H. M. Badr

Unsteady flow past a rotating circular cylinder at Reynolds numbers 10 3 and 10 4

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier-Stokes equations, while the experimental investigation is based on visualisation of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier-Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Laminar combined convection from a horizontal cylinder—Parallel and contra flow regimes

Abstract The laminar combined convection heat transfer from an isothermal horizontal circular cylinder is studied for the two cases when the forced flow is directed either vertically upward (parallel flow) or vertically downward (contra flow). The investigation is based on the solution of the full vorticity transport equation together with the stream function and energy equations. The velocity and thermal boundary layers are developed in time until reaching steady conditions. The variations of vorticity and Nusselt number are obtained over all the cylinder surface including the zone beyond the separation point. The predicted values of the average Nusselt number are compared with the available experimental data and the agreement is satisfactory. The streamline and isotherm patterns are plotted for several cases to show some of the flow field characteristics.

A theoretical study of laminar mixed convection from a horizontal cylinder in a cross stream

Abstract The problem of laminar mixed convection from a horizontal isothermal cylinder is considered. The free stream direction is assumed to be horizontal and perpendicular to the cylinder axis. The study is based on the solution of the full Navier-Stokes and energy equations for 2-dim. flow of a Boussinesq fluid. The free stream is assumed to start impulsively from rest and the velocity and thermal boundary layers are developed in time until reaching steady conditions. The investigation covered the ranges of Reynolds number 1

Flow Structure in the Wake of a Rotationally Oscillating Cylinder

The characteristics of the flow in the wake of a circular cylinder performing rotational oscillation about its own axis and placed horizontally in a cross-stream is investigated. The governing equations based on stream function-vorticity formulation are solved numerically to determine the flow field structure. The parameters dominating flow structure are Reynolds number, Re, amplitude of oscillation, Θ A and frequency ratio F R =S/S 0 where S is the forcing frequency and S 0 is the natural frequency of vortex shedding. The ranges considered for these parameters are 40≤Re≤200, 0≤Θ A ≤π and 0≤F R ≤2. The lock-on phenomenon has been predicted and its effect on the flow hydrodynamics has been determined. The lock-on phenomenon is found to occur within a band of frequency encompassing the natural frequency. This band, however, becomes wider as the amplitude of oscillation increases

Forced convection from a rotationally oscillating cylinder placed in a uniform stream

Abstract Forced convection from a heated cylinder performing rotational oscillation about its own axis and placed in a uniform stream is investigated. The governing equations of motion and energy are solved numerically to determine the flow field characteristics and the heat transfer coefficients. The main dominating parameters are Reynolds numbers, Re , Prandtl number, Pr , amplitude of oscillation, Θ A , and the frequency ratio, F R , which represents the ratio between the frequency of oscillation, f , and the natural frequency of vortex shedding, f 0 . The ranges considered for these parameters are 40≤ Re ≤200, 0≤ Θ A ≤ π and 0≤ F R ≤2, while the Prandtl number is kept constant at 0.7. The lock-on phenomenon has been detected and its effect on the thermal field has been determined. The results show that the lock-on phenomenon occurs within a band of frequency near the natural frequency and the heat transfer coefficient has shown appreciable increase in the lock-on frequency range.

Combined convection from an isothermal horizontal rod buried in a porous medium

Abstract This paper reports the results of a numerical investigation of mixed convection heat transfer from a horizontal rod of circular cross-section that is embedded in a porous medium. The rod temperature is first assumed to be the same as that of the medium and then suddenly increased to a higher constant value. The steady-state problem has been solved by the method of series truncation in combination with a finite-difference scheme for the two flow configurations of parallel and counter-flow regimes. The flow and thermal fields as well as the variations of the average and local heat transfer rates with a wide range of Reynolds number, Grashof number and buoyancy parameter have been examined in detail for a Prandtl number of 0.7. One of the interesting features found is the occurrence of a recirculating flow zone near the upper half surface of the rod in the case of the counter-flow regime. The numerical method and the results presented fill in a gap in the literature on one of the most fundamental problems in the field of mixed convection in porous media.

Laminar forced convection from a rotating cylinder

Abstract The problem of laminar forced convective heat transfer from an isothermal circular cylinder rotating about its own axis and placed in a uniform stream is considered. The direction of the forced flow of the cooling fluid is assumed to be normal to the cylinder axis. The study is based on the solution of the unsteady two-dimensional conservation equations of mass, momentum and energy. The problem is solved for Reynolds number (based on the free stream velocity) up to Re = 100 and for velocity ratios (ratio between cylinder circumferential velocity and free stream velocity) up to α = 4. Major emphasis is given to the effect of the speed of rotation on the thermal boundary layer geometry and also on the local Nusselt number distribution.

Laminar natural convection from an elliptic tube with different orientations

The problem of two-dimensional natural convection heat transfer from a straight tube of elliptic cross section is investigated. The tube, which has an isothermal surface, is placed with its axis horizontal in an initially quiescent fluid of infinite extent. The velocity and thermal fields are obtained by studying the time development of these fields following a sudden increase of the tube surface temperature until reaching steady state. The study is based on the solution of the full conservation equations of mass, momentum, and energy with no boundary layer simplifications. The paper focuses on the effects of the tube orientation, axis ratio, and Rayleigh number while keeping the Prandtl number unchanged ( Pr = 0.7). The study revealed that the maximum average Nusselt number is obtained when the tube major axis is vertical. Within the range of axis ratios considered (Ar = 0.4 to 0.98), smaller Ar resulted in higher heat transfer rate in most cases. Higher Rayleigh number leads to higher velocities and also higher local and average Nusselt numbers in all cases considered. The details of the steady flow and thermal fields are presented in the form of local Nusselt number and surface vorticity distributions as well as streamline and isotherm patterns for some selected cases

Free convection from an elliptic cylinder with major axis vertical

Abstract The problem of free convection heat transfer from a horizontal elliptic cylinder placed with its major axis vertical in a fluid of infinite extent is investigated. The investigation is based on the solution of the conservation equations of mass, momentum, and energy. The problem is solved for Rayleigh numbers ranging from 10 to 1000 and for a constant value of Prandtl number ( pr = 0.7 ). The cylinder axis ratio (minor to major) varies from 0.1 to 0.964 approaching a flat plate at one end and a circular cylinder at the other. Results are presented for the local and average Nusselt numbers along with details of the thermal and velocity fields given in the form of isotherm and streamline patterns. The method of solution is validated by comparing results with the available theoretical and experimental data for the circular cylinder and the flat plate as limiting cases.

Mixed convection from a straight isothermal tube of elliptic cross-section

Abstract The problem of laminar mixed (natural and forced) convective heat transfer from a straight isothermal tube of elliptic cross-section placed in a uniform stream is investigated. The free stream direction is horizontal and normal to the tube axis and the flow field is essentially two-dimensional. The investigation is based on a numerical solution of the conservation equations of mass, momentum, and energy. The resulting velocity and thermal fields both are found to be either steady or quasi-steady depending on vortex shedding. The parameters involved are the Reynolds number, Re , Grashof number, Gr , Prandtl number, Pr , the tube geometry represented by its axis ratio (minor to major), A r , and its orientation represented by its angle of inclination, λ. The study focuses on the effects of Re , Gr , and λ on the heat transfer process in the Re range from 20 to 500, Gr range from 0 to 1.25 × 10 6 and for angles of inclination varying from 0° to 180°. The average Nusselt number is found to increase considerably with the increase of the ratio Gr Re 2 . The response of the total rate of heat transfer to changes in the inclination angle is found to depend on the Reynolds number. The results also indicate that the increase of Gr for a given value of Re tends to suppress vortex shedding. The details of the velocity and thermal fields are presented in the form of isotherm and streamline patterns in addition to the surface vorticity and local Nusselt number distributions.