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Entropy generation analysis of a steady fluid flow with internal heat generation between two rotating cylinders was presented. The surface of the inner cylinder was kept at constant temperature while the surface of the outer cylinder was exposed to convection cooling. Analytical expressions for velocity and temperature distributions within the fluid were obtained. The effects of velocity ratio, Biot number, Brinkman number and other dimensionless parameters on the temperature distribution and local and total entropy generation rates were investigated and the results were presented graphically.

Heat transfer analysis in annuli with rotating inner and outer cylinders is an important research field and has a wide range of many engineering applications such as swirl nozzles, commercial viscometers, journal bearings, chemical mixing devices, and electric motors.

Entropy generation and its minimization have been considered as an effective tool to improve the performance of any heat transfer process. Entropy generation minimization of diabatic distillation column with trays has been investigated using a new approach [

Entropy generation analysis in an annuli flow with inner cylinder at rest, and rotating outer cylinder has been presented [

As can be seen from the above research works related to annular flow between two rotating cylinders, the effect of internal heat generation on local and total entropy generation rates has not yet been investigated in the literature and this study is considered as a first approach to consider that effect.

In this section, We developed a mathematical model for the flow and thermal characteristics of a fluid between two rotating cylinders which rotate in the same direction. The schematic diagram of the physical problem is illustrated in Figure

Schematic diagram of concentric rotating annuli.

Under the above flow conditions, the momentum equation can be written as

The energy equation of the fluid with internal heat generation between the two rotating cylinders can be expressed as

The local entropy generation rate due to fluid temperature gradient and fluid friction (viscous dissipation) is given as [

Entropy generation of a steady fluid flow with internal heat generation between two rotating cylinders is presented for different parameters. The tangential velocity profiles along the radial direction for the radius ratio (

Velocity distribution ((a)

The dimensionless temperature distributions of the rotating fluid as function of

Temperature distribution ((a)

Temperature distribution ((a)

Temperature distribution ((a)

The effect of Biot number on the fluid temperature distribution as function of

The maximum temperature is an important factor because the contribution of thermal effect on entropy generation will be equal to zero at that maximum value. Figures

The variations of local entropy generation number

Local entropy generation number distribution ((a)

Local entropy generation number distribution ((a)

Local entropy generation number distribution ((a)

Local entropy generation number distribution ((a)

Figures

Effect of

Effect of

Effect of

Effect of

A mathematical model of a fluid with internal heat generation between two rotating cylinders has been developed for velocity, temperature, local entropy generation rate, and total entropy generation rate. It has been proved that the local and the total entropy generation rates have minimum values for all the parameters considered in this work. It is concluded that decreasing Brinkman number, increasing Biot number, decreasing the internal heat generation, and increasing the temperature ratio

Cross-sectional area (

Biot number

Brinkman number

Specific heat capacity (

Constant (

Constant (

Constant (

Eckert number

Cylinder length (m)

Entropy generation number

Dimensionless total entropy generation rate

Internal heat generation (

Dimensionless internal heat generation

Prandtl number

Radial distance (m)

Dimensionless radial distance

Total entropy generation rate (

Local entropy generation rate (

Temperature ratio

Temperature (K)

Tangential velocity (

Dimensionless velocity

Velocity ratio

Radius ratio.

Convective heat transfer coefficient (

Viscous dissipation function (

Thermal conductivity (

Dynamic viscosity (

Dimensionless temperature

Angular velocity (

Inner cylinder surface

Outer cylinder surface

Coolant at the outer cylinder surface.