Investigation on influence of dimpled surfaces on heat transfer enhancement and friction factor in solar water heater

Abstract

The solar water heating system efficiently converts available solar energy into useful thermal energy. The collector is the predominant unit of the solar water heating system. Using a heat transfer enhancer in the tube is pondered as one of the effective methods to improve the thermal efficiency of the system. Dimples are used as heat transfer enhancer and created using a punching machine. The primary objective of the research is to endow a numerical investigation on the influence of dimples and its various parameters on the thermal efficiency and friction factor of the solar collector. Simulation is performed by varying pitch-to-dimple diameter ratio (P/D_d), number of dimples and mass flow rate. For the result to be independent of mesh, the optimum number of control volumes is identified as 2.2 million. Numerical modeling is done in such a way that the experimental and CFD results are in good agreement with each other and the error percentage is below 10%. Dimples on the tube disturb the fluid flow and reduce the hydraulic diameter, thus enhancing the heat transfer rate and efficiency of the collector. A maximum of 2.5 times increment in the Nusselt number was observed for the dimpled tube with P/D_d ratio 3 and six dimples between two pitches than plain tube at a mass flow rate of 2.5 kg min⁻¹. The friction factor due to the presence of dimples increased by 11.1% compared to that of the normal tube. The relative better enhancement in thermal efficiency with less friction factor makes dimples a superior heat transfer enhancer.

Introduction

Proliferation in the usage of fossil fuels to meet the energy demand has imposed severe problems like global warming and climate change [1]. Moreover, the depletion of fossil fuel has made the researchers turn their attention toward renewable energy. Owing to easy availability, eco-friendly and economically viable nature, solar energy has been considered as the most used renewable energy. Solar water heater (SWH) is one of the prominent technologies that effectively uses solar energy. Various parameters like solar irradiation, ambient temperature, thermal conductivity of the working fluid, inlet temperature of the working fluid, tube geometry and insulating material influence the performance of the SWH system [2]. Collectors are the predominant part of the SWH system. Based on the collector types, SWH system is categorized as (i) concentrating and (ii) non-concentrating. Flat plate and evacuated tube collector come under the category of non-concentrating, while compound parabolic collector (CPC) and parabolic trough collectors come under the category of the concentrating type of solar collector [3]. CPC has gained interest among the researchers as it can collect solar radiation over a wide range of daily hours without the use of a tracking system and it is considered to be the most financially feasible choice in the stationary mode [4]. More recently, Rajendran et al. studied the various parameters that influence the performance of the CPC which includes the material, design and heat transfer fluid [5]. Hinojosa et al. studied the effect of tilt angle of CPC enclosure [6], while Reichl et al. simulated the flow pattern and heat transfer inside the CPC enclosure [7]. A novel CPC solar collector was fabricated for the application of steam generation which showed better performance and reduction in cost compared to the conventional CPC solar collector [8]. Chamsa-ard et al. fabricated and tested a heat pipe evacuated tube with CPC [9]. Waghmare and Gulhane performed ray tracing of CPCs and determined the relationship between the limiting diameter and maximum diameter [10]. Xu et al. experimentally investigated a solar collector by integrating a pulsating heat pipe (PHP) and CPC [11]. Fracesconi and Antonelli numerically studied the thermal losses in the panel containing several CPCs and suggested that an increased number of concentrators would reduce the thermal loss [12]. Recently, Hadjiat et al. presented a novel design of integrated collector storage solar water heater with CPC and predicted the thermal behavior of the system under Saharan climate.

To improve the performance of the collector, various methods have been used, namely geometry modification of the collector, using nanofluid as working fluid and so on. Any technique that is implemented to improve the performance of the SWH system or any heat exchanging system is regarded as ‘heat augmentation technique’ [13]. Heat augmentation technique results in the reduction in size and cost of the system. This technique is further classified as active and passive methods. Active methods use external energy sources like electric field and vibration, whereas passive method uses heat transfer enhancement devices (inserts) to augment the heat transfer. These heat transfer enhancement devices cause swirl in the motion of the absorbing fluid. The swirl motion is intended to increase the heat transfer coefficient compared to that of the plain tubes. The pressure drop created in the system is the crucial drawback of using heat transfer enhancement devices. In the past few years, diverse heat enhancement devices were designed to improve the augmentation of heat transfer with less pressure drop.

The performance of thermosyphon solar water heater with left–right twisted tape was studied by Jaishankar et al. [14]. The left–right twisted tape has shown better heat transfer enhancement and friction factor than plain tube. The improvement in heat transfer and friction factor is attributed to the bidirectional swirl. Later, Ananth and Jaishankar [15] compared twisted tape with rod and spacer of three different lengths at the trailing edge with the full-length twisted tape on the performance of the thermosyphon solar water heater. With an increase in the length of rod & spacer, Nusselt number decreased and pressure drop increased. Hence, the performance of the full-length twisted tape was found to be better than the rod & spacer twisted tape. Experimental study on heat transfer and pressure drop characteristics with twisted tape of varying width was conducted by Patil [16]. Comparing short- and full-length twisted tape, short-length twisted tape performs low heat transfer and pressure drop than full-length twisted tape. The performance decrement is attributed to the weak swirling flow over the whole tube caused by short-length twisted tube [17]. Twist ratio is considered as the prominent parameter in the twisted tape; using minimum twist ratio and pitch in the helically twisted tape would enhance the heat transfer and pressure drop [18]. The ratio of pitch to insert diameter is represented as the twist ratio. Regularly spaced twisted elements were also utilized to improve the heat augmentation [19]. Although all these typical twisted tape inserts generate lesser pressure drop, considerable yield of less heat transfer diminished the overall performance.

To further ameliorate the heat transfer rate, various design modifications are attempted in the aspect of better fluid mixing. Convergent and divergent conical ring inserts in the transient regime are investigated experimentally [20]. Although the heat transfer rate increased, using convergent and divergent insert suffered a significant pressure loss. The optimum trade-off between increased heat transfer rate and friction factor using uniform/non-uniform twisted tape was investigated [21]. For non-uniform twisted tape, heat transfer characteristics depend on the alternate length than variation of length. Friction and heat transfer characteristics with alternate clockwise and counterclockwise twisted tape were examined [22]. With a double-twisted tape insert, Eiams-ard found that counter-twisted tape was more efficient than co-swirl and single-twisted tape [23].

The influence of combined effect due to the presence of wire nails on the twisted tape insert was studied [24]. The presence of wire nails improved the fluid mixing, thus improving the heat transfer rate, friction factor and thermal performance. Creating perforations in the twisted tape would decrease the pressure drop as it decreases resistance against the flow caused by twisted tape. Guo et al. [25] identified that center-cleared twisted tape provided better heat transfer enhancement (7–20%) compared to plain tube analysis. Further enhancement can be obtained by suitable improvement in the central clearance ratio. The square cut in the twisted tape enhances the heat transfer rate by 1.06 times and friction factor by 1.25 times compared to plain twisted tape by producing improved disturbances and secondary flow in the locality of the tube wall [26]. The V-cut twisted tape provides better heat transfer enhancement with nearly same friction factor compared to that of plain twisted tap. The depth of the V-cut influenced the heat transfer characteristics than its width [27]. The performance ratio of trapezoid cut twisted tape is more than unity; therefore, the heat transfer enhancement is considered to be more competent in the perception of energy saving [28]. Experimental investigation in horizontal tube using twisted tape with Teflon rings with different Reynolds numbers, twist ratio and clearance ratio was conducted [29]. Numerical study on heat transfer rate and friction factor characteristics with perforated, notched and jagged twisted tape was performed [30]. The jagged insert exhibited improved performance than other twisted tapes.

The use of surface roughness would improve the heat transfer with less pressure drop in the transition regime [31]. Ravigururajan et al. [32] proved that the presence of artificial roughness promoted the turbulent flow at Reynolds number below 2000. Barba et al. studied the effect of the corrugated tube on heat transfer enhancement in laminar and transitional flow [33]. The overall pressure drop increased by 2.5 times, while the Nusselt number augmented about 17 times for Reynolds number 800. Experimental investigation of heat transfer enhancement in a heat exchanger with different dimpled tube configuration was performed by Chen et al. [34]. The authors provided the correlation for heat transfer and pressure drop and concluded that the size and volume of the heat exchanging system can be reduced by a factor of almost 2 using the dimpled tube. Experimental investigation on continuous and longitudinal interrupted fins was analyzed by El-Sayed et al. [35]. The staggered arrangement of interrupted fins provided better heat transfer and pressure drop than the inline arrangement and continuous fins. The combined effect of micro-fin and double-twisted tape on heat transfer, friction factor and thermal performance characteristics has also been studied experimentally [36].

More recently, Balaji et al. identified that non-contact of heat enhancement devices with the inner wall of the tube is responsible for the ineffective augmentation of heat transfer and used a novel technique to improve the performance of the collector by introducing rod and tube heat transfer enhancers in riser tube [37]. The authors achieved a maximum instantaneous efficiency of 14% using rod heat transfer enhancer, while the pressure drop and operating cost increased by 1.44 times and 1.081 times, respectively, compared to that of the plain tube. The exergy analysis reported an increase in useful exergy rate of 1.29 and 1.25 times higher for rod and tube heat transfer enhancers than plain tube [38].

From the literature survey, we can infer that surface modification on the absorber tube helps to enhance the heat transfer rate with reduced pressure drop. Only a few researchers have studied the influence of surface modification of the absorber tube on the heat transfer enhancement of the SWH system. Similarly, computational studies in the application of solar water heater are also found to be limited in the literature. This paper aims to present numerical analysis of the SWH system with and without dimples for various mass flow rates and to study the effect of various parameters such as P/D_d ratio and the number of dimples on the thermal efficiency and pressure drop characteristics of the system.

Experimental setup and data collection

The schematic diagram and picture of the experimental setup of open-loop solar water heating system used for the present study are shown in Fig. 1. In the open-loop system, cold water storage tank was connected to the inlet of the collector and the outlet of the collector was connected to hot water storage. The cold water is pumped into the collector through the bottom of the header pipe and moves through the riser to the top header pipe. As the water moves through the riser tube, it gets heated by the buoyancy due to the temperature difference between the top and bottom header.

Fig. 1

a Schematic diagram of experimental setup, b position of thermocouples along the absorber tube c and d picture of experimental setup

As the experiment is conducted in indoor conditions, an array of tungsten–halogen lamps each of capacity 500 W with a maximum intensity of 1000 W m⁻² were used to supply the required heat input. The radiation heat flux is measured by pyranometer, while the inlet and outlet water temperature and surface temperatures at different positions along the absorber tube are measured using K-type thermocouple. The different positions along the absorber tube where the water temperature is measured are shown in Fig. 1b. The analysis is performed for five different flow rates ranging from 0.5 kg min⁻¹ to 2.5 kg min⁻¹ with an interval of 0.5 kg min⁻¹. The flow of the water is measured and controlled using a flowmeter. The pressure drop in the collector accounted for frictional resistance, and fitting joints were measured using a manometer. Experiments are performed five times, and the average is used to reduce the experimental error.

The collector used in this experiment is compound parabolic collector (CPC). The cross section of the collector is shown in Fig. 2. The compound parabolic collector consists of a brazed riser and header tube made of copper, parabolic reflective glass, insulating casing and glass cover. The receiver tube is kept at the focus point (F) where solar rays are reflected and concentrated. The collector is fabricated in such a way that two parabolic segments are assembled at a certain angle called acceptance angle. The details of the solar collector are given in Table 1.

Fig. 2

Cross section of the collector

Table 1 Details of the solar collector

The surface modification in the tube is provided in the form of Dimples. The sketch of the dimpled tube and the dimpled tube used in the study are shown in Fig. 3. Pitch is the center-to-center distance between two dimple arrangements, and D_d is the diameter of the dimple. D_o and D_i are the inner and outer diameters of the riser tube. The dimples are created with the tailor end punching machine shown in Fig. 4. The machine consists of male die, female die and clamp. The clamp holds the tube, the female die is fixed inside the tube, and the male die is punched onto the tube to create dimples of exact dimension.

Fig. 3

Dimpled tube

Fig. 4

Punching machine to create dimples

Theoretical calculations

Thermal efficiency

Thermal efficiency is one important parameter that determines the performance of the collector. Incident solar radiation, area of the collector and outlet temperature are factors that influence the thermal efficiency of the collector. The thermal efficiency of the collector is given by Eq. 1:

$$ \eta = \frac{Q}{{I A_{\text{c}} }} $$

(1)

where Q is the heat transfer rate, I is the incident solar insolation and A_c is the area of the collector. The heat transfer rate is given by Eq. (2)

$$ Q = {\text{mc}}_{\text{p}} \left( {T_{\text{out}} {-} \, T_{\text{in}} } \right) $$

(2)

where T_out and T_in are the inlet and outlet water temperatureSo the thermal efficiency of the collector is determined by substituting Eq. (2) in Eq. (1). The final equation of thermal efficiency of the collector is

$$ \eta = \frac{{mC_{\text{p}} \left( {T_{\text{out}} {-} T_{\text{in}} } \right) }}{{I A_{\text{c}} }} $$

(3)

Pressure drop and friction factor

Pressure drop in the system occurs due to fitting joints, frictional resistance and buoyancy. Pressure drop due to fitting joints and frictional resistance is measured using U-tube manometer. The frictional factor is the parameter that measures the frictional resistance caused by the dimples and the fitting joints. The frictional factor is calculated by the equation as follows:

$$ f = \frac{\Delta P}{{\left( {\frac{L}{{D_{\text{h}} }}} \right)\left( {\frac{{\rho V^{2} }}{2}} \right)}} $$

(4)

where $\Delta P$ is the pressure drop between the inlet and outlet of the collector, L and D_h are the length and hydraulic diameter of the tube, ρ is the density of the working fluid (water) and V is the velocity of the fluid flow. The velocity of the fluid flow is the function of mass flow rate, hydraulic diameter of the tube and the density of the working fluid, which can be calculated by the following equation:

$$ V = \frac{m}{{\frac{{\rho \pi D_{\text{h}}^{2} }}{4}}} $$

(5)

Nusselt number

The variation of Nusselt number is given by Dittus–Boelter equation

$$ Nu = 0.023Re^{0.8} Pr^{0.3} $$

(6)

where Re is the Reynolds number and Pr is the Prandtl number. Reynolds number and Prandtl number are calculated using the following expressions:

$$ \text{Re} = \frac{{D_{\text{h}} \rho V}}{\mu } $$

(7)

$$ \Pr = \frac{{\mu C_{\text{p}} }}{{k_{\text{t}} }} $$

(8)

where µ is the dynamic viscosity, C_p is the heat capacity and k_t is the thermal conductivity of the working fluid.

Uncertainty analysis

The experimental result is the function of various independent variables. Uncertainty analysis is performed to evaluate the accuracy of the obtained experiment result. Uncertainty analysis is carried out by calculating the error that arises from observation, reading, calibration and testing conditions [39]. The uncertainty in the result R is given by the following expression:

$$ W_{\text{R}} = \sqrt {\left[ {\left( {\frac{\partial R}{{\partial x_{1} }}w_{1} } \right)^{2} + \left( {\frac{\partial R}{{\partial x_{2} }}w_{2} } \right)^{2} + \cdots \cdots \cdots + \left( {\frac{\partial R}{{\partial x_{\text{n}} }}w_{\text{n}} } \right)^{2} } \right]} $$

(9)

where X₁, X₂ … X_n are the independent variables and W₁, W₂… W_n are the uncertainties in the independent variable. Uncertainties in the independent variable are given in the table. The uncertainty in the thermal efficiency and friction factor is 4.17% and 2.68%, respectively, which is under permissible limit [2]. Table 2 shows the uncertainty in each independent variable.

Table 2 Uncertainty in the independent variable

Numerical simulation

Numerical analysis of flow and heat transfer characteristics of solar water heater is performed using academic research-licensed CFD program ANSYS Fluent 17. Figure 5 shows the three-dimensional model of the SWH system and the dimpled tube used in the study.

Fig. 5

a Model of solar collector, b model of dimpled tube with four dimples between two consecutive plane c model of dimpled tube with six dimples between two consecutive plane

Governing equations of the mean flow

In order to assess the thermohydraulic properties of the working fluid in the SWH system, the governing equations are solved by assuming that the flow is steady and incompressible. The physical properties of the fluid are assumed to be constant throughout the analysis. Also, the effect of buoyancy is assumed to be negligible [40, 41]. Thus, the governing equations are

$$ \nabla \cdot \left( {\rho v} \right) = 0 $$

(10)

$$ \nabla \cdot \left( {\rho vv} \right) = - \nabla P + \nabla \cdot \left( {\mu \nabla v} \right) $$

(11)

$$ \nabla \cdot \left( {\rho vC_{\rm{p}} T} \right) = \nabla \cdot \left( {k_{\rm{t}} \nabla T} \right) $$

(12)

Turbulent modeling

To simulate the turbulent flow, k–ɛ RNG model with enhanced wall functions for near-wall treatment has been used [40, 41]. The k–ɛ RNG model solves turbulent kinetic energy (k) and dissipation rate (ɛ). The equations for k-ɛ RNG model are expressed as follows:

$$ \frac{\partial }{\partial t}\left( {\rho k} \right) + \frac{\partial }{{\partial x_{\rm{i}} }}\left( {\rho kv_{\rm{i}} } \right) = \frac{\partial }{{\partial x_{\rm{j}} }}\left[ {\left( {\frac{{\mu + \mu_{\rm{t}} }}{{\sigma_{\rm{k}} }}} \right)\frac{\partial k}{{\partial x_{\rm{i}} }}} \right] + \mu_{\rm{t}} \left( {\frac{{\partial v_{\rm{i}} }}{{\partial x_{\rm{j}} }} + \frac{{\partial v_{\rm{j}} }}{{\partial x_{\rm{i}} }}} \right)\left( {\frac{{\partial v_{\rm{i}} }}{{\partial x_{\rm{j}} }}} \right) - \rho \varepsilon $$

(13)

$$ \frac{\partial }{\partial t}\left( {\rho \varepsilon } \right) + \frac{\partial }{\partial t}\left( {\rho \varepsilon v_{\rm{i}} } \right) = \frac{\partial }{{\partial x_{\rm{j}} }}\left[ {\left( {\frac{{\mu + \mu_{\rm{t}} }}{{\sigma_{\varepsilon } }}} \right)\frac{\partial \varepsilon }{{\partial x_{\rm{j}} }}} \right] + C_{1\varepsilon } \frac{\varepsilon }{k}\mu_{\rm{t}} \left( {\frac{{\partial v_{\rm{i}} }}{{\partial x_{\rm{j}} }} + \frac{{\partial v_{\rm{j}} }}{{\partial x_{\rm{i}} }}} \right)\left( {\frac{{\partial v_{\rm{i}} }}{{\partial x_{\rm{j}} }}} \right) - C_{2\varepsilon } \rho \frac{{\varepsilon^{2} }}{k} - \, \alpha \rho \frac{{\varepsilon^{2} }}{k} $$

(14)

The term turbulent viscosity can be expressed as

$$ \mu_{\text{t}} = \rho C_{\upmu } \frac{{k^{2} }}{\varepsilon } $$

(15)

Table 3 provides the needed coefficients [42].

Table 3 Constant values of k–ɛ RNG turbulence model

Numerical setup

For solving the governing equation of the flow, double precision pressure-based solver is considered. The SIMPLE scheme is used to couple the pressure and velocity. Body force-weighted scheme is used for pressure discretization, and second-order upwind scheme is considered for spatial discretization. Since the experiment is conducted in indoor conditions, the energy input is given as heat flux of 1000 W m⁻² and it is applied on the wall of the riser tube. The convergence condition to finish the numerical solution is assumed to be 10⁻⁶ for scaled residuals of energy and 10⁻⁵ for continuity and momentum equation. The inlet boundary condition is specified as mass flow rate ranging from 0.5 kg min⁻¹ to 2.5 kg min⁻¹ with an interval of 0.5 kg min⁻¹. The outlet boundary condition is specified as pressure outlet with pressure specified as atmospheric pressure. Also, no-slip and impermeable wall conditions are applied at the fluid–solid interface.

Grid independence test

In the numerical simulation, the grid independence test is conducted to ensure mesh independence and to evaluate the sensitivity of results to the number of control volume generated during mesh. Figure 6 shows the meshed view of the SWH system. Analysis of the meshing module of the SWH system reveals that the elements are composed of tetrahedral and hex-dominant elements. The average relative error in heat transfer at the mass flow rate of 1.5 kg min⁻¹ is considered as the criteria for the test. Figure 7 shows the average relative error for different mesh densities. The relative error between 2.1 million elements and 3.4 million elements is less than 0.5%. So, 2.1 million control volume is selected as optimum mesh density, considering better accuracy and less computational effort.

Fig. 6

a Meshed view of the collector. b Meshed view of smooth tube. c Meshed view of cross section of the tube. d Meshed view of dimpled tube

Fig. 7

Grid independence test

Experimental and numerical comparison

To ensure the accuracy of the numerical solution, it has to be compared with the experimental results. A comparison of experimental result and numerical solution for efficiency, pressure drop and Nusselt number is shown in Fig. 8. The relative error between experimental results and numerical simulation is calculated using the equation as follows:

$$ {\text{Error}} \left( \% \right) = \frac{{\left| {X_{\text{sim}} - X_{\exp } } \right|}}{{X_{\text{sim}} }} \times 100 $$

(16)

The relative error between any corresponding experimental and simulation results is found to be less than 10% which indicates that the simulation results are in good agreement with the experimental results. It is also noted from Fig. 8 that the simulation result of the efficiency of the collector is slightly higher than the experimental results. It is attributed to relatively higher convective heat loss during the experimentation, while on the other side, the pressure drop results are slightly higher for the experimental condition compared to simulation results. It is attributed to the presence of surface roughness of the experimental pipe compared to the smoothness assumed in the numerical model. To further validate the numerical model, the surface temperature measured experimentally at various positions along the absorber tube is compared with the simulation result at the same position as in Fig. 8d. This comparison further proved that results yielded by the developed numerical model are in good accord with the experimental result.

Fig. 8

a Experimental and simulation comparison on thermal efficiency. b Experimental and simulation comparison on pressure drop. c Theoretical and simulation comparison on Nusselt number. d Experimental and simulation comparison on surface temperature at various positions along the absorber tube

Results and discussion

In this section, the influence of dimpled tube and its various parameters on thermal efficiency, friction factor and Nusselt number of SWH system is presented. Parameters like pitch-to-dimple diameter ratio (P/D_d) and the number of dimples between each pitch are varied under different mass flow rates. The mass flow rate for the present study is varied from 0.5 kg min⁻¹ to 2.5 kg min⁻¹. The diameter of the dimple is taken as 5 mm, and the pitch distance between two consecutive dimples is varied as 15, 30 and 45. The number of dimples between each pitch is taken as 2, 4 and 6. The arrangement of dimples of different numbers for the P/D_d ratio 3 is shown in Fig. 9. The dimples are arranged in such a way that no two consecutive dimples are straight in the direction which would improve the disruption in the fluid flow.

Fig. 9

a Two dimples between each pitch. b Four dimples between each pitch. c Six dimples between each pitch

Thermal efficiency

The thermal efficiency of the SWH system is increased by enhancing the heat transfer rate. The heat transfer rate in the SWH system is influenced by various factors such as surface area of the absorber tube, thermal conductivity of the working fluid and swirl/turbulence in the motion of the fluid particle. The provision of dimples on the tube changes the surface geometry, increases the surface area and creates swirl motion at the fluid–solid interface. These combined effects cause the proliferation of the rate of energy transfer. Figure 10 shows the path line traced by the fluid particles in the dimpled tube. From the figure, we can understand that the fluid experiences swirl motion around the circumference of the dimple at the fluid–solid interface. This swirl motion at the vicinity of the boundary layer disturbs the nearby fluid particle and enhances the fluid mixture. Apart from providing a better mixture, the swirl motion also accounts for the acceleration of the fluid particles. This is clearly explained in the velocity vector plotted at the mid-plane of the dimpled tube. Velocity vector plot and temperature contour taken at the mid-plane of the dimpled tube are shown in Fig. 11. As the fluid particles hit the dimples, it easily glides over the top surface of the tube and propagates the disturbance to the nearby fluid particle. The propagation of the disturbances to nearby fluid particle accelerates the fluid flow. The presence of dimples also increases the surface area of the tube compared to the plain tube. As a result of the better mixture, enhanced flow acceleration and improved surface area, the augmentation of heat transfer from the dimpled tube to the fluid particles is higher than the plain tube. Thus, the provision of dimples in the absorber tube improves the efficiency of the SWH system.

Fig. 10

Fluid particle flow in the dimpled tube

Fig. 11

Velocity vector plot and temperature contour at the mid-plane of the dimpled tube

Influence of mass flow rate

Mass flow rate plays a crucial role in the thermal efficiency of the system. The influence of the mass flow rate on the thermal efficiency of the SWH system is shown in Fig. 12. Thermal efficiency of the system is less at low mass flow rate and increases with an escalation of mass flow rate. At lower flow rate, heat absorbed by the working fluid will be higher compared to the absorption at high flow rate. It is attributed to the increment in the velocity of the water. The increment in the velocity of the water reduces the temperature rise of the working fluid. Though the amount of heat absorbed by the working fluid is low, the rate of heat transfer is high at high mass flow rate. At a higher flow rate, the specific heat capacity and thermal conductivity of the working fluid play a critical role which aids the working fluid to absorb more energy from the tube wall. This enhances the heat flux between the fluid particle and tube wall. Thus, the heat transfer rate and thermal efficiency of the system increase. It is also noted that the rate of increase in heat transfer is higher during transition at low flow rate and it is found to be negligible during the transition at high flow rate. The thermal efficiency of the SWH system increases by 27% from 0.5 to 1 kg min⁻¹, while the increase in flow rate from 2 to 2.5 kg min⁻¹ yielded thermal efficiency increment below 3%. Thus, the optimum flow rate for the system to have better thermal efficiency is found to be 2.5 kg min⁻¹.

Fig. 12

Effect of mass flow rate on thermal efficiency

Influence of pitch-to-dimple diameter ratio and number of dimples

The comparison of the rate of energy transfer and thermal efficiency of the SWH system with plain tube and dimpled tube of different configurations is shown in Figs. 13 and 14. The diameter of the dimple is 5 mm. The axial distance between the two consecutive planes of dimple is 15 mm, 30 mm and 45 mm, which refers to the P/Dd ratio as 3, 6 and 9, respectively. The total number of dimples between two consecutive planes of dimple is varied as 2, 4 and 6. The energy transfer rate of the SWH system with the dimpled tubes is better than the plain tube. Table 4 shows the enhancement of energy rate of the SWH system with dimpled tube of different configurations at higher and lower mass flow rates. From the table, we can infer that the enhancement is higher at high mass flow rate compared to the low mass flow rate. This further proves that apart from the effect of dimples, the Reynolds number also plays crucial role in the enhancement of energy rate. The combined effect of Reynolds number and the presence of dimples have huge impact on the energy rate of the SWH system. Maximum thermal efficiency and energy transfer rate enhancement of 32.3% were observed for the dimpled tube with a P/Dd ratio of 3, number of dimples as 6, at mass flow rate of 2.5 kg min⁻¹. This is due to swirl motion generated and the acceleration of the fluid flow at the maximum mass flow rate and number of dimples with a minimum P/Dd ratio. Because of these additional effects, the rate of heat extracted by the fluid particles from the tube wall is maximum. In case of SWH system with plain tube, the absence of swirl flow and fluid acceleration, the heat transfer is less, and hence it affects the thermal efficiency of the system. Figure 15 shows the comparison of variation of water temperature in the SWH system with plain tube and dimpled tube for the highest and lowest mass flow rate. In the identical condition, the amount of heat extracted by the fluid particles in the dimpled tube is higher than the plain tube.

Fig. 13

a Influence of P/D_d ratio on the energy rate. b Influence of number of dimples on energy rate

Fig. 14

a Influence of P/D_d ratio on the thermal efficiency. b Influence of number of dimples on thermal efficiency

Table 4 Comparison of enhancement of energy rate of SWH system with dimpled tube and plain tube

Fig. 15

a Variation of water temperature for SWH system with plain tube at the lowest mass flow rate. b Variation of water temperature for SWH system with dimpled tube at the lowest mass flow rate. c Variation of water temperature for SWH system with plain tube at the highest mass flow rate. d Variation of water temperature for SWH system with dimpled tube at the highest mass flow rate

Nusselt number

Observations indicate that the Nusselt number increases with an increase in mass flow rate. The increase in mass flow rate increases the Reynolds number, and hence the Nusselt number increases. Lower pitch-to-dimple diameter ratio results in higher Nusselt number. A maximum improvement in the Nusselt number of around 2.5 times is observed for P/D_d ratio 3 for the tube with six dimples at the highest mass flow rate. Under the similar condition, the enhancement was about 1.94 times at the lowest mass flow rate. The dimpled tube reduces the hydraulic diameter and increases the swirl motion in the fluid particle. This swirl motion creates energy fluctuation between the fluid particles, and hence there is an enhancement in heat transfer between the fluid and tube wall. The enhancement in heat transfer is replicated in the Nusselt number. Since there is no disruption in the fluid flow for a plain tube, the heat transfer between the fluid and wall is low compared to that of the dimpled tube. It is also observed that at low mass flow rate the effect of dimples on the Nusselt number is less, but as the mass flow rate increases the impact of dimples on the Nusselt number also increases. This is because the magnitude of heat augmentation at low flow rate is less compared to that at high mass flow rate. This shows that the effect of dimples has a better impact on heat augmentation at high flow rate. Figure 16a, b shows the influence of P/D_d ratio and the number of dimples on the Nusselt number, respectively. Figure 17 shows the influence of dimple on the Nusselt number. It is clear from the figure that the Nusselt number increases around the circumference of the dimple where the swirl motion is generated. Thus, the swirl motion generated by the dimple influences the enhancement of Nusselt number.

Fig. 16

a Influence of P/D_d ratio on Nusselt number. b Influence of number of dimples on Nusselt number

Fig. 17

Influence of dimples on Nusselt number

Friction factor

As the mass flow rate increases, the shear produced between the wall and fluid particles increases. This shear produced at the boundary layer resists the fluid flow. So, as the mass flow rate increases the frictional resistance also increases. The frictional resistance further increases with the disruptions caused by dimples in the fluid particles. The frictional resistance is measured by the parameter called friction factor. It is evident from the figure that the friction factor decreases gradually with an increase in flow rate. Figure 18a, b shows the influence of P/D_d ratio and the number of dimples on the friction factor. The friction factor increased about 11.11% for the dimpled tube with P/D_d ratio 3 at low mass flow rate. The increment is attributed to the enhanced dissipation of dynamic pressure into the fluid particles.

Fig. 18

a Influence of P/D_d ratio on friction factor. b Influence of number of dimples on friction factor

Conclusions

The numerical investigation on the influence of dimple surface in a solar water heater was performed and presented. A dimple-making machine was fabricated to create dimples with a specified dimension onto the tube. Grid independence test was conducted, and the optimized number of cells was identified to be 2.1 million. The error between the experimental result and the CFD simulation is below 10%. The following conclusions were identified after the CFD simulation.

• 1. Providing surface modification in the form of dimples disrupts the flow, which in turn enhances the heat transfer rate. As the heat transfer rate increases, the efficiency of the collector increases.

• 2. A maximum enhancement in collector efficiency of about 32.3% was observed for P/D_d ratio 3 with six dimples at 2.5 kg min⁻¹. The increment is attributed to the increased surface area and disruptions of fluid particles at the boundary layer.

• 3. As the heat augmentation increases, the Nusselt number also increases. Maximum rise of 2.5 times is observed in Nusselt number for a P/D_d ratio 3 with six dimples at 2.5 kg min⁻¹. The increment is attributed to the increased heat transfer rate due to the presence of dimples.

• 4. Frictional resistance plays a vital role in the performance of the collector. The friction factor due to the presence of dimple increased by 11.11%. The increase in friction factor is attributed to the enhanced dissipation of dynamic pressure into the fluid particles due to the presence of dimples.

• 5. Surface modification in the form of dimples in the tube enhances the thermal efficiency of the collector with less pressure drop due to friction. So dimples can be considered as heat enhancer for solar collectors, especially at high mass flow rate. In this study, dimples of circular shape were taken into account. Further dimple shapes shall be changed and the influence of it shall also be studied.