This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries. Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation. Because of little maintenance, the heat exchanger of such type is extensively used. Here, we generate simulation of flow and heat transfer using non-isothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation (RANS) model of the turbulent flow together with heat equation. Simulation is tested with Prandtl number (Pr = 0.7) with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2 × 10^{5} to 4.4 × 10^{5} with turbulence kinetic energy and the dissipation rate in ranges (3.75 × 10^{−3} to 1.5 × 10^{−2}) and (3.73 × 10^{−3}−3 × 10^{−2}) respectively. Two correlations available in the literature are used in order to check validity. The results are displayed through streamlines, surface plots, contour plots, isothermal lines, and graphs. It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15% to a maximum of 514%. The temperature at the middle shows the consistency in value but declines immediately at the end. This process becomes faster with the decrease in inlet velocity magnitude.

The implication of the circular rings or cylinders in the channel of any shape to execute the efficient heat exchanger is extensively used in the field of engineering, science and industry where the improvement of the heat transfer or heat energy is important or beneficial [

The turbulent flow simulation along with the heat transfer over the circular cylinder was studied by [

The simulation has been expanded to explore the rectangular heat exchanger enclosed by the three circular cylinders of steels for temperature configuration and analysis of fluid flow over these cylinders. The inner radius of all cylinders and thickness is 0.25 [m] and 0.05 [m] respectively. The cylinder at the lower boundary is at the middle of the channel whereas the other two cylinders are placed at 25% and 75% of the total length of the channel at the upper boundary. Air as experimenting fluid is practiced and Flow is considered to be non-isothermal flow where the thermal properties are essentially time and temperature-dependent. For this goal, a rectangular tube is conjectured to have a length of 4 [m] and a height of 1 [m] see _{in} = 232 [K] whereas the three solid circular cylinders are initially kept at constant temperature of T_{p} = 278 [K]. The simulation for such type of fluid flow is based on the questioning to check just for the pattern of velocity field and the temperature distribution on the circular tubes and other variables of interest. The channel is open on the right whereas the pressure is kept zero with stifling the backflow condition. This implies that the fluid and heat can enter and leave from the exit of the channel. Moreover, the symmetrical walls are well insulated.

The selected rectangular channel has been meshed with irregular, triangular and the quad meshes. In _{in}. We achieved excellent results when compared with the available literature.

U_{in} |
Iteration number | u-velocity component and pressure | Heat transfer T | Turbulence variables |
---|---|---|---|---|

71 | 2.73E−06 | 1.70E−06 | 6.35E−06 | |

469 | 8.46E−07 | 9.17E−07 | 6.00E−06 | |

904 | 1.11E−06 | 1.64E−06 | 7.68E−06 |

Turbulent flows are difficult to analyze due to addition of energy terms along with Navier Stokes equations. We might state that the turbulence is another form of energy. Due to the basis of complexity and addition of the energies in the fluid, the simulation through the Navier Stokes equation is controlled by time average quantities. The Reynolds averaged Navier Stokes equation is essential to predict the fluid flow for the turbulence, the idea was given by Osborne Reynolds. The equations are based on the experience for the turbulence flow which divines the approximate solution of the Navier Stokes equation. The equations are acquired with the use of the basic Navier Stokes equations when to write in the Einstein notation in the scalar form:

The derivation of the RANS model is accompanied by the Reynolds decomposition. According to his idea, each variable used to predict the flow can be disintegrated into time-averaged component

Due to the assumption, the fluctuating terms in the RANS model would be omitted. The term in

To examine the heat transfer problem, the governing steady-state heat equation is accompanied by the

The heat transfer coefficient will be computed by the following correlation (a famous Dittus-Boelter equation) for the turbulent flows:

where,

d = Hydraulic Diameter of the channel

k = Thermal conductivity

j = Mass flux of the flow per unit area

The local Nusselt numbers and the local Reynolds numbers will be computed by the formula:

To approve the numerical results obtained with the least Square scheme of the finite element method, the two correlations Bejan et al. [

The current fluid flow problem along with heat distribution is checked by using the turbulent ^{5} to 4.4 × 10^{5} with the turbulent kinetic energy from 3.75 × 10^{−3} to 1.5 × 10^{−2}, dissipation rate from 3.73 × 10^{−3} to 3 × 10^{−2} and with the fixed Prandtl number Pr = 0.7. The air as the effective fluid is inquired with the inlet temperature of 323 [K] and steel cylinders are assumed at temperature of 278 [K]. The fine mesh is practiced to get a better convergence. The model equations of RANS and two-dimensional energy equations are discretized with the finite element scheme. The whole simulation is stocked on Comsol Multiphysics 5.4. The results are confirmed with the two experimental correlations linking local Nusselt number, local Reynolds number, and Prandtl number. The results are delivered with the help of surface plots and streamlines with arrow plots. The motion of the fluid will be described at the middle of the channel for components of velocity field, pressure and the heat distribution. Variation of the temperature on the circle attached at 75% of the length on upper boundary is expressed against the flow rate of the particles, pressure, local Nusselt number and local Reynolds number.

The velocity field streamlines with the arrow and surface plots are exhibited in

u_{in} |
1 | 1.2 | 1.4 | 1.6 | 1.8 | 2 |
---|---|---|---|---|---|---|

U_{min} |
1.70E−06 | 3.06E−06 | 4.43E−06 | 5.93E−06 | 7.40E−06 | 8.48E−06 |

U_{max} |
4.269 | 5.196 | 6.142 | 7.036 | 7.884 | 8.671 |

In

u_{in} |
1 | 1.2 | 1.4 | 1.6 | 1.8 | 2 |
---|---|---|---|---|---|---|

P_{min} |
−0.6434 | −0.7937 | −1.0535 | −1.6152 | −2.4215 | −3.3980 |

P_{max} |
10.4209 | 15.4583 | 21.6638 | 28.4897 | 35.8121 | 43.3500 |

The isothermal contours are exhibited in

u_{in} |
1 | 1.2 | 1.4 | 1.6 | 1.8 | 2 |
---|---|---|---|---|---|---|

Tmin | 300.7608 | 302.3421 | 303.8115 | 305.3100 | 306.6392 | 307.7789 |

Tmax | 323 | 323 | 323 | 323 | 323 | 323 |

In the portion we are working to explain the changing of temperature over the surface circular cylinder attached at 75% of the length of the channel against the velocity magnitude, pressure, local Nusselt number and the Reynolds number see

The convective process is lagging over the surface of the cylinder for each inlet velocity. See

It is to assert that while the fluid is departing the region the whole model of the flow can be analyzed in the best fashion in the middle of the channel. Because the motion of the fluid is adjusted in that circumstantial direction. In the part we are going to perceive the pattern of flow for u and v components of velocity pressure and the temperature at the middle of the channel in terms of presented input velocities see _{in} = 1–2 m/sec, the u-component of velocity is raised while passing the narrow paths enclosed by the three cylinders. It endeavors some optimum values and then declines.

It is also noticeable that the greater the velocity greater the achievement of optimum values of the flow rate over the domain. While inspecting the velocity in y-direction it starts from zero for all given inlet velocities. The y-component of velocity moves in oscillating paths and attempts some minimum values before arriving at the exit of the channel. From

The heat flow with the help of air flow was discussed with the use of non-isothermal interface in the finite-element based software Comsol Multiphysics 5.4 which implements the Reynolds averaged Navier Stokes model for the ^{5} to 4.4 × 10^{5} with the kinetic energy for turbulence in the range from 3.75 × 10^{−3} to 1.5 × 10^{−2} and with dissipation rate in the range 3.73 × 10^{−3} to 3 × 10^{−2}. The cylinders are initially set at the constant temperature 278 [k] and the air is allowed to enter with temperature 323 [K]. The two correlations for the local Nusselt number were compared with the present work and concluded that our numerical results with the good convergence are in good agreement with the experimental results about 20% of the error. The results are presented for streamlines with surface plots of the velocity field, contours for pressure and isothermal lines for temperature distribution over the surface. The course of the temperature was also expressed in terms of velocity magnitude, pressure local Nusselt number and Reynolds number at the upper boundary of the last circle for inlet velocities. At the middle of the channel the velocity components, pressure and temperature were expressed against the length of the channel. We write the following findings from the simulation.

The discussion of the streamlines pattern and the surface plots indicated that the velocity magnitude is increasing in the range of 333.5% to 514% and due to such arrangement of the cylinders creates the more hydraulic jumps to accelerate the fluid motion. The Rapid variation in the pressure can be seen in the region which is surrounded by the cylinder. For the current problem of the turbulent flow quick distribution of the temperature was seen in the domain.

When to express the distribution of the temperature over the circular cylinder against velocity it is found that temperature is maximum at the middle of the cylinder. With the increase in the pressure the temperature of the cylinder is increasing for each input velocity. The range of the pressure is also increasing with the increase in input velocity field. Temperature on the surface of the circular cylinder declines due to increase in local Nusselt number as well as the Reynolds number for each input velocity. But for each input velocity the range for local Reynolds number as well as the local Nusselt number is increased.

Since the channel is horizontal therefore the x-component of the velocity plays a major role in developing the flow at the start of the channel in the middle line and increase in magnitude during the whole flow. Whereas the y-component of the velocity is starting from zero position and remain fluctuate in the domain. The pressure at the middle line is increasing with inlet velocity magnitude and will be zero at the exit of the channel. The temperature in the middle line remains at the same value given at the inlet and declines quickly before reaching at the domain.

Authors are very much thankful to Sukkur IBA University, Sukkur, Pakistan for providing conducive environment for research.

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