic fluid in a convectively heated vertical channel filled with porous medium.

Project description:Utilizing porous media in a new mathematical model to improve convective heat transfer characteristics in a variety of applications, such as radiation nuclear disposal storing, evaporation cooling, sieving, geological extraction, crude petroleum refining, and building heating and cooling, is becoming increasingly important. This study proposed a numerical analysis of the unsteady magnetohydrodynamic free convection flow of an exothermic fluid with Newtonian heating. This discovery reveals two types of solutions: steady state and unsteady state. After transforming the governing equation from dimensional form to dimensionless form, the steady state governing equation was solved by the Homotopy Perturbation Method. However, the implicit finite difference approach is used to solve the time-dependent governing equations numerically. The impact of various emerging parameters, namely the Hartmann number, Boit number, Darcy number, Navier slip parameter, and the Frank-Kamenetskii parameter, was discussed and graphically analyzed. During the computations and analysis, it was discovered that a minor rise in the Hartman number results in the Lorentz force, which streamlines the momentum barrier layer and hence slows the fluid flow. The fluid velocity, on the other hand, rose as the porous medium, thermal Biot number, slip parameter, and temperature field increased as the viscous reactive fluid parameter and Newtonian heating increased. The skin friction and Nusselt number were also examined and reported. By comparing the finding to an existing work, a great agreement was revealed.

| S-EPMC9283519 | biostudies-literature

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

Project description: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.

| S-EPMC7070459 | biostudies-literature

Unsteady boundary-layer flow over jerked plate moving in a free stream of viscoelastic fluid.

Project description:This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0 ≤ τ < ∞. Flow properties of the viscoelastic fluid are discussed through graphs.

| S-EPMC4032718 | biostudies-other

Effects of Relative Magnetic Field, Chemical Reaction, Heat Generation and Newtonian Heating on Convection Flow of Casson Fluid over a Moving Vertical Plate Embedded in a Porous Medium.

Project description:The aim of this article is to study the combined effects of heat generation and chemical reaction on magnetohydrodynamic (MHD) natural convection flow over a moving plate embedded in a porous medium. Natural convection is caused due to buoyancy forced which has been induced because of temperature and concentration gradients. The general condition of velocity has been considered on the plate surface with Newtonian heating and constant wall concentration. The effect of thermal radiation is also considered in the energy equation. The main objective here is to study the relative behavior of the magnetic field. That is the magnetic field shows two types of relative behavior. More exactly, when the magnetic field is fixed relative to the fluid (MFFRF) and the magnetic field is fixed relative to the plate (MFFRP). The general exact solution of the problem is determined by the Laplace transform method. Particular solutions for two special cases namely the plate with variable vibration and the plate with sine and cosine oscillations are also determined. Moreover, the solutions when ????? for both cases i.e. MFFRF and MFFRP are also obtained as special cases. The velocity profile is presented in the form of mechanical, thermal and concentration components. Velocity obtained for oscillating plate condition is written in terms of steady-state and transient parts. Exact solutions obtained in this paper are interpreted graphically using computational software Mathcad-15 to examine the effects of various pertinent parameters such as Casson fluid parameter, the permeability of porous medium, chemical reaction parameter, heat generation parameter, buoyancy force parameter, magnetic parameter, and radiation parameter. Results for Sherwood number, skin-friction, and Nusselt number are numerically computed and discussed.

| S-EPMC6344514 | biostudies-literature

Unsteady stagnation-point flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet.

Project description:In this paper, the unsteady stagnation-point boundary layer flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet has been studied. Similarity transformation is used to transform the system of boundary layer equations which is in the form of partial differential equations into a system of ordinary differential equations. The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab. The numerical solutions for the skin friction coefficient and heat transfer coefficient as well as the velocity and temperature profiles are presented in the forms of tables and graphs. Dual solutions exist for both cases of stretching and shrinking sheet. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

| S-EPMC4835756 | biostudies-other

Convection Enhanced Delivery in the Setting of High-Grade Gliomas.

Project description:Development of effective treatments for high-grade glioma (HGG) is hampered by (1) the blood-brain barrier (BBB), (2) an infiltrative growth pattern, (3) rapid development of therapeutic resistance, and, in many cases, (4) dose-limiting toxicity due to systemic exposure. Convection-enhanced delivery (CED) has the potential to significantly limit systemic toxicity and increase therapeutic index by directly delivering homogenous drug concentrations to the site of disease. In this review, we present clinical experiences and preclinical developments of CED in the setting of high-grade gliomas.

| S-EPMC8071501 | biostudies-literature

Investigating Low-Velocity Fluid Flow in Tumors with Convection-MRI.

Project description:Several distinct fluid flow phenomena occur in solid tumors, including intravascular blood flow and interstitial convection. Interstitial fluid pressure is often raised in solid tumors, which can limit drug delivery. To probe low-velocity flow in tumors resulting from raised interstitial fluid pressure, we developed a novel MRI technique named convection-MRI, which uses a phase-contrast acquisition with a dual-inversion vascular nulling preparation to separate intra- and extravascular flow. Here, we report the results of experiments in flow phantoms, numerical simulations, and tumor xenograft models to investigate the technical feasibility of convection-MRI. We observed a significant correlation between estimates of effective fluid pressure from convection-MRI with gold-standard, invasive measurements of interstitial fluid pressure in mouse models of human colorectal carcinoma. Our results show how convection-MRI can provide insights into the growth and responsiveness to vascular-targeting therapy in colorectal cancers.Significance: A noninvasive method for measuring low-velocity fluid flow caused by raised fluid pressure can be used to assess changes caused by therapy. Cancer Res; 78(7); 1859-72. ©2018 AACR.

| S-EPMC6298581 | biostudies-literature

Delay chemical master equation: direct and closed-form solutions.

Project description:The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

| S-EPMC4528653 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data