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This paper performs a simulation study of the heat transfer phenomena in a tubular U-loop pipe. We have investigated the enhancement of heat transfer with mass flow in a pipe without insert, with full length and short length twisted tape inserts. The length of the pipe is approximately 2436.80 mm long with 29 mm inner and 33 mm outer diameter respectively. A constant heat flux is taken which generated the boundary layer of the pipe close to the flowing fluid around the boundary. The simulations are considered for the stationary and the time dependent module for 35 seconds with different length of inserts. The comparisons are made among the results. We observed that the transfer of heat is enhanced significantly with the increase of the length of inserts inside the computational domain. We also found that, full length twisted tape inserts are more effective than comparing with the short length inserts and without insert.

The enhancement of heat transfer is the method of developing the performance of heat transfer device. There exist two methods to improve the enhancement of heat transfer. One is active method and another is passive. Both of them are used for augmentation of laminar flow heat transfer [

In the year 1896, Whitham studied about the twisted tape inserts in fire tubes of stream boilers and their effects in the flow dynamics and heat got an expected satisfactory result [

In the year 2009, Rahimi et al. reported computational and experimental investigation of the three modified twisted tapes (perforated, notched and jagged tape) and suggested that this jagged twisted tape gives higher thermal performance comparing to the other two types [

In the above discussion we have found that numerous studies are performed about the heat transfer enhancement through the circular tube with different geometrical configurations for laminar flow. However, none of the studies report about the heat transfer augmentation and pressure drop in the tubular pipe with different twisted tape inserts. A non-isothermal flow form is well selected for the simulation. The important effort to utilize different methods is to increase the heat transfer rate by using different kinds of inserts. In the intervening time, it is established that, this way can diminish the manufacturing cost and save up the energy.

In this paper, our main goal is to present the heat transfer phenomena in a circular pipe using inserts by the Finite Element Method. The Finite Element Method (FEM)-based software COMSOL Multiphysics 4.2a version is used for this numerical study [

The rest of the paper is prepared as follows: In Section 2, mathematical model is presented while governing equations of heat transfer flow in Section 3; Boundary conditions for the domain is given in Section 4; Computational domain and the mesh design of the domain are presented in Section 5; In Section 6, numerical results for the heat transfer phenomena is shown followed by conclusion in Section 7.

The aim of this study is to get better performance of the enhancement of heat transfer in a tubular U-loop pipe using different twisted tape inserts. Our model has been conscious as the geometry forms across the flow which enhances the heat transfer. The purpose of using inserts in our model is to increase layer to layer friction and presence of the inserts promotes enhanced heat transfer due to mixing.

In this model we consider the heat transfer phenomena from side to side a U-loop tubular pipe. Thus we have preferred the physics, as non-isothermal laminar flow. In this physics heat flows by conduction, convection via flowing fluid it can be referred as both transportation of heat and mass. The governing equations which describe the flows are the Continuity equation and the Navier-Stokes equations given below:

∂ ρ ∂ t + ∇ ⋅ ( ρ u ) = 0 (1)

ρ ∂ u ∂ t + ρ ( u ⋅ ∇ ) u = ∇ ⋅ [ − P I + λ ] + F (2)

It also solves the heat transfer through a fluid and governed by the following equation:

ρ C p ( ∂ T ∂ t + ( u ⋅ ∇ ) T ) = − ( ∇ ⋅ q ) + τ : S − T ρ ∂ ρ ∂ t | p [ ∂ ρ ∂ t + ( u ⋅ ∇ ) p ] + Q (3)

where,

S = 1 2 ( ∇ u + ( ∇ u ) T ) (4)

And Q contains heat source other than viscous heating (SI unit: W/m^{3}). For obtaining the heat transfer term used Fourier law of heat conduction, the convective heat flux; q is proportional to the temperature gradient.

q i = − K ∂ T ∂ x i (5)

where K is the thermal conductivity can be an isotropic and K becomes a tensor. The convective heat flux is given by

q i = − ∑ j K i j ∂ T ∂ x i

The term τ : S represents viscous heating of a fluid can be written on the following form:

τ : S = ∑ n ∑ m τ n m τ m n

The term T ρ ∂ ρ ∂ t | p [ ∂ ρ ∂ t + ( u ⋅ ∇ ) p ] represents a pressure work is responsible

for the heating of a fluid under adiabatic compression and for some thermo acoustic effects. By using the Equations (3) and (4) we can find

ρ C p ∂ T ∂ t + ρ C p ( u ⋅ ∇ ) T = − ∇ ⋅ ( K ∇ T ) + Q (6)

If the velocity is to zero the equation becomes

ρ C p ∂ T ∂ t − ∇ ⋅ ( K ∇ T ) = Q (7)

Convective heat transfer coefficient is obtain from

h = Q T w − T b (8)

where T_{w} and T_{b} are the wall and bulk temperature, where T b = T o u t + T i n 2 .

Nusselt number is calculated by

N u = h D k (9)

D is the diameter of the tube.

Thermal performance is calculated as

η = h s h p (10)

where η is the thermal performance and h_{s}, h_{p} and h_{f} are the heat transfer for short length, plain tube and full length inserts heat transfer coefficient respectively.

In the study, the boundary conditions are assumed an uniform velocity i.e. u = u i n = 0.07 m / sec at the inlet, and the temperature of the fluid is T = T i n = 293.15 K , the no slip condition i.e. u = 0 at the inner wall of the tube and the laminar outflow at the outlet of the domain governed by the following equation:

L o u t ∇ t [ − P o u t I + μ ( ∇ t u + ( ∇ t u ) T ) ] = − P o u t n , ∇ t u = 0 (11)

A design of computational domain without insert, with short length twisted tape inserts and full length twisted tape inserts are shown in Figures 1(a)-(e). In our simulation we have considered a typical U-loop circular tube whose length is 2436.80 mm, inner diameter 29 mm, outer diameter 33 mm. To reach a satisfactory computational exactness we continually change the mesh design until the outcomes obtained. The Mesh element becomes higher near the inserts positions have shown in Figures 2(a)-(c). A comparison of mesh design among different insert combinations has shown in the

The main intention of our study is to ensure the enhancement of heat transfer phenomenon in a U-loop tubular pipe for a non-isothermal laminar flow. The total time taken for the simulation was 35 seconds in the time dependent study. For this investigation the tube thickness is neglected and the boundary conditions for the tube are being measured a uniform heat flux adjoining the water domain layer. As we have only given attention on improving the heat transfer

rate by considering the flowing fluid thus we ignored the flow heat in the solid tube.

To realize the effect of inserts in to the heat transfer phenomenon, we carried out the simulations by varying the twisted tape inserts. The temperature distributions plot for water domain with move view has shown in

To investigate the results we put the initial temperature at the inlet 293.15 k. From our simulation we observed that the outlet temperature is 368.63 k for without insert, for the short length twisted tape inserts we found outlet temperature is 496.01 k which is better than the without insert. Finally we observed for the full length inserts and found the outlet temperature is 502.47 k. We can conclude that, the full length inserts done better than the other two types of inserts.

Figures 3(a)-(c) describe the above temperature.

In the position of 500 mm, The fluid temperatures are found the without insert after 15 sec, 25 sec, 35 sec are 333.6 k, 348.45 k, and 357.43 k respectively. Again for the short length twisted tape inserts and full length twisted tape inserts temperature after 15 sec, 25 sec, and 35 sec are 403.14 k, 426.63 k, and 443.26 k, for short length twisted tape inserts 412.6 k, 440.38 k, and 458.44 k respectively for full length twisted tape inserts. It is very clear that, full length twisted tape inserts gives better heat transfer rate compare with the other design which are shown in the Figures 4(a)-(c) for without insert Figures 4(d)-(f) for short length twisted tape inserts and Figures 4(g)-(i) for full length twisted tape inserts respectively. Again, in the position of 500 mm, changing the mesh design

we found the temperatures for without insert after 15 sec, 25 sec, 35 sec are respectively 344.92 k, 366.52 k, 379.52 k and for the short length twisted tape inserts and full length twisted tape inserts temperature after 15 sec, 25 sec, 35 sec are 415.24 k, 474.08 k, 504.66 k for the short length twisted tape inserts 429.76 k, 513.19 k, 539.68 k for the full length twisted tape inserts. This is shown in the Figures 5(a)-(c) for without insert Figures 5(d)-(f) for short length twisted tape inserts and Figures 5(g)-(i) for full length twisted tape inserts respectively. The

A computational study of heat transfer phenomenon of a fluid flow through a tubular pipe with inserts and without insert for a non-isothermal laminar flow has been studied. A typical U-loop circular tube with inserts and without insert is considered for our simulation. The working fluid is considered as water in our study and the initial temperature is assumed at the inlet is 293.15 k. The total time taken for the simulation was 35 seconds in the time-dependent study. The temperature distributions at the inserts position have been described. In this investigation, we found that the tube with inserts enhanced significant amount of heat than the without insert. Moreover, the full length twisted tape inserts gives the better results than the short length twisted tape inserts and without insert.

The authors gratefully acknowledge the technical supports provided by the Centre of Excellence in Mathematics, Department of Mathematics, Mahidol University, Bangkok 10400, Thailand.

Bhuyan, M.M., Deb, U.K., Shahriar, M. and Acherjee, S. (2017) Simulation of Heat Transfer in a Tubular Pipe Using Different Twisted Tape Inserts. Open Journal of Fluid Dynamics, 7, 397-409. https://doi.org/10.4236/ojfd.2017.73027