Mahmoud A. Ismail^a, Shadia Fathi Mohamed El Sherif ^a , A. A. El-Bary^b,*, Hamdy M. Youssef^c

Frontiers in Heat and Mass Transfer, Vol.14, pp. 1-7, 2020, DOI:10.5098/hmt.14.3

Abstract In this paper we will discuss the problem of distribution of thermal stresses and temperature in a generalized magneto–thermo-viscoelastic solid spherical cavity of radius R according to Green- Naghdi (G-N II) and (G-N III) theory. The surface of the cavity is assumed to be free traction and subjected to a constant thermal shock. The Laplace transform technique is used to solve the problem. The state space approach is adopted for the solution of one dimensional problem. Solution of the problem in the physical domain are obtained by using a numerical method of MATLAP Programmer and the expression for the temperature,… More >

Alaa K. Khamis^a , Allal Bakali^a, A. A. El-Bary^b,c,*, Haitham M. Atef^d

Frontiers in Heat and Mass Transfer, Vol.15, pp. 1-6, 2020, DOI:10.5098/hmt.15.24

Abstract In this paper the effect of the magnetic field and Seebeck parameter was investigated. Modified Ohm's law that includes effects of the temperature gradient (Seebeck effect More >

Najat A. Alghamdi¹, Hamdy M. Youssef^2,3,*

FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.5, pp. 597-611, 2019, DOI:10.32604/fdmp.2019.05131

Abstract A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity. A generalized set of governing equations is formulated in the context of three different models of thermoelasticity: the Biot model, also known as “coupled thermoelasticity” model; the Lord-Shulman model, also referred to as “generalized thermoelasticity with one-relaxation time” approach; and the Green-Lindsay model, also called “generalized thermoelasticity with two-relaxation times” approach. The Adomian’s decomposition method is used to solve the related mathematical problem. The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain. Numerical results for the temperature,… More >

Tai C. Lee¹, Huan J. Keh²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 317-333, 2013, DOI:10.3970/cmes.2013.093.317

Abstract A theoretical study of the thermocapillary migration of a fluid sphere located at an arbitrary position inside a spherical cavity is presented in the quasisteady limit of small Reynolds and Marangoni numbers. The applied temperature gradient is perpendicular to the line through the drop and cavity centers. The general solutions to the energy and momentum equations governing the system are constructed from the superposition of their fundamental solutions in the spherical coordinates originating from the two centers, and the boundary conditions are satisfied by a multipole collocation method. Results for the thermocapillary migration velocity of the drop are obtained for… More >

A. Sellier¹

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.3, pp. 165-180, 2008, DOI:10.3970/cmes.2008.025.165

Abstract The slow viscous and either imposed or gravity-driven migration of a solid arbitrarily-shaped particle suspended in a Newtonian liquid bounded by a spherical cavity is calculated using two different boundary element approaches. Each advocated method appeals to a few boundary-integral equations and, by contrast with previous works, also holds for non-spherical particles. The first procedure puts usual free-space Stokeslets on both the cavity and particle surfaces whilst the second one solely spreads specific Stokeslets obtained elsewhere in Oseen (1927) on the particle's boundary. Each approach receives a numerical implementation which is found to be in excellent agreement with accurate results… More >