The unsteady mixed convection flow within a vertical concentric cylindrical annulus with Time-dependent moving walls is investigated. Fluid is suctioned/injected through the cylinder walls of the annulus. The effects of wall movement on flow and heat transfer characteristics inside the cylindrical annulus are sought. An exact solution of Navier-Stokes and energy equations is obtained in this problem, for the fi rst Time. Here, the heat transfer occurs from the walls of the hot cylinder with constant temperature to the moving fluid with a cooling role. It is interesting to note that the results indicate that the Time-dependency of cylinder wall movements has no effect on the temperature pro le. The results also indicate that usage of an inverse of Time for velocity movement causes a signifi cant increase in velocity, stress tensor, and Nusselt number in the vicinity of the moving wall. Also, increasing the mixed convection and suction/injection parameters increases the Nusselt number and decreases the stress tensor on the inner and outer cylinders, respectively; no matter what velocity function is chosen for the moving wall. Therefore, using the velocity function of the wall movement and the change in other nondimensional governing parameters, flow and heat transfer can be controlled.

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an ‎infinite moving cylinder with Time=dependent axial velocity is investigated. The ‎impinging free stream is steady with a strain rate k. An exact solution of the Navier-‎Stokes equations is derived in this problem. A reduction of these equations is obtained ‎by use of appropriate transformations. The general self-similar solution is obtained ‎when the axial velocity of the cylinder varies as specified Time-dependent functions. ‎In particular, the cylinder may move with different velocity patterns. For ‎completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations ‎have been obtained numerically using a finite-difference scheme. These solutions are ‎presented for special cases when the Time-dependent axial velocity of the cylinder is a ‎step-function, a ramp, and a non-linear function. All the solutions above are ‎presented for Reynolds numbers, Re=ka^2/2n#, ranging from 0.1 to 100 where a is ‎cylinder radius and n# is kinematic viscosity of the fluid. Shear stresses corresponding ‎to all the cases increase with the Reynolds number. The maximum value of the shear ‎stress increases with increasing oscillation frequency and amplitude. An interesting ‎result is obtained in which a cylinder moving with certain axial velocity function and ‎at particular value of Reynolds number is axially stress-free‏.‏

In the present study, the conjugate turbulent free convection with the thermal surface radiation in a rectangular enclosure bounded by walls with different thermophysical characteristics in the presence of a local heater is numerically studied. The effects of surface emissivity and wall materials on the air flow and the heat transfer characteristics are the main focus of the present investigation. The conjugate convective heat transfer for the fluid (air), described in terms of linear momentum, continuity, and energy equations combined with k-ε turbulence model, is predicted by using the finite difference method. The results for the isotherms, streamlines, and average Nusselt numbers along the heat source are presented. The numerical experiments show that an increase in thermal conductivity of solid walls illustrates the enhancement of heat transfer. Eventually, the main result obtained in this work provides a good technical support for the development and research of energy-efficient building materials.

Effect of Time dependent normal transpiration Uo (t) on the problem of unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder moving simultaneously with Time-depended angular and axial velocities and with Time-dependent wall temperature or wall heat flux are investigated. The impinging free stream is steady with a strain rate `k. A reduction of Navier-Stokes equations and energy equation is obtained by use of appropriate transformations. The general semi-similar solutions are obtained when angular and axial velocities of the cylinder and also its wall temperature or its wall heat flux vary as certain functions of Time. The cylinder may perform different types of motions. It may move or rotate with constant speed, with exponentially increasing/decreasing axial/angular velocity, with harmonically varying axial/angular speed, or with accelerating/decelerating oscillatory axial/angular speed. The cylinder surface temperature or its surface heat flux may have the same type of behavior as the cylinder motion. Semi-similar solutions of the unsteady Navier-Stokes and energy equations are obtained numerically using a finite-difference scheme. All the solutions above are presented for different Reynolds numbers (Re=`ka2/2u) and different functions of dimensionless transpiration rate, S(t)=Uo (t)/(`ka), where a is cylinder radius and u is kinematic viscosity of the fluid. Shear stresses corresponding to all the cases increase with the increase of Reynolds number and decrease with the increase of suction rate. The maximum value of shear stress increases with increase of oscillation frequency and amplitude. An interesting result is obtained in which a cylinder moving with certain angular/axial velocity function and at particular values of Reynolds number is azimuthally/axially stress-free. Heat transfer rate increases with the increase of the rate of suction, Reynolds number, and Prandtl number. Interesting means of heating and cooling processes of cylinder surface are obtained using different rate of transpiration.

The present study is the first to analyze the dynamic response of a poroelastic beam subjected to a moving force. Moreover, the influences of attached mass-spring systems and non-ideal supports (with local movements in the supporting points or base due to the presence of factors such as gaps, unbalanced masses, and friction or seismic excitations) on the responses were investigated. Non-ideal support experiences Time-dependent deflection and moment. To evaluate the effects of both the theory type and the material properties, three models were investigated for the beam with mass-spring attachment and non-ideal supports: i) elastic Euler-Bernoulli-type beam, ii) elastic Timoshenko-type beam, and iii) poroelastic beam. The governing-coupled PDE equations of the forced vibration of the saturated poroelastic beam were analytically solved via Laplace and finite Fourier transforms. The effects of various parameters on the responses were investigated comprehensively and illustrated graphically. The poroelastic nature of the material properties was found to attenuate the vibration amplitude, and it is assumed that the attached mass can considerably affect the vibration pattern.

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite moving plate with transpirationW0 are investigated when the axial velocity and wall temperature vary arbitrarily with Time. The free stream is steady and with a strain rate of a. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also Time-dependent, but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the plate and its wall temperature vary as specified Time-dependent functions. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite difference scheme. All the solutions above are presented for different values of dimensionless transpiration rate, S=W0/Öau, where u is the kinematic viscosity of the fluid. The effects of the sundry parameters, including transpiration rate, Prandtl number, oscillation frequency and accelerating/decelerating parameter, on the velocity and temperature profiles, as well as surface shear stresses and heat transfer coefficient, are investigated and results are shown through graphs.

In this work, we investigate a Timedependent dissipative scalar field. Inspired by the Bateman lagrangian, we showed a procedure for quantizatizing the massive scalar field with the Time-dependent dissipative term. So, the properties of a quantum dissipative scalar field are analyzed by the Caldirola-Kanai model. Also, we construct the Hilbert space for the system and calculate the wave eigen-functions and probability distribution of the system.