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Journal of Industrial Engineering Research, 1(6) September 2015, Pages: 25-32

IWNEST PUBLISHER

Journal of Industrial Engineering Research

(ISSN: 2077-4559)

Journal home page: http://www.iwnest.com/AACE/

Corresponding Author: Arif bin Ab Hadi, Department of Chemical and Process Engineering, Faculty of Engineering and

Built Environment, National University of Malaysia, 43600 UKM, Bangi Selangor, Malaysia

Spreadsheet Modelling for Temperature Profile inside Palm Oil Fresh Fruit Bunch Arif bin Ab Hadi, Prof. Dato’ Ir. Dr. Abd. Wahab Mohammad, Prof. Ir. Dr. Mohd Sobri Takriff

Department of Chemical and Process Engineering, Faculty of Engineering and Built Environment, National University of Malaysia, 43600

UKM, Bangi Selangor, Malaysia

A R T I C L E I N F O A B S T R A C T

Article history:

Received 23 July 2015 Accepted 25 August 2015

Available online 12 September 2015

Keywords:

Unsteady-state conduction, specific

heat capacity, heat transfer coefficient, thermal diffusivity, thermal

conductivity, model validation.

A spreadsheet mathematical model that was developed using finite difference explicit

method is used as a tool to predict the FFB center temperature based on FFB temperature profile inside sterilizer cage. The estimated values of FFB physical

properties, operating conditions and model assumption were done accordingly. The

model was validated by adjusting the value of thermal conductivity, k until simulated data is close to the published data from Mongana Report, Chan SY and Ang et al. The

correlation coefficient, R and coefficient of determination, R2 between the spreadsheet

data and published data was determined accordingly. The result obtained based on the determined correlation suggests the modeling tool is capable of predicting the FFB

temperature profile inside FFB with a very high certainty.

© 2015 IWNEST Publisher All rights reserved.

To Cite This Article: Arif bin Ab Hadi, Prof. Dato’ Ir. Dr. Abd. Wahab Mohammad, Prof. Ir. Dr. Mohd Sobri Takriff., The study of

Temperature Distribution for Fresh Fruit Bunch during Sterilization Process. J. Ind. Eng. Res., 1(6), 25-32, 2015

INTRODUCTION

The main purpose of having a mathematical modeling for single fresh fruit bunch is to predict the center

temperature of FFB during sterilization process to indicate whether the fruit is sufficiently “cooked”. The model

is used as a practical approach to determine the adequacy of sterilization instead of having to insert the

temperature sensor probe into the center of fresh fruit bunch every time.

The spreadsheet user interface is one of the common engineering tools for quantitative analysis. Not only it is

easily found in the market, it is also user-friendly, making it an easy to learn tool. Spreadsheet tools can be used

to model heat penetration problems which allow the user to evaluate change in parameters and its significance

towards overall efficiency of heat penetration.

The model allows us to estimate the amount of heat transfer and steam consumption based on the center

temperature of FFB at different locations inside the sterilizer cage. Besides that, it can also be used for analyzing

the significance of changes in the operating conditions such as heating steam temperature, sterilization period,

and different FFB weight and so on for optimization purposes during the process.

The modeling work of heat transfer for fresh fruit bunch was made by applying finite differential explicit

method for two dimensions using spreadsheet. An overview of previous work which was based on heat

conduction spreadsheet model to predict time required for mesocarp to attain thermal equilibrium with the steam

temperature is given by Mohd. Halim Shah. I [3]. Another modeling study conducted by Chan SY of using two

theoretical bulk models developed for heat transfer model using computer software to investigate the temperature

and time required for the center of fresh fruit bunch to become “cooked” [2].

In this paper, the development of the model was made based on finite difference explicit method using

spreadsheet by considering the heat transfer by conduction through the interior nodes of fresh fruit bunch and

convection through the surface nodes. Several assumptions have been made in order to simplify the model

calculation as per discussed later.

METHODS AND METHODOLOGY

26 Arif bin Ab Hadi et al, 2015


Model Description:

This model simulates the actual condition of sterilization process in batch process. During the process, the

FFBs inside the sterilizer cage are heated up gradually from ambient temperature of atmospheric pressure up to

140°C and 3 bar g for 80 minutes. After the end of cooking time, the FFB is cooled down.

Assumptions:

1) Two-dimensional, time dependent, unsteady state, heat conduction heat transfer.

2) Assume to be rectangular block with equivalent volume, actually is ellipsoidal.

3) Comprises of various parts of an oil palm fresh fruit bunch (FFB), namely fruitlet mesocarp or fiber, shell

and nut, and the stalk.

4) The estimated physical properties for fresh fruit bunch is obtained for all various parts of FFB as per stated

above.

5) The mode of heat transfer from steam to outer surface of FFB is by convection and from outer surface that

penetrates radially inwards FFB is by conduction.

6) The rectangular surface temperature is assumed to be the same as steam temperature.

7) Model is divided into a number of concentric rectangular nodes in the fresh fruit bunch (FFB) layer.

8) The estimated diameter of FFB is 0.30m, equivalent to the thickness of rectangular block.

9) Divided equally into 36 square sub-regions by network of mesh size dx = dy = 0.06m (0.3/5). See Figure

3.21.

10) Time domain is divided into small time step, dt and each node represents temperature, which depends to

time changes.

Fig. 1: 36 nodes for the entire region

Rectangular Physical Properties:

A set of initial values which was either measure experimentally or by estimation are taken from existing

literatures and the source will be referred to as per below. The initial values are taken as average or mean value to

simplify the calculation in this model. The initial values used in this calculation are as per Table 1 below:

Table 1: Physical Properties of Individual Components of FFB

Thermal Diffusivity, α Density, ρ Specific Heat, Cp Thermal Conductivity, k

(m2/s x 10-7) (kg/m3) (kJ/kgK) (W/mK)

Mesocarp 1.24 993 2.816 0.347

Stalk 1.81 929 4.038 0.679

Nut 1.92 1203 2.291 0.529

Chan, S.Y., 1985. Modeling and Simulation of the Fresh Fruit bunches (FFB) during Sterilization Process,

Universiti Malaya: Master Thesis. [2]

Masitah Hasan and Abdullah Hashim [4] had quoted in their studies a previous work by Choi and Okos

(1983) in order to estimate the overall specific heat value, Cp of a liquid food by correlating the individual

specific heat with the mass fraction and temperature using polynomial fitting equation in order to determine the

overall specific heat for FFB based on individual components of fresh fruit bunch, FFB namely mesocarp, shell,

kernel and stalk.



In this study, the overall specific heat of fresh fruit bunch which was represented by the mean weighted

average based on the mass fraction can be expressed as

where

= Overall specific heat for fresh fruit bunch

= Mass fraction of fresh fruit bunch component

= Specific heat at temperature T for component i

Since the specific heat for fresh fruit bunch can be estimated using this method, therefore other physical

property values such as thermal conductivity, density etc can also be estimated by applying this method.

Previous studies by Rajanaidu, Tan, Rao and Chow [5] on the typical values of FFB mass fraction

determined experimentally is used to calculate the overall physical properties of fresh fruit bunch.

The overall physical properties of fresh fruit bunch estimated using the above is tabulated as per Table 2.

Table 2: Mean values of FFB physical properties

Thermal Diffusivity, α Density, ρ Specific Heat, Cp Thermal Conductivity, k

(m2/s x 10-7) (kg/m3) (kJ/kgK) (W/mK)

1.55647 991.845 3.230955 0.498787

Estimation Of Convective Heat Transfer Coefficient:

Considering the nature of heat transfer due to forced convection between the steam and fresh fruit bunch, the

heat transfer coefficient correlation for prescribed sphere type geometry recommended by Whitaker [8] takes an

expression of the form

All thermal properties are evaluated at free stream temperature, T∞ except µS, which is evaluated at surface

temperature.

The estimated heat transfer coefficient value for fresh fruit bunch is obtained by comparing to an initial value

which was taken from previous research on heat transfer coefficient with similar operating condition as the model

using the above correlation. Few assumptions were made in order to estimate the variables above. In this case, the

difference in the characteristic length of the fresh fruit bunch as compared to the fruitlet is taken into account in

this case.

A heat transfer coefficient value for fruitlet, h = 2000-11000W/m2K is used as initial value for estimation of

heat transfer coefficient for fresh fruit bunch. [6]

The Prandtl number can be calculated as per below

The thermal properties are evaluated at free stream temperature, in this case, the saturated steam at 2.6 bar g

of 140°C saturation temperature. In this case, we assumed that the Prandtl number is the same for both fruitlet and

fresh fruit bunch since the pressure and temperature is assumed to be about the same. The value obtained falls

within the correlation constraint.

As for the Reynold number, the calculation which involves the velocity of steam coming into contact with

the fresh fruit bunch is rather difficult due to lack of instrumentation during the experiment. The initial steam

flow into the sterilization chamber could be highly turbulent due to high steam velocity followed later by laminar

flow when the velocity drops due to low pressure differential between the incoming steam pressure and the

sterilizer chamber pressure [7]. Therefore, it is assumed that the value of Re falls within the correlation constraint

due to the laminar flow during part of the heating process.

The ratio of Nusselt number for both fruitlet and fresh fruit bunch was determined as per reduced equation

below:



In this case, the diameter variable for FFB for Nusselt number in the denominator is assumed to be 10 times

greater than the size of fruitlet, which is about 30cm diameter for FFB and 3 cm diameter for fruitlet. The terms

of Prandtl number, dynamic viscosity, density and velocity and including diameter coefficient were simplified

based on equation above. The value of Re number in the correlation constraint is assumed to be at the maximum

limit of 76000 in order for the correlation to be valid and accurate, which then the ratio becomes

Hence, the initial value for heat transfer coefficient for fruitlet was substituted in the above equation which

gave the estimated value of heat transfer coefficient for fresh fruit bunch as per below

= 773-4250 W/m2K

Heat Transfer Equation In The Numerical Calculation:

The temperatures for all nodes are solved by applying the derived energy equations depending on the

boundary conditions for each case node [8]. The appropriate equation was assigned to each node accordingly.

The temperature node (T8, T9, T10, T11, T14, T15, T16, T17, T20, T21, T22, T23, T26, T27, T28, T29) is

calculated using the following equation

Fig. 2: Temperature setup for interior node

The temperature node at plane surface (T2, T3, T4, T5, T7, T12, T13, T18, T19, T24, T25, T30, T32, T33,

T34, T35) is calculated using the following equation

35343332

30

24

18

12

25

19

13

7

0.3m

0.3m

0.06m

2 3 4 5

Fig. 3: Temperature setup for node at plane surface



The temperature node at exterior corner (T1, T6, T31, T36) is calculated using the following equation

Fig. 4: Temperature setup for node at exterior corner

The stability of numerical solution for a steady state value of the nodal temperature based on explicit method

is dependent on the stability criterion called Fourier number, Fo [8]. The limiting factor which is Fourier number

is used to determine the maximum allowable value of ∆t. A violation of this criterion will result in instability of

solution, causing erroneous results.

In this case, the most stringent value of Fo is selected based from the equations for all node cases.

Data Used For Model Simulation And Model Validation:

The FFB raw temperature data gathered at the mill inside sterilizer cage measured using temperature sensor

located in between the FFB bunches which represents heating steam temperature, T∞ for the model. A set of

estimated initial data for the model is tabulated as per Table 3.

Table 3: Estimated initial parameters for model

FFB density, ρ (kg/m3) 992

FFB Specific Heat,Cp (kJ/kgK) 2816

Distance between node, dx (m) 0.065

Bunch Volume Equivalent Radius (m) 0.1625

Bunch Initial Temperature (°C) 30

Sterilization time (s) 4800

FFB thermal conductivity, k (W/mK) 0.4988

FFB thermal diffusivity, α (m2/s) 1.556 x 10-7

Convective Heat Transfer Coefficient, h (W/m2K) 4250

Selected dt (s) 5

Biot number, Bi 553.829

Fourier number, Fo 0.000184171

The bunch size is taken as average 17kg with equivalent radius of 0.1625m. The initial temperature was set at

30°C. The sterilization period is set accordingly for duration of 80 minutes for one sterilization cycle. The initial

value of thermal diffusivity, Biot and Fourier number were calculated accordingly.

The condensing steam that causes a continuous liquid film to be formed over the bunch and other factors

such as air occluded inside bunch will have an impact towards effectiveness of heat transfer towards FFB,

specifically thermal conductivity, k value of fresh fruit bunch. Hence, a correction factor for effective thermal

conductivity of FFB, keff is introduced. The values of heat transfer coefficient for fresh fruit bunch, together with

thermal conductivity were used as an initial guess to determine the initial temperature profile for fresh fruit bunch

during sterilization process. The result was then compared with the experimental data from Mongana report [1] ,

experimental Ang et al data obtained from Chan SY studies [2] together with the modeling by Chan SY [2]. The

values were adjusted and the model is tested again until the simulated data were closest to the experimental data.

The data used for model validation is represented as per Table 4. The temperature data from Mongana report

was based on 17kg bunch, triple peak sterilization and thermocouple inserted into FFB rachis (stalk) [1] while the

data taken from Chan SY and Ang et al was based on thermocouple inserted into a hole drilled near or beside

stalk. [2]



Table 4: Temperature data based on Mongana Report and Modeling by Chan SY

RESULT AND DISCUSSION

Based on the numerical solution from the model, the temperature profile at the center of FFB obtained for

temperature node location (T1 Z1) based on initial and adjusted value of thermal conductivity is shown as per

Figure 5. The temperature profile at the top location of the cage, which represents the heating steam temperature

is chosen for model validation.

Fig. 5: Temperature profile at T1 Z1 node location (before and after adjustment)

Fig. 6: Finite Difference Time Step Iteration (T1 Z1) excel calculation sheet chart (before adjustment)



Fig. 7: Finite Difference Time Step Iteration (T1 Z1) excel calculation sheet chart (after adjustment)

Figure 6 and 7 shows the finite difference time step iteration (T1 Z1) temperature node location using excel

calculation sheet chart before and after adjustment of thermal conductivity value, respectively. Based on the

results, we observe that the temperature profile hardly shown any increase until the end of sterilization period

prior to adjusting the thermal conductivity value of overall fresh fruit bunch, k = 0.4988 W/mK. After a few

numbers of runs, it was found that the experimental data was best represented by the model with adjusted value of

effective thermal conductivity, keff = 8.7 W/mK which is approximately 17 times the overall FFB thermal

conductivity, k = 0.4988 W/mK. The ratio of estimated theoretical value of thermal conductivity of overall fresh

fruit bunch, k = 0.4988 W/mK as compared to condensed steam, k = 0.0288W/mK at 140°C and air, k =

0.03434W/mK at 140°C [3] is approximately 17 times.

Most of the steam condensate formed had to flow down by gravity. The flowing condensate might cause a

continuous liquid film to be formed over the bunch. Therefore the effect of this liquid film on the heat transfer

should not be overlooked. This explains the possible reason for the effective thermal conductivity value, keff = 8.7

W/mK to be approximately 17 times that of estimated theoretical value, k = 0.4988 W/mK for overall fresh fruit

bunch. Similar adjustments were made accordingly by Chan SY [2] for effective fruitlet thermal conductivity, keff

= 4 W/mK as compared to theoretical value, k = 0.347 W/mK by taking into account the effect of this liquid film

towards heat transfer.

The convective heat transfer coefficient, h was set as high as possible at 4250 W/m2K in order to best suit

the experimental data.

Fig. 8: Temperature profile from experimental and modeling data from Mongana Report and Chan SY



Figure 8 shows a comparison between the result obtained for the FFB center temperature profile from the

model in this study with the temperature data from Mongana Report together with FFB modeling temperature

profile Chan SY modeling result. The correlation coefficient, R, which indicates the strength and direction of a

linear relationship between two variables together with the coefficient of determination, R2

value which indicates

ability of the regression line to represent the experimental data was determined from an excel program data

analysis under regression analysis. The variable input for the analysis was set to be the temperature profile

obtained from spreadsheet modeling and experimental data from Mongana Report, Chan SY and Ang et al.

The calculated value for correlation coefficient, R and coefficient of determination, R2

between the

temperature profile obtained from spreadsheet modeling and experimental data from Mongana Report is R =

0.9966 and R2 = 0.9932 which indicate a very strong linear correlation between experimental and spreadsheet

modeling data and indicates how well the experimentally determined data can be represented by the modeling

data. The calculated values for R and R2 between the spreadsheet data and Chan SY model data and Ang et al

experimentally data were R = 0.9967, R2 = 0.9934 and R = 0.997, R

2 = 0.9940, respectively. This also indicates

strong linear correlation and a very high agreement between the spreadsheet data and Chan SY model data and

Ang et al experimental data.

Conclusion:

Based on the result obtained, it is clear that the model is capable of predicting the temperature profile inside

fresh fruit bunch (FFB) during sterilization process at almost 100% certainty based on the results of determined

correlation coefficient, R and correlation of determination, R2 value. This spreadsheet tool can be used in

conjunction with temperature distribution studies to estimate the amount of heat transfer and steam consumption

together with analyzing the significance of changes in the operating conditions such as heating steam

temperature, sterilization period, different FFB weight etc.

REFERENCES

[1] Mongana Report, 1955. First Volume.

[2] Chan, S.Y., 1985. Modeling and Simulation of the Sterilised of Fresh Oil Palm Fruit Bunches (FFB),

University Malaya: Master Thesis.

[3] Mohd Halim Shah, I., A.A. Mustapa Kamal, M. Noor Azian, 2009. A system approach to Mathematical

Modeling of Sterilization Process in Palm Oil Mill. European Journal of Scientific Research.

[4] Masitah Hasan and Abdullah Hashim, 1990. Determination of the specific heat of Oil Palm Fruit

Bunch.The Planter, Kuala Lumpur, 66: 282-290.

[5] Rajanaidu, N., Y.P. Tan, V. Rao and C.S. Chow, 1983. Comparison of bunch and oil quality before and

after the introduction of weevil; Proceeding of the workshop on quality in the Palm Oil Industry, PORIM,

p: 40.

[6] Mustafa Kamal, A.A., 2003. The study of heat penetration in palm oil fruitlets by developing a new

technique for measuring oil content in fruitlet during sterilization process.

[7] Ravi Menon, N., Innovation Potentials in Palm Oil Mill Design. Palm Oil Engineering Bulletin, 104: 9-12.

[8] Frank, P., Incropera, David P. Dewitt, 2002. Fundamentals of Heat and Mass Transfer, 5th

edition. John

Wiley & Sons.

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