4.4 Overall Cost Analysis

The final proposed design consists of islands as seen below.

The total cost of the entire system is:

$\mathrm{SGD24,521}+(\mathrm{SGD272.96}\times 126)+(\mathrm{SGD544.7}\times 126)=\mathrm{SGD127,546.16}$

For the hotel in indonesia, with electricity costs of Rp1444,70/kWh, [26] or SGD0.11 (as of 6 April 2026), the electricity costs is expected to be SGD5,249.61 per year. (see Appendix C for calculations). Thus, the payback period is 24.30 years. This indicates that under current costs and electricity prices, the system may not be economically attractive without further improvements in efficiency, reduction of initial costs or increase in electricity prices.

However, for businesses, the incentives of adopting renewable energy goes beyond saving electricity costs. The Indonesian government is actively encouraging industries, including tourism industry, to adopt sustainable energy and reduce their reliance on non-renewable resources. [27][28][29] For hotels, adoption of renewable energy drives them to the direction of attaining green building or green hotel standards, making them eligible for incentives or awards. [30][31] Overall, beyond monetary benefits, they seek to gain government support and even more customers from their status.

Appendix A: System design detailed process with all results

The main MATLAB script is system_scaling_single.m for series configuration and system_scaling_separate.m for parallel configuration.

Key assumptions

• Temperature difference across TES = 5°C
• Heat loss in pipes neglected for flow rate calculations
• Flow is assumed turbulent
• Heat losses occur only through piping network
• Ambient temperature = 25°C, water temperature = 60°C for heat loss analysis

Pipe size

The mass flow rate is determined using an energy balance across the TES, $Q=\dot{m}c\Delta T$, where a temperature difference of 5°C is used. The corresponding mass flow rate and volumetric flow rate are calculated. All flow rates presented in this report refer to volumetric flow rate.

For the parallel configuration, the flow rate is constant at 0.409 L/min for all island sizes. For the series configuration, the flow rate varies with island size and is determined using the same energy balance. The results are shown below.

System head is given by: System head = Static head + Hydraulic losses

For a closed loop system, the static head is 0m.

Hydraulic losses are the sum of pipe losses and minor losses. Pipe losses are calculated using the Darcy–Weisbach equation:

$h={\sum }_i{\mathrm{f}}_i\frac{L}{d}\frac{V^2}{2g}$

Minor losses are calculated using loss coefficients (K-values) for each fitting:

$h={\sum }_j{\mathrm{K}}_j\frac{V^2}{2g}$

A constant friction factor (f) of 0.02 is assumed, corresponding to turbulent flow. The rig layout to obtain internal pipe length (within island) and fittings required are below.

The system head is computed using a MATLAB function (NPSH_system_head_single.m for series configuration and NPSH_system_head_separate.m for parallel configuration). The resulting system head for each pipe size is shown below.

For the parallel system

For the series system

Thermal efficiency of pipes in island

The thermal efficiency is defined as:

$\eta =\frac{\text{output energy}}{\text{input energy}}$

Heat loss is calculated using a rate of 7.1722 W/m, obtained from the following assumptions:

1. 25mm thickness of aircon insulation
2. 3/4" pipe
3. 35ºC temperature difference between water and atmosphere

The heat loss per meter is derived from conduction (through pipe and insulation) and convection (within the pipe and to atmosphere):

$q^{\prime }=\frac{2\pi L(T_i-T_o)}{\frac{1}{r_1{h}_i}+\frac{\ln \left(\frac{r_2}{r_1}\right)}{k_{\mathrm{pipe}}}+\frac{\ln \left(\frac{r_3}{r_2}\right)}{k_{\mathrm{insulation}}}+\frac{1}{r_3{h}_c}}$

$q^{\prime }$ : Heat loss per unit length (W/m)

$L$ : Length of the pipe (m)

$T_i$ : Water temperature (°C)

$T_o$ : Ambient temperature (°C)

$r_1$ : Inner radius of the pipe (m)

$r_2$ : Outer radius of the pipe/Inner boundary of insulation (m)

$r_3$ : Outer radius of the insulation (m)

$h_i$ : Convective heat transfer coefficient of water (W/m²·K) – Inside pipe

$h_c$ : Convective heat transfer coefficient of air (W/m²·K) – Outside insulation

$k_{\mathrm{pipe}}$ : Thermal conductivity of the pipe (W/m·K)

$k_{\mathrm{insulation}}$ : Thermal conductivity of the insulation (W/m·K)

Using the pipe length estimation from layout above, the thermal efficiency of the pipes in a system of rigs is obtained for the series and parallel configuration. Thermal efficiency is computed uisng a MATLAB function (pipe_efficiency_single.m for series configuration and pipe_efficiency_separate.m for parallel configuration.)

The resulting thermal efficiency is shown below:

Optimal island size: Design 1

The island size is evaluated based on the following analysis. The layout of the islands on one of the rooftop is obtained (see Appendix B), using the sample connection plans below.

The length of pipe between the islands and to the hot water storage tank (total external pipe length) are inserted into the MATLAB script overall_sys_eff.m and is calculated with referenced to the sketches in Appendix B.

The total external pipe length and the sum of all the internal pipe length (within each island) are used to evaluate system performance, including thermal efficiency and pipe loss.

The thermal efficiency of the entire piping system on one rooftop is obtained (see below).

Pipe loss (expressed as a percentage of energy loss relative to output energy) is defined as:

$\frac{\mathrm{energy} \mathrm{loss}}{\mathrm{output} \mathrm{energy}}\times \mathrm{100\%}$

Using this equation, the results are shown below.

Cost analysis: Design 1

The cost of the system are compared considering the layout provided in the figures. The additional fittings required along with the pipes are:

1. Tank connectors, to connect the pipes to the TES tank
2. Couplers, to connect the pipes to the pump and to join pipe to the receiver
3. Pressure relief valve, for safety against high pressure
4. Non-return valve, to prevent backflow

Using cost of purchasing in bulk we get the costs below.

Optimal island size: Design 2

In design 2, we limit the number of rigs to meet the requirements of the hotel. Of the total 7500 L required, 3750 L is allocated to each roof to ensure equal distribution of hot water production. The minimum number of rigs required per roof is 370, with each rig contributing approximately 10 L of heated water per day. From here, we get the new layout (see Appendix B), where the values are inputted in the MATLAB script overall_sys_eff_shortened.m. All other calculations are the same as in design 1.

Appendix B: Layout of islands

Design 1

Design 2

Appendix C: Cost analysis calculation

Calculation for cost per year to heat water for showering

$\mathrm{Energy\; required\; per\; day}=\mathrm{mass}\times {\mathrm{C}}_p\times \mathrm{\Delta }\mathrm{T}=\mathrm{7,500}\times 4184\times (40-25)=\mathrm{470,700,000J}$ $\mathrm{Power\; used\; per\; day}=\mathrm{470,700,000}÷3.6e+6=\mathrm{130.75kWh}$ $\mathrm{Cost\; per\; year}=130.75\times 0.11\times 365=\mathrm{SGD5,249.6125}$