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Rapid evaluation for plate heat exchanger is vital in energyintensive chemical epoxidation as plant shutdown is not always feasible. In this paper, critical parameters for three different sizes of plate heat exchanger were determined based on temperature assessment via infrared thermometer. Extent of fouling was determined based on values of overall heat transfer coefficient, U_{0}. Number of heat transfer unit (NTU) larger than 1.25 and Nusselt (Nu) higher than 50 was found to be efficient and had sufficient degree of convection for epoxidation. Furthermore it was found that NTU had a significant and nonlinear relationship with heat flux, q" and Nusselt, Nu for the durationsensitive epoxidation. However in this study, LMTD showed insignificant difference with respect to plate heat exchanger performance.
Epoxidation, Fouling, Heat Transfer, Infrared, Performance.
Epoxidation is a type of oxidative reaction that transform an unsaturated bonds into an epoxy group (Figure 1). The conventional method of epoxidation had been established by T. Finedley et al. [1] and the nature of it has been reported widely [24]. Epoxidized vegetable oil is an important precursor in oleochemical sector and manufacturing it involves two consecutive steps. The first step is the insitu formation of highly unstable peroxocarbonic acid and the second step is consumption of the peroxocarbonic acid by olefinic double bond to form epoxy group and regenerate acid catalyst. Concentrated hydrogen peroxide and insitu formed peroxocarbonic acid are both thermodynamically unstable and their decompositions are very likely and vehemently exothermic. Heat of reaction for epoxidation was 218 kJ/mol for each double bond functionalized [5]. In current practice, concentrated hydrogen peroxide was used in excess molar ratio than acid catalyst and olefinic double bond as it rapidly decomposed above 333 K and generated another 98 kJ/mol [6] of energy. Furthermore temperature of reaction mixture beyond 333 K was detrimental as it induced side reaction.
Runaway was not uncommon especially for batchepoxidation and could caused reaction temperature transgressed higher than 333 K in typically less than 5 minutes and escalated to 373 K in 10 minutes. These resulted in an intensified energy burst and followed by release of a large volume of toxic hydrogen peroxideorganic gaseous. The sensitivity towards explosion had been reported on the same magnitude with trinitrotoluene (TNT) or nitroglycerine [7]. Hence a crucial factor of an epoxidation process is the design of heat exchanger which responsible for regulating effluent temperature at beneficial level and mitigate reaction runaway.
Figure 1. Two exothermic reactions in vegetable oil epoxidation. Individual schemes are labeled as: (a) Transformation of unsaturated double bond in vegetable oil into epoxy group, (b) Thermal decomposition of hydrogen peroxide into water and gaseous oxygen
Countercurrent plate heat exchanger (Figure 2) is commonly employed throughout oleochemical manufacturing facilities as it is capable of handling highly viscous fluids, has high heat transfer coefficient due to corrugationenhanced turbulences [8, 9], and has low fouling. It is known that surface area, A required for a specific heat duty, Q is given as:
$A=\int_{0}^{Q} \frac{d Q}{U_{0} \Delta T}$(1)
where U_{0} is the overall heat transfer coefficient and ΔT is the difference between the hot and cold streams at a given point. Driving force in heat exchanger can be described as logarithmicmean temperature difference (LMTD), T_{lm}, and in countercurrent configuration, LMTD is determined as:
$T_{l m}=\frac{\left(t_{1}^{\prime}t_{2}^{\prime \prime}\right)\left(t_{2}^{\prime}t_{1}^{\prime \prime}\right)}{\ln \left(\frac{t_{1}^{\prime}t_{2}^{\prime \prime}}{t_{2}^{\prime}t_{1}^{\prime \prime}}\right)}$(2)
where (t_{1}'  t_{2}") is the temperature difference at one end of the exchanger and (t_{2}'  t_{1}") is the temperature difference at the other end. The U_{0 }is largely dependent on the type of fluids where heat exchange occurred. LMTD calculation is convenient in practice as it is based on terminal temperature and assumes that heat exchanger operating at steady state and overall heat transfer coefficient is constant.
Rapid evaluation for heat transfer in epoxidation process become necessary in debottlenecking heat exchanger system. Identifying faulty heat exchanger in the heat exchanger network was a challenge when epoxidation plant is operational or in the absence of working builtin temperature monitoring device. Fast screening allows engineers to isolate malfunctioned heat exchanger and redistributed heat duty accordingly without plant downtime or turnaround. As infrared thermometer gained more accurate in recent years at competitive price, it is of interest to evaluate such method capability to deliver rapid evaluation on the suspected heat exchanger. Infrared method appears to be advantageous as being nonintrusive, fast response time, and has high sensitivity. Infrared thermometer is easy to handle and relatively cheaper.
Figure 2. Typical flow of fluids in singlepass countercurrent plate heat exchanger
2.1 Materials
A digital infrared thermometer was provided by Rolson® (model 27279), and had a builtin laser pointer for exact location measurements, temperature range between 253 to 473 K, and accuracy of ±2.5 %. The measurement required focal ratio (distancetospot, D:S) 5:1 area and recorded at emissivity, ε = 0.95.
Three singlepass (11) countercurrent plate heat exchangers were obtained from an established commercial plate heat exchanger manufacturer. The first and small plate heat exchanger was PHXS (0.18 m^{2} total surface area, 11 plates) and attached to the main reactor in Multipurpose Reactor Pilot Plant with volume capacity 150 L. The second and big plate heat exchanger was PHXB (18 m^{2} total surface area, 77 plates) and attached to the main reactor in Polyol Pilot Plant with volume capacity 1 ton. The third plate heat exchanger and served as control was PHXC (2.4 m^{2} total surface area, 17 plates) and attached to the Polyol Pilot Plant. PHXB and PHXS had identical mixture composition coming from an epoxidation reactor (i.e. monooleate, performic acid) in the hot stream and cooling water in the cold stream. PHXC had heat transfer from watertowater system.
2.2 Measurement
Temperature measurement was carried out during operational of the epoxidation process. A small piece of white masking tape was attached on the nozzles of heat exchanger and left for 30 minutes to equilibrate before measurement by infrared thermometer. Temperature measurement via infrared method [10, 11] typically rely on Wien's displacement law which states $\lambda_{\max } T=2.898 \times 10^{3} \mathrm{m} . K$ where λ_{max} represents wavelength at which maximal spectral emissive power of a perfect black body. As metallic or shinny surfaces give inaccurate reading based on Kirchhoff's law, measurement on a small piece of white masking tape was used instead in this study. Temperature variation were recorded three times and averaged. Flow rate for each stream was measured by triplicate bucket method and averaged. The same procedure was repeated for each heat exchanger evaluation.
3.1 Critical heat exchanger parameters (LMTD, U_{0}, and Fouling)
The challenge in controlling epoxidation process is narrow permissible temperature regime. In this study, the hot reactor effluent was only allowed to cool by 10 K and resulted in narrow LMTD (Table 1). Extending the temperature range would upset the reaction and impair the final quality of the epoxidized vegetable oil. Figure 3 describes the temperatureenthalpy (TQ) diagram of the process and total heat exchanged was 375 kW. The slope from temperatureenthalpy diagram is the inverse of stream enthalpy flowrate, 1/(FC_{p}), with C_{min} was the hot stream. Minimum temperature approach (ΔT_{min}) was 21 K and occur on the cold side of heat exchanger. As shown on Table 1, LMTD (equation (2)) for PHXB and PHXS were comparable despite working at different heat duty.
Table 1. Evaluation on heat exchanger performance
Heat Exchanger 
PHXS 
PHXB 
PHXC 
System 
Vegetable oil derivativetowater 
Vegetable oil derivativetowater 
Watertowater 
Condition 
Unfouled 
Fouled 
Fouled 
LMTD, T_{lm} (K) 
8 
8 
15 
U_{o} (J/s.m^{2}.K) 
694 
868 
4275 
NTU 
0.40 
1.29 
2.20 
Temperature ratio 
0.76 
0.80 
0.63 
Figure 3. Temperatureenthalpy (TQ) diagram representing heat exchanger employed in epoxidation process
Table 2. The average possible error for the experimental parameters

Equation for Uncertainty 
Uncertainty, % 
Re 
$\frac{\Delta R e}{R e}=\sqrt{\left(\frac{\Delta \dot{m}}{\dot{m}}\right)^{2}+\left(\frac{\Delta d_{e}}{d_{e}}\right)^{2}}$ 
1.88 
$T_{l m}$ 
$\frac{\Delta T_{l m}}{T_{l m}}=\sqrt{\left(\frac{\Delta t_{1}^{\prime}}{t_{1}^{\prime}}\right)^{2}+\left(\frac{\Delta t_{2}^{\prime \prime}}{t_{2}^{\prime \prime}}\right)^{2}+\left(\frac{\Delta t_{2}^{\prime}}{t_{2}^{\prime}}\right)^{2}+\left(\frac{\Delta t_{1}^{\prime \prime}}{t_{1}^{\prime \prime}}\right)^{2}}$ 
1.56 
U_{0} 
$\frac{\Delta U_{0}}{U_{0}}$$=\sqrt{\left(\frac{\Delta t_{1}^{\prime}}{t_{1}^{\prime}}\right)^{2}+\left(\frac{\Delta t_{2}^{\prime \prime}}{t_{2}^{\prime \prime}}\right)^{2}+\left(\frac{\Delta t_{2}^{\prime}}{t_{2}^{\prime}}\right)^{2}+\left(\frac{\Delta t_{1}^{\prime \prime}}{t_{1}^{\prime \prime}}\right)^{2}+\left(\frac{\Delta \dot{m}}{\dot{m}}\right)^{2}}$ 
1.98 
NTU 
$\frac{\Delta N T U}{N T U}=\sqrt{\left(\frac{\Delta t_{1}^{\prime}}{t_{1}^{\prime}}\right)^{2}+\left(\frac{\Delta t_{2}^{\prime}}{t_{2}^{\prime}}\right)^{2}+\left(\frac{\Delta t_{1}^{\prime \prime}}{t_{1}^{\prime \prime}}\right)^{2}+\left(\frac{\Delta \dot{m}}{\dot{m}}\right)^{2}}$ 
1.69 
Nu 
$\frac{\Delta N u}{N u}=\sqrt{\left(\frac{\Delta \dot{m}}{\dot{m}}\right)^{2}+\left(\frac{\Delta d_{e}}{d_{e}}\right)^{2}}$ 
2.05 
The values of U_{0} were experimentally determined using Q = U_{0}A(T_{lm}) = C_{min}(ΔT) relationship by utilizing specific heat capacity, C_{p} of reactor effluent. The temperature was obtained via the infrared thermometer. Note that for the analysis to be rigorous, the countercurrent heat exchanger would require number of channels per pass higher than 20. The detailed systematic error analysis was made based on the repeatability of the experiments and provided the accuracy of the experiments. The errors were based on the sensitivity of measuring devices and the least counts (Table 2). Values of uncertainty for Re was 1.88 %, LMTD was 1.56 %, U_{0} was 1.98 %, NTU was 1.69 %, and Nu was 2.05 %. This was in agreement with report demonstrated by Kandlikar [12] and Muthamizhi et al. [13]. Improvement on the infrared measurement capability such as 2dimensional infrared thermal imager would yield more accurate result and beyond the scope of this paper.
U_{0} for heat transfer from epoxidation effluent to cooling water in this process was determined to be 1600 J/s.m^{2}.K without fouling and 868 J/s.m^{2}.K for fouled plates. Heavy fouling was found primarily on the hot side of heat exchanger PHXB with overall heat transfer resistance of 0.00039 m^{2}.K/W. PHXB had been in operational state for more than 7 years since previous major service. It was observed that PHXS experienced reduction in stream flow rate by half on the hot side. Typically a slight pressure drop across plate heat exchanger was expected due to development of enhancedcorrugation turbulence with maximum allowable pressure drop at 0.2 bar. The mean channel pressure drop, ΔP_{chm} can be determined as:
$\Delta P_{c h m}=\Delta P_{p o r t}\Delta P_{e c}\Delta P_{f, p i p e}$(3)
where ΔP_{port} is the pressure drop between inlet and outlet ports in plate heat exchanger, ΔP_{ec} is related to expansion and contraction in enhancedcorrugation, and ΔP_{f,pipe} is pressure drop due to friction in pipe connection. However, sudden change in crosssectional area between process streams to channel port had increased flow maldistribution and affect hydraulic performance. Furthermore there were only 5 channels for the hot stream and 6 channels for the cold stream in PHXS as compared to 38 channels for the hot streams and 39 channels for cold streams in PHXB. It was known that plate heat exchanger experience momentous pressure drop for the first ten channels. However this detrimental effect is diminished by increasing number of channels [14]. As PHXS had number of channels less than 10 and relatively small ports diameter i.e. 20 mm as compared to 100 mm in PHXB, the maldistribution effect was substantial and excessive pressure drop across the PHXS was inevitable. Combined with endplate effect [12], this had severely affected heat conduction [14, 15] and contributed lowered value of U_{0} than it was designed for. PHXS was a brand new plate heat exchanger and unfouled, thus it was expected to have U_{0} approximately at 1600 J/s.m^{2}.K instead of 694 J/s.m^{2}.K (Table 1).
To further understand the heat transfer differences between PHXB and PHXS, it was of interest to determine the degree of convective heat transfer as prescribed in Nusselt number, Nu. For fully developed turbulent flow in plate heat exchanger and by applying Martin constants, Nu was determined as [16]:
$N u=0.122 \operatorname{Pr}^{\frac{1}{3}}\left(\frac{\mu_{m}}{\mu_{w}}\right)^{\frac{1}{6}}\left(f \cdot R e^{2} \sin 2 \beta\right)^{0.374}$(4)
where Nu is Nusselt number, Pr is Prandtl number, μ_{m} is fluid viscosity at bulk fluid temperature, μ_{w} is fluid viscosity at heat transfer boundary surface temperature, f is friction factor for turbulence regime as defined from Focke et al. [17] and Bobbili et al. [14], Re is Reynolds number, and β is chevron angle. Heat transfer dimensionless parameters are tabulated on Table 3. PHXS, PHXB, and PHXC had fully developed turbulent as all streams had values of Re larger than 400 [17, 18]. However values of Re for PHXS were much smaller than PHXB and might explained why it was underperformed. As Nu is a strong function of Re, PHXS was found to have lower value of Nu and implied that it had lower degree of convection than PHXB. PHXB and PHXC had larger values of Nu as both heat exchangers had very high values of Re. On the other hand, it was found that values of Pr (Pr = μC_{p}/k) for PHXB and PHXS were comparable as it is known to be independent of geometry and velocity boundary in both heat exchangers were fully developed than thermal boundary.
Table 3. Heat transfer dimensionless parameters for plate heat exchanger employed in epoxidation process
Heat Exchanger 
PHXS 
PHXB 
PHXC 

System 
Epoxidized vegetable oiltowater 
Epoxidized vegetable oiltowater 
Watertowater 

Reynolds,Re 
Hot side 
1043 
2197 
5834 
Cold side 
1344 
3053 
4131 

Prandtl,Pr 
Hot side 
11.46 
8.59 
2.62 
Cold side 
7.97 
4.97 
2.61 

Nusselt,Nu 
Hot side 
32.68 
49.77 
65.51 
Cold side 
34.28 
51.74 
51.49 
Fouling on the hot side of heat exchanger was responsible for the total heat transfer resistance, R_{Total}. R_{Total} is known to be inversely proportional with U_{0} ( $\left(R_{\text {Total}} \propto \frac{1}{U_{0} A}\right.$ ). Furthermore it was known that heat transfer resistance, R_{total} constituted by summation of heat transfer resistance on both sides, foulings resistance, and wall resistance:
$R_{\text {Total}}=R_{\text {hot}}+R_{f, h o t}+R_{\text {wall}}+R_{f, \text {cold}}+R_{\text {cold}}$(5)
where R_{hot} is the resistance on the hot side, R_{f,hot} is the fouling resistance on the hot side, R_{wall} is heat transfer resistance of the wall, R_{f,cold} is the fouling resistance on cold side, and R_{cold} is the resistance on the cold side. In order to determine degree of fouling, we employed Aspen EDR program under Design mode. Figure 4 denotes heat transfer resistance from the hot stream to the cold streams. Fouling on the hot side of heat exchanger constituted majority of the heat transfer resistance and accounted nearly half of overall heat transfer resistance. Deposits such as dirt, biological foul, and scales had formed on the heat exchange surface and introduced additional heat transfer resistance which reduced U_{0}. Thus it needed more than twice surface area, A to accommodate such foulings. Values of U_{0 } for PHXB were
determined to be as high as 1600 J/s.m^{2}.K for unfouled situation and as low as 740 J/s.m^{2}.K for dirty plates. Unlike PHXS which suffered from excessive pressure drop, the low value of U_{0} in PHXB signaled the fouling buildup across the plates. Similar trend of heat transfer resistance due to fouling was found on PHXC for watertowater heat transfer, which never has undergone major service for more than 10 years. For R_{Total} = 0.0013 m^{2}.K/W, the U_{0} for PHXC was determined to be approximately 6,200 J/s.m^{2}.K and 3100 J/s.m^{2}.K for clean and dirty plates, respectively.
Figure 4. Heat transfer resistance diagrams for PHXB and and PHXC
3.2 Number of heat transfer unit (NTU)
The effectiveness, E, of countercurrent heat exchanger was governed by number of heat transfer unit (NTU) and heat capacity ratio, C_{r}:
$E=\frac{1\exp \left[N T U\left(1C_{r}\right)\right]}{1C_{r} \exp \left[N T U\left(1C_{r}\right)\right]}$(6)
As C_{r} was a fixed parameter for epoxidation, effectiveness often relies on the value of NTU alone. NTU is expressed as:
$N T U=\frac{U A}{C_{\min }}$(7)
where C_{min} was the limiting or minimum heat capacity flowrate, which in this analysis was the hot stream. There are several factors affecting NTU such as the plate gap, chevron angle, β, the pass arrangements and the heat flux.
Figure 5. Heat flux, q”, normal to a plate with thickness L
Consider the steady, twodimensional (Figure 5) convection flow where heat transfer occurred from high temperature channel to low temperature channel, heat is neither generated nor destroyed, temperature gradient in yaxis is negligible, and heat loss to surrounding is negligible. Under these assumptions, the continuity equation is:
$\frac{d u}{d x}+\frac{d v}{d y}=0$(8)
$u \frac{d T}{d x}+v \frac{d T}{d y}=\alpha \frac{d^{2} T}{d x^{2}}$(9)
where u and v are the velocity component along the x, yaxes. Further α is the thermal diffusivity. The boundary conditions are:
$\frac{d T}{d x}=\frac{q^{\prime \prime}}{k}$ at $x=0$(10)
$v \rightarrow 0, T \rightarrow T_{\text {bulk}}$ as $x \rightarrow \infty$(11)
where k is the thermal conductivity of the plate. At time t with for incompressible fluid:
$\frac{d T}{d t}=\alpha \nabla^{2} \mathrm{T}$(12)
where by the definition the Laplacian operator is:
$\nabla^{2}=\nabla \cdot \nabla=\frac{\mathrm{d}}{\mathrm{dx}^{2}}+\frac{\mathrm{d}}{\mathrm{dy}^{2}}$(13)
Hence equation (12) become:
$\frac{d T}{d t}=\alpha\left(\frac{d^{2} T}{d x^{2}}+\frac{d^{2} T}{d y^{2}}\right)=\frac{k}{\rho c}\left(\frac{d^{2} T}{d x^{2}}+\frac{d^{2} T}{d y^{2}}\right)$(14)
where ρ is fluid density and c is specific heat.
The physical rate of heat transfer per unit area or heat flux, q” across a plate in Figure 5 was proportional to temperature gradient, ∇T across the plate:
$q^{\prime \prime}=k \nabla \mathrm{T}=\mathrm{k}\left[\frac{\mathrm{dT}}{\mathrm{dx}}+\frac{\mathrm{dT}}{\mathrm{dy}}\right]$(15)
Under steady state operation where temperature gradient existed in xaxis direction only and the dT/dy became negligible, equation (15) can be simplified to:
$q^{\prime \prime}=\mathrm{k}\left[\frac{\mathrm{dT}}{\mathrm{dx}}\right]=\mathrm{k}\left[\frac{\mathrm{T}_{\mathrm{low}}\mathrm{T}_{\mathrm{high}}}{\mathrm{L}}\right]$(16)
Therefore the total heat transferred, Q, in a plate heat exchanger was dependent on the q”:
$q^{\prime \prime}=\frac{Q}{A}$(17)
The interaction between NTU (equation (7)) and q" (equation (17)) was unknown for oleochemical sector. Under some circumstances, design was limited by knowledge of NTU alone. NTU of 1.0 and less was regarded as low NTU and typically suitable for nondemanding process. On the other hand, NTU of 2.5 and above is considered as high NTU and often avoided as it is susceptible to excessive pressure drop. However we found that NTU = 1.29 met our requirements to effectively regulate the process at 333 K. NTU of 0.4 was severely suffered from process runaway. PHXB (NTU = 1.29) was able to cool epoxidation reactor faster and more efficient in preventing reaction runaway than PHXS (NTU=0.40). Shorter cooling duration was preferred in durationsensitive process such as epoxidation. Lower NTU reflected lower value of q" that undermined temperaturesensitive epoxidation process. As duration for reactor cool down was a key parameter for heat exchanger employed in epoxidation process, it was further proposed that the heat exchanger performance for temperaturesensitive process to be better described as q".
To further understand this concept, we employed Aspen EDR to simulate the plate heat exchanger under Design mode and 11 pass arrangement. A total of 9 heat exchangers with total surface area between 18 m^{2} and 48 m^{2} and NTU between 0.36 and 1.67 were evaluated. Based on the EDR and experimental results, we compared the values of q” and Nu (Figure 6 and Figure 7, respectively). It is interesting to note that NTU had a sigmoid relationship with the q" for the countercurrent plate heat exchanger (Figure 6). Nonlinear regressions based on sigmoidallyshaped function were carried out in both figures using GaussNewton method (Table 4). The precision of analysis for both regressions were denoted as standard of error of regression, S at 1003 W/m^{2} and 1.05, respectively. Results from EDR were in harmony with experimental data. The proportional relationship between q” and NTU also resemble the effectivenessNTU relationship interrelated report [19]. Note that this analysis was validated only for 11 pass arrangement with bounded 0.36 < NTU < 1.67.
Figure 6. NTU relationship with heat flux, q". Heat exchanger with higher NTU had higher transfer rate of heat per area, resulting in an intensive heat transfer. Individual legend is labeled as: Triangle = Experimental; Circle = EDR.
Table 4. Nonlinear regression parameters of function $\theta_{1}+\frac{\theta_{2}\theta_{1}}{1+e^{\left(\frac{X\theta_{3}}{\theta_{4}}\right)}}$ and 95 % confidence interval for Figure 6 and 7
q" = q"(NTU) 
Nu = Nu (NTU) 

θ 
Estimate 
95 % Confidence Interval 
Estimate 
95 % Confidence Interval 

Lower 
Upper 
Lower 
Upper 

1 
25,201 
23,159 
28,756 
49.973 
48.448 
51.663 
2 
7,452 
4,557 
8954 
33.256 
31.471 
34.617 
3 
1.00 
0.9 
1.1 
0.8423 
0.786 
0.903 
4 
0.20 
0.1 
0.3 
0.0976 
0.043 
0.161 
Common approaches to enhance NTU are to make multiple pass arrangement such as 21 as suggested by Kandlikar et al. [12], and by increasing the number of plates preferably more than 15 per pass. For epoxidation process, it was found that plate heat exchanger with NTU above 1.2 could expedite cooling of reaction mixture as countercurrent heat exchanger inherit higher efficiency at increasing capacity ratio [20]. PHXS was intentionally designed at reduced surface area and incapable to meet the heat duty requirement within stipulated cooling duration specified between 3 to 5 minutes. Despite PHXB exchanged more heat than PHXS, it generated less amount of entropy as indicated by temperature ratio $\left(\frac{t_{1}^{\prime \prime}}{t_{1}^{\prime}}\right)$ in Table 1. An ideal heat exchanger delivers maximum amount of heat and generates minimum amount of entropy when operating at ideal conditions [20]. On the other hand, PHXC had lower temperature ratio as it was used for capacity ratio at unity.
Figure 7. Nusselt as a function of NTU. Individual legend is labeled as: Triangle = Experimental; Circle = EDR
Fast screening on plate heat exchangers performance in oleochemical application was accomplished by employing nonintrusive infrared thermometer. Indication of fouling was provided by comparing U_{0} with theoretical value (clean). To avoid excessive pressure drop which was not related to fluid friction, it was found that number of channels must be larger than 10. Performance of countercurrent plate heat exchanger was indicated by values of NTU and dimensionless Nu. NTU between 0.36 and 1.67 exhibited a nonlinear and sigmoidallyshaped curve relationship with heat exchanger performance needed for epoxidation process. It was demonstrated that plate heat exchanger with NTU > 1.25 and Nu > 50 was able to minimize runaway reaction in epoxidation.
The authors acknowledge DirectorGeneral of Malaysian Palm Oil Board (MPOB) for permission to publish the article. Special thanks to personnel at Process Engineering and Design Unit at MPOB for providing assistance in operating oleochemical pilot plants.
A 
surface area, m^{2} 

C_{min} 
minimum heat capacity flowrate, J/(s.K) 

C_{p} 
stream heat capacity, J/(kg.K) 

C_{r} 
heat capacity ratio 

C 
specific heat 

d_{e} 
hydraulic diameter 

E 
effectiveness 

F 
stream flowrate, kg/hr 

f 
friction factor 

k 
thermal conductivity, J/(K.m.s) 

$\dot{m}$ 
mass flux, kg/(hr.m^{2}) 

NTU 
number of heat transfer unit, dimensionless 

Nu 
Nusselt number, dimensionless 

Pr 
Prandtl number, dimensionless 

Q 
heat duty, W 

q” 
heat flux, W/m^{2} 

$R_{\text {Total}}$ 
total of heat transfer resistance, m^{2}.K/W 

$R_{h o t}$ 
resistance on hot side, m^{2}.K/W 

$R_{f, h o t}$ 
fouling resistance on hot side, m^{2}.K/W 

$R_{\text {wall}}$ 
heat transfer resistance of wall, m^{2}.K/W 

$R_{f, \text {cold}}$ 
fouling resistance on cold side, m^{2}.K/W 

$R_{\text { cold }}$ 
resistance on cold side, m^{2}.K/W 

T_{lm} 
logarithmicmean temperature difference (LMTD), K 

$t_{1}^{\prime}$ 
inlet temperature of hot stream, K 

$t_{2}^{\prime}$ 
outlet temperature of hot stream, K 

$t_{2}^{\prime \prime}$ 
outlet temperature of cold stream, K 

$t_{1}^{\prime \prime}$ 
inlet temperature of cold stream, K 

$(\frac{t_{1}^{\prime \prime}} {t_{1}^{\prime}})$ 
temperature ratio, dimensionless 

U_{0} 
overall heat transfer, J/s.m^{2}.K 

u, v 
velocity components along the x and y directions, respectively 

x, y 
Cartesian coordinates normal to and along the surface, respectively 

Greek symbols 

a 
thermal diffusivity, m^{2}/s 

b 
chevron angle, ° 

ε 
emissivity 

ρ 
fluid density, kg/m^{3} 

θ 
regression parameter 

μ_{m} 
fluid viscosity at bulk fluid temperature, cP 

μ_{w} 
fluid viscosity at heat transfer boundary surface temperature, cP 

$\Delta H_{r}$ 
standard enthalpy of reaction, J/mol 

ΔP_{chm} 
mean channel pressure drop in plate heat exchanger, bar 

ΔP_{port} 
pressure drop between inlet and outlet ports in plate heat exchanger, bar 

ΔP_{ec} 
pressure drop due to expansion and contraction in enhancedcorrugation, bar 

ΔP_{f,pipe} 
pressure drop due to friction in pipe connection, bar 

ΔT 
change in temperature stream, K 

ΔT_{min} 
minimum temperature approach, K 

$\nabla \mathrm{T}$ 
temperature gradient, K 

λ_{max} 
wavelength at maximal spectral emissive power of a black body, μm 
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