International Journal of Engineering and Applied Physic

The aim of the current research is to evaluate the flow characteristics and heat transfer enhancement in a circular hose having a diameter of 12.5 mm and 1500 mm Length subjected to a constant solar heat flux of (1000 W/m2) using numerical simulation. The study evolves the changing Reynolds numbers (5000 &lt;Re &lt; 10500) and its effect on the Nusselt number during variable flow rate conditions from 0.45 m/sec to 0.90 m/sec. The heat transfer phenomenon was evaluated during controlled conditions with working fluid as water. The results obtained from numerical investigations were studied to understand the flow and heat transfer enhancement, Nusselt number phenomenon, outlet temperature, and fluid fully developed region. State the most important part of your findings and achievement

Chaudhari, Chandan

V.Chavan, Kaustubh

   
 
 
     90 
  
Journal homepage: https://ijeap.org/ 
International Journal of Engineering and Applied Physics (IJEAP) 
Vol. 1, No. 2, May 2021, pp. 90~95 
ISSN: 2737-8071 
 
 
 
Chandan D. Chaudhari
1
, Kaustubh V. Chavan
2
 
1,2Dept. of Mechanical Engineering, SIES Graduate School of Technology, University of Mumbai, India 
 
 
Article Info  ABSTRACT  
 
Received Jan 19, 2021 
Revised Apr 14, 2021 
Accepted Apr 20, 2021  
            The aim of the current research is to evaluate the flow characteristics 
and heat transfer enhancement in a circular hose having a diameter of 12.5 
mm and 1500 mm Length subjected to a constant solar heat flux of (1000 
W/m2) using numerical simulation. The study evolves the changing 
Reynolds numbers (5000 < Re < 10500) and its effect on the Nusselt number 
during variable flow rate conditions from 0.45 m/sec to 0.90 m/sec. The heat 
transfer phenomenon was evaluated during controlled conditions with 
working fluid as water. The results obtained from numerical investigations 
were studied to understand the flow and heat transfer enhancement, Nusselt 
number phenomenon, outlet temperature, and fluid fully developed region. 
State the most important part of your findings and achievements 
Keywords: 
Nusselt Number 
Solar flux 
Computational Fluid Dynamics 
Reynolds Number 
Heat transfer augmentation 
 
 
This is an open access article under the CC BY license. 
 
Corresponding Author: 
Prof. Chandan D. Chaudhari,  
SIES Graduate School of Technology,  
Mumbai, India. 
Email: chaudhari.chandan22@gmail.com 
 
1. INTRODUCTION  
The heat transfer augmentation has been urbanized and extensively advantageous in heat exchanger 
applications over the past decade in numerous submissions which may include refrigeration sector, 
automotive, process industries, nuclear reactors technologies, and solar technologies etc. [1,2]. There have 
been many attempts made by researchers to enhance the heat transfer with diminishing the size and the costs 
of the heat exchangers. The most protruding factors analyzed such as heat transfer coefficients and pressure 
drop, which generally lead to reduction of capital cost [3]. Energy is one of the important concerns for 
sustainable development for developing countries like India. The ample availability and truncated cost are the 
two tactical advantages of solar energy [4]. As solar energy is an imperative portion of renewable energy 
sources; to overcome energy difficulties issues, solar energy can be used with different configuration of 
collectors such as flat plate collector, heliostat field and compound parabolic collectors etc. For efficient 
energy conversion process, exact position of the receiver is required since It depends upon the various 
parameters such as ambient temperature, fluid inlet temperature, heat flux, working fluid, receiver material, 
fluid flow rate, surface friction between working fluid and receiver material, reflector material etc [7].  Many 
heat transfer improvement methods were examined and designated by various researchers in past decades. 
Although abundant studies have been investigated the thermal performance of solar receivers, the effect of 
water and other fluids with variable Nusselt number and Reynolds number during constant heat flux 
condition to advance thermal performance of the receiver is not available in the literature. The Nusselt 
number (NU) is found as the function of Reynold number and Prandlt number respectively this function 
based on energy and momentum transfer analogies to calculate heat transfer coefficient in pipe for turbulent 
flow Dittus-bolter equation expressed in Equation 2. Here exponent term associated with Prandlt number 
used 0.4 which is used for heating of fluid. For Uniform Heat Flux (UHF) for pipe domain with turbulent 
Article history:
Simulation of heat transfer augmentation during constant solar 
heat flux in circular pipe
Int J Eng & App Phy ISSN: 2737-8071  
 
Simulation of heat transfer augmentation during constant solar heat flux in circular pipe (C. D. Chaudhari) 
91 
flow regime approximately thermal entry length would be ten times of the hydraulic diameter of the pipe 
domain. Research found that thermal entry length is 115 mm. The length of pipe section must be considered 
as per the standard norms i.e. L/D> 60. 
 
2. SIMULATION METHOD  
The following are the basic assumptions considered for the Numerical Simulation. The assumptions are listed 
for Numerical analysis: 
 Condition of heat transfer: - Stead State 
 Flow behavior of fluid in receiver: - Uniform with Fully developed condition. 
 Fluid Nature: - Incompressible condition. 
 Velocity Inlet and Outflow boundary Condition,  
 Semi Implicit Pressure Linked Equations (SIMPLE) scheme is used 
 
2.1 Geometric Aspects: The Commercial software was used for geometry creation and modeling. The 2D 
fluid geometry modeled was considered for analysis for simplicity since it can be validated easily. The 
Length of pipe is 1500 mm, diameter of 12.5 mm. The meshing of the geometry is done by use of the ICEM 
tool. The figure. 1 shows computation domain model with mesh. 
 
 
 
Figure 1: Meshing of Pipe Domain 
 
The physical properties of water are considered for the numerical simulation and listed as shown in Table 1. 
 
Table 1. Thermal properties of working fluid (water) 
Properties Water 
Density  998.2 (kg/m3) 
Specific heat  4182 (J/kg.K) 
Viscosity  0.001003 (kg/m·s) 
Thermal conductivity  0.6 (W/m.K) 
  
 
2.2 Meshing Approach for Modeling:  The CFD analysis is carried out with uniform heat flux. In presented 
study constant heat flux of value 1000 W/m2 is instigated on pipe wall surface using UHF i.e. uniform heat 
flux condition. Some assumption was considered during numerical simulation such as steady state condition, 
incompressible turbulent flow, no heat loss etc. Outlet flow and temperature fields are assumed fully 
developed as ((x/D) > 10) [11]. The velocity inlet is used for specifying the velocity for different flow 
conditions and Outflow boundary condition was used since this boundary condition specifies zero normal 
gradients for all flow variables excluding pressure [12]. The computational simulation follows basic 
governing equations such as continuity equation, Momentum equation and energy equation as expressed 
follows:   
0)..( 




t                                                                                     (1) 
Fgp
t



 ).()(
                                                            (2) 
                ISSN: 2737-8071 
Int J Eng & App Phy, Vol. 1, No. 2, MAY 2021:  90 - 95 
92
   0.)( 


pEE
t

                                                                 (3) 
 
The Navier-Stokes equation tied with energy equation and turbulent viscosity model is solved for 
fully developed water flow condition. SIMPLE Technique i.e. [Semi Implicit Pressure Linked Equations] is 
suggested for simulation for lesser computational efforts [17, 18]. Second order up winding scheme was 
selected for Pressure, Momentum, and Energy. To control the variables of each cell under relaxation factors 
keeping to a constant default value. As per the theory suggested by Rayleigh Ritz, the residue is an error for 
any computational method. So, keeping the value of residue minimum the accuracy of the solution is 
achieved. Hence Simulation run for the of 1x10-6 [19]. The workstation used is a i5 Processor (4 threads) 
processor, 2.3 GHz CPU with 16 GB RAM. Each iteration took average time of 4 hours. Grid sensitivity is 
checked for pipe domain for every iteration. The grid used in the present analysis was 120 × 1500, 120 in r-
direction and 1500 in x-direction. We also tested 180×1600 and 200 × 1500. All gave similar values of 
velocity and temperature at the outlet. Therefore, 120×1500 was selected as the optimal grid size. The 
number of elements formed are 270000. This grid size was validated by our computational results as shown 
in Figure. 3 and 4. The Orthogonal Quality of mesh metric plays an important role during computation as 
orthogonal quality of mesh lies between 0 to 1. Higher the value of orthogonal quality results in less 
skewness of mesh i.e. less distortion of Mesh element. So, with the selected grid size   the orthogonal quality 
of mesh is found to be 1 [20]. Hence Numerical Simulations were agreed on for different values of Reynold 
number. The inlet temperature Tin is considered as 300 K i.e. 27 °C. 
 
2.3 Modeling Technique: In order to validate the computational model, the numerical results were compared 
with the theoretical data available for the conventional fluids [23].  
The Darcy’s friction factor equation given by Blasius as,   
 
 
                                                               (4) 
 
 
 
Figure 2: Friction Factor vs Reynold Number 
The Figure.2 shows the comparison of Darcy friction factor from Blasius formula and computed values from 
simulation. An excellent agreement is observed with maximum deviation and average deviation of computed 
values from theoretical equation being 3.2 and 1.9%, respectively, over the range of Reynolds numbers 
studied. 
 
3. RESULT AND DISCUSSION  1 
                                                        
 
Int J Eng & App Phy ISSN: 2737-8071  
 
Simulation of heat transfer augmentation during constant solar heat flux in circular pipe (C. D. Chaudhari) 
93 
The detail study was carried out to understand the effect of change in Reynolds Number and Nusselt number. 
The Reynolds number plays important role in heat transfer process and temperature at the outlet of the pipe. 
The different equations are used to understand the Nusselt Number, Reynolds Number, Turbulent kinetic 
energy and diameter etc. was studied [24].   
 
Dittus Bolter equation 
                                                                                                                                         (5) 
 
Pak and Cho equation  
                                                                                                                                         (6) 
 
Maiga equation  
                                                                                                                                    (7) 
 
Gnieinkski equation  
                                                                                                                 (8) 
      
                                          [a]      [b] 
 
Figure 3: [a] Skin friction coeffiecient vs Length; [b] Tempreture vs Length 
 
      
                                              [a]          [b] 
Figure 4: [a] Temperature variation at interval lengths; [b] Turbulant kinetic energy variation at interval 
length 
 
                ISSN: 2737-8071 
Int J Eng & App Phy, Vol. 1, No. 2, MAY 2021:  90 - 95 
94
 
Figure 5: Variation of Nussel number w.r.t Reynold number 
 
Figure 6: Velocity plot in circular hose pipe 
          
Figure 7: Temperatuer plot in circular hose pipe 
 
The Figure 3 [a] and [b] shows a comparison between the numerically results and the Nusselt number 
correlations. The results compared with lower range of Reynolds number shows predicted results of Nusselt 
number is very close to all correlations at lower velocity as compared to higher range of Reynolds number. 
Exactly the same trend was observed for all computed concentrations. 
 
4. CONCLUSION & FUTURE PERSPECTIVE   
In this research paper, the detail analysis of effect of numerical parameters on the dimensionless 
numbers like Nusselt number, Reynolds number and Prandtl number. Various Nusselt number equations are 
identified and compared to study the effect and result analysis. The Dittus Bolter equation shows close results 
as compared to other Nusselt number equations and theoretical results. Also, the study was carryout to 
understand turbulent kinetic energy verse diameter of pipe shows the proper flow distribution in case of 
Dittus Bolter equation. The percentage error between the theoretical and numerical results in case of Dittus 
Bolter equation results was 6 to 8 percentage. The results were found to be in good agreement between the 
numerical simulation and other numerical equations. The numerical study can be further extended to 
investigate another configuration and optimized. 
 
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