Medical, Pharma, Engineering, Science, Technology and Business

**Aneesh Somwanshi ^{1*}, Amrit Dixit^{1} and Anil Kumar Tiwari^{2}**

^{1}Disha Institute of Management and Technology, Raipur 492101, India

^{2}National Institute of Technology, Raipur 492001, India

- Corresponding Author:
- Aneesh Somwanshi

Disha Institute of Management and Technology

Raipur 492101, India

**Tel:**+919752322262

**E-mail:**[email protected]

**Received date:** December 20, 2013; **Accepted date:** January 29, 2014; **Published date:** February 06, 2014

**Citation:** Somwanshi A, Dixit A, Anil Kumar T (2013) Shape Factor for Steady State Heat Transfer between Swimming Pool Water and Surrounding Ground. J Fundam Renewable Energy Appl 4:128 doi:10.4172/2090-4541.1000128

**Copyright:** © 2013 Somwanshi A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Visit for more related articles at** Journal of Fundamentals of Renewable Energy and Applications

A simple, efficient, and abundantly available agricultural waste material, banana pseudo-stem (BPS) was examined as raw material for the extraction of potassium. The effects of various process parameters such as temperature, initial pH, contact time, banana pseudo-stem dosage and size of banana pseudo-stem particles on potassium extraction efficiency were studied by running batch experiments in Erlenmeyer flasks. Response Surface Methodology (RSM) was used to design the experimental runs. Modelling and optimization of process variables to obtain maximum extraction of potassium from raw material were done using RSM.The maximum extraction efficiency of potassium was found to be 83.96% at a temperature of 400C, pH of 1, contact time of 30 min, BPS weight of 26.076 g and initial BPS size of 300. The results revealed that banana pseudo-stem can be used as good source for potassium extraction.

Shape factor, Thermal simulation, Characteristic length, Swimming pool

Solar energy has been widely used for heating of swimming pools; a number of papers [1-13] on the implementation, analysis and validation, corresponding to the exploitation of various options have been published. The starting point for all the analyses is an energy balance equation, which takes into account the relevant modes of energy exchange between the pool and the surroundings; however a significant aspect viz. the energy exchange between the pool water and the surrounding ground has either been ignored or inadequately addressed to (usually based on one dimensional flow of heat in the ground). In this paper the authors have used the method of experimental simulation for the evaluation of the energy exchange between the pool water and the surrounding ground in the steady state. Such an investigation is also relevant to temperature conditioning of water in a pool by exchange of heat with earth, as proposed recently [14]. The energy storage in the ground has for long been exploited for heating and cooling of buildings [15-19] and hence some attention (not enough) has been given to the study of energy exchange between a building and surrounding ground. For a theoretical analysis one has to solve the Fourier equation of heat conduction with appropriate boundary conditions; except for the simplest cases with high symmetry [20-22] it is not possible to obtain analytical solutions. Numerical solutions have of course been obtained [23-26] for structures with less symmetry. Full scale experiments, to evaluate the rate of heat exchange between a building and surrounding ground are not practicable; further the results are of little use on account of the variety of building designs.

With this background Sodha et al. [27-30] have developed the methods of electrical and thermal simulation (by experiment) to evaluate the heat transfer between a fully or partially underground structure and surrounding ground, where by results on small scale model can be scaled up for bigger realistic situations.

Sodha et al. [27,10,31] modeled the steady state temperature distribution in the ground, the boundary conditions and the heat exchange between the body and the ground viz,

∇^{2}(T) = 0, (1a)

T (z=0) = T_{g}, (1b)

T(Surface of body) =T_{s} (1c)

and,

(1d)

The method of simulation is based on the fact [27,31] that in general for the steady state Eq. (1d) may be put in the form,

Q = KLF(T_{s} −T_{g} ), (2)

Where F depends on the relative (divided by L) dimensions of
the body, relative depth and the orientation of the body and L is a
characteristic dimension. Thus the steady state heat transfer between a
body and the ground under any situation (characterized by L, thermal
conductivity K of the medium and (T_{s}-T_{g})) can be evaluated with
a knowledge of the shape factor F, which may be determined by an
experiment on a convenient scale or value of L (keeping the relative
depth, relative dimensions of the body and the orientation of the
body with respect to the surface the same) and convenient values of K
and (T_{s}-T_{g}). In this paper, the shape factor corresponding to the heat
transfer between the ground and three designs of swimming pools have
been obtained by simulated experiments on a small scale.

This paper reports on the experimental determination of the shape factor for heat transfer between the pool water and the ground for the following three designs:-

(I) Length (*l*) = 60m, Breadth (*b*) = 25m, Depth (*d*) = 2m. (Olympic
size horizontal base pool [32]).

(II) Length (*l*) = 60m, Breadth (*b)* = 30m: vertical section normal to
the breadth is shown in **Figure (1a)**. (Slanted base pool [33]).

(III) Length (*l*) = 35ft, Breadth (*b*) = 20ft: vertical section normal to
the breadth is shown in **Figure (1b)**. (Diving pool [33]).

In all the cases the characteristic length is L= b/2 and the pool is full of water; the water surface is on level with the horizontal ground surface. The models are open boxes without cover; for the three pool designs the simulated dimensions are reduced by the reduction factor as follows:-

(I) Design I= (1/400). (II) Design II= (1/300). (III) Design III= (1/150).

The corresponding characteristic length *L= b/2* for these models
are 3.125×10^{-2} m, 5×10^{-2} m and 2×10^{-2} m, respectively. The models are
closed by thick insulating pads at the top face.

**Determination of Thermal conductivity of sand**

The ground is simulated by a 1.5 m×l.5 m×l.5 m box full of sand. The
thermal conductivity of the sand is determined before every experiment
for determining the shape factor. The experimental arrangement for
determination of the thermal conductivity of sand is diagrammatically
illustrated in **Figure 2**. A hollow copper sphere of diameter (*2a*) 6 cm is
buried in the sand, so that the Centre of the sphere is at depth d. There
is an incandescent bulb or an insulated heating element in the sphere
which is connected to a source of alternating emf. The rms values of the
potential difference (*V*) and the current (I) flowing through the bulb/
element is measured; in the steady state the power output of the bulb/
element is equal to the power loss from sphere to the ground. Hence
from Eq. (2) one gets,

VI = FaK(T_{s}-T_{g}); (3)

Here the radius a of the sphere is the characteristic length. The
temperature difference (T_{s}-T_{g}) is determined by thermocouples. The
shape factor F for a sphere of radius a at a depth d in the ground has
been analytically evaluated [29,34] as,

(4)

Where,

cosh*β*=(d/a)

Substituting for F from Eq.(4) in Eq. (3) and using the measured
steady state values of* V, I, T _{s},T_{g}* and a, the thermal conductivity of sand
can be determined for d/a= 2 and 3, It is seen from Eq.(4) that the
values of shape factor F are 15.3 and 14.5 for

**Determination of shape factor F for three pool designs**

The experimental arrangement is diagrammatically illustrated in **Figure 3**. The copper model of the pool is so buried in sand that the
top horizontal surface of the sand is in level with the open face of the
model. Ceramic insulation is placed on the model, so that there is no
heat loss from the top side. A heating element with mica insulation is
placed inside the model and connected to an A.C source, through a
mille ammeter and rheostat; the potential difference across the element
and the current passing through it are measured by a voltmeter and
micro ammeter. Temperature sensors measure the temperature
difference (T_{s}-T_{g}) between the surface of the model and the top surface
of the sand. Observations are taken when steady state values of T_{s} and
T_{g}are indicated.

Referring to the half width of the pool as the characteristic length Eq. (2) may be rewritten as

VI = F (b/2) K (T_{s}-T_{g}); (5)

V and I are the r.m.s values of the potential difference across and
the current through the heating element. Knowing all the terms in
this equation the shape factor F for the specific pool designs can be
evaluated. It may be remembered that as stated earlier in the paper
thermal conductivity K for sand is taken as *0.271W/m°C.*

These are presented in **Tables 1-3**. Thus the shape factors for
designs I, II, and III are (16.77 ± 0.73), (15.91 ± 0.15) and (34.12 ± 1.38) the uncertainty in the values is less than 5% and should be acceptable
for design purpose.

Experimental simulation has been used to evaluate the shape factor F, corresponding to steady state heat transfer between water in a swimming pool and the surrounding ground; the shape factor has been determined, corresponding to three designs of the swimming pool. The uncertainty in the values of F is less than 5% and thus acceptable for design purpose.

The authors are grateful to Prof. MS Sodha, Visiting and Emeritus Professor, CES, IIT Delhi, India for suggesting the problem and valuable guidance.

- Root Jr DE (1959) Simplified engineering approach to swimming pool heating. Solar Energy 3: 60-63.
- Root Jr DE (1960) Practical aspects of heating swimming pools by solar energy. Solar Energy 4: 23-24.
- Francey JLA, Golding P, Clarke R (1980) Low cost solar heating of community pools using pool covers. Solar Energy25: 407-416.
- Francey JLA, Golding P (1981)The weathering of solar pool covers. Solar Energy26: 237-242.
- Francey JLA, Golding P (1981)The optical characteristic of swimming pool covers used for direct solar heating. Solar Energy26: 59-63.
- Lazzarin R (1983) Alternative heating of a municipal swimming pool. International Journal of Refrigeration 6: 118-122.
- Govind,Sodha MS (1983) Thermal model of solar swimming pools. Energy Conversion and Management 23: 171-175.
- Sodha MS, Kumar A, Govind (1988) Solar heating of open swimming pool. International journal of Energy Research 12: 511-519.
- YadavYP, Tiwari GN (1987) Analytical model of solar swimming pool; transient approach. Energy Conversion and Management 27: 49-54.
- Rokopoulos CD, Vazeos E (1987)A model of energy fluxes in a solar heated swimming pool and its experimental validation. International journal of Energy Conversion and Management 27: 189-195.
- Alkhamis AI, Sherif SA (1992) Performance analysis of solar assisted swimming pool heating system. Energy 17: 1165-1172.
- Wooley J, Hannington J, Modera M (2011) Swimming pool as a heat sink for air conditioners: model design and experimental validation for natural behavior of the pool. Building Environment 46: 187-295.
- Dang A (1986) A parametric study of swimming pool heating. Energy Conversion and Management 26: 27-31.
- Somwanshi A, Tiwari AK, Sodha MS (2013)Feasibility of earth storage for all weather conditioning of open swimming pool water. Energy Conversion and Management 68: 89-93.
- Sodha MS, Sharma AK, Singh SP, Bansal NK, Kumar A (1985) Evaluation of an earth air tunnel system for cooling/heating of a hospital complex. Building and Environment 20: 115-122.
- Sodha MS, Budhhi D, Sawhney RL (1981) Thermal performance of underground air pipe: different earth surface treatments. Energy Conversion and Management 31: 95-104.
- Sodha MS, Mahajan U, Sawhney RL (1994) Thermal performance of a parallel earth air pipes.International Journal of energy Research18: 437-447.
- Bansal NK, Sodha MS (1986)An earth air tunnel system for cooling buildings. Tunneling and Underground Space Technology 1: 177-182.
- Sawhney RL, Mahajan U (1994) Heating and cooling potential of an underground air pipe system. International Journal of Energy Research18: 509-524.
- Shelton J (1975) Underground storage of heat in a solar heating system. Solar Energy 17: 137-143.
- Claesson J,Dunand A (1983) Heat extraction from the ground by horizontal pipes: a mathematical analysis. Swedish Council of Building ResearchStockholm Document D1.
- Carslaw HS, Jaeger JC (1947) Conduction of heat in solids
*.*Clarendon Press Oxford. - Claesson J, Eftring B (1980)Optimal distribution of thermal insulation and ground heat losses. Swedish Council of Building Research Stockholm Document D33.
- Boileau GG, Latta JK (1968) Calculation of basement heat losses technical paper 292. Division of Building Research NRC Canada.
- MitalasGP (1983) Calculation of basement heat loss. Ashare Transactions 89: 420-437.
- Shen LS, Ramsey JW (1983) A simplified thermal analysis of the earth sheltered building using a Fourier series boundary method Ashare Transactions 89: 438-448.
- Sodha MS, Sawhney RL, Jaishankar JC (1990) Estimation of steady state ground losses from earth coupled structures by simulation. International Journal Energy Research 14: 563-571.
- Sodha MS, Sawhney RL, Singh SP, Jaishankar BC (1990) Electrical stimulation of thermal losses from underground structures. International Journal of Energy Research 14: 245-248.
- Sodha MS (2001) Simulation of periodic heat transfer between ground and underground structures.International Journal of Energy Research 25: 689-693.
- Sodha MS (2001) Simulation of dynamic heat transfer between ground and underground structures.International Journal of Energy Research25: 1391-1394.
- Sodha MS, Mishra D, Tiwari AK (2010) Validation of the basis of experimental simulation of heat transfer between a building and surrounding earth. Journal of Solar Energy Society of India.
- Mearig T, Morgan M (1997) Swimming pool guidelines. Alaska Department of Education Alaska. USA
- Pool size shape and depth options for UK indoor and outdoor pools.Bluepools custom pools and deck designs
- Labedev NN, Skalskaya IP, Uflynd YS (1965) Problems of mathematical physics. Prentice Hall Inc Englewood Cliffs

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