Innovative Heat Exchanger Dryer Solution in Equipment Design PDF

**CHAPTER 1: INTRODUCTION** Heat exchangers are thermodynamic equipment used in several industrial applications such as automotive, chemical and process engineering, industrial heating, cooling and heat-recovery processes, etc. In the most common applications, the heat transfer occurs under steady...

**CHAPTER 1: INTRODUCTION** Heat exchangers are thermodynamic equipment used in several industrial applications such as automotive, chemical and process engineering, industrial heating, cooling and heat-recovery processes, etc. In the most common applications, the heat transfer occurs under steady state operating conditions. Priority is then given to steady state heat transfer which does not allow any possibility of thermal energy storage in the heat exchanger. In some specific applications such as thermal conditioning of beverage in agro-food industries, the heat exchange between the heat transfer fluids occurs under transient state operation through a conductive element which allows a better management of the heat or cold demand by storing part of the thermal energy in the heat exchanger. Thermal energy can be stored under sensible, latent, or chemical forms. Heat exchangers are widely used in the food industry, employed for heating among other purposes, though they are so expensive and energy consuming. To overcome this, integrated heating systems are considered alternatives. This research indicated that for an integrated heating system, the energy efficiency is approximately 95.00%, whereas second-law efficiency is at 46.56% relative to the conventional heating system with an electric boiler. Therefore, this implies that guided approaches can give better alternatives for the food industry. (Basaran, et. al., 2018) One of the major features relevant to the preservation of food is the transfer of heat, which regulates chemical reactions, texture, and properties of food. Such a structural element as water has a large influence on the stability of food. Evaporation also enhances the heat-transfer efficiency and is frequently applied to solidify food solids. New designs are trying to decompose their products through thin tubes or surfaces of heat transfer to make the process more efficient and minimize thermal degradation (Lee & Tastemir, 2023) 1. **Feedstock** The soft drink industry relies on a diverse range of feedstock ingredients, each contributing to the final product\'s flavor, appearance, and stability. Understanding these components is crucial for optimizing processes in heat exchanger dryers, which play a vital role in removing moisture while preserving the quality of the beverage. This essay explores the specific feedstock used in soft drink production, detailing the characteristics, roles, and processing considerations for each ingredient, according to industry standards and research. **1.1.1 Water** Water serves as the primary solvent in soft drink formulations, constituting the majority of the beverage\'s volume. Its purity is paramount, requiring adherence to standards for potable water, with turbidity levels below 1 NTU and total coliform counts under 500 CFU/mL (American Water Works Association, 2020). Prior to use, water typically undergoes rigorous purification processes, such as filtration and reverse osmosis, to eliminate contaminants. This ensures that the final product is safe for consumption and maintains the intended flavor profile. **1.1.2 Sugars and Sweeteners** Sugars and sweeteners are integral to soft drink formulations, providing the desired sweetness and influencing mouthfeel. Commonly used natural sugars include sucrose, which is usually found in crystalline form and has a solubility of approximately 2000 g/L in water at room temperature (Food Chemistry, 2019). High-fructose corn syrup (HFCS), particularly HFCS 55, is also prevalent; it is a liquid sweetener consisting of about 55% fructose and 42% glucose, with a viscosity of approximately 1.5--2.5 cP (USDA, 2021). Additionally, artificial sweeteners, such as aspartame, are used in low-calorie beverages. Aspartame is highly concentrated, being around 200 times sweeter than sucrose, and is typically incorporated at levels of 0.1% to 0.5% in the formulation (FDA, 2022). **1.1.3 Flavorings and Extracts** Flavorings and extracts are essential for creating the distinctive taste of soft drinks. Natural fruit extracts, such as those derived from oranges and lemons, are commonly used and can be found in both liquid and concentrated forms. However, these extracts are sensitive to heat; their volatile compounds may degrade at temperatures exceeding 70°C, necessitating careful temperature control during the drying process (Zhao et al., 2020). Synthetic flavorings, like ethyl maltol, are also utilized for their sweetness, typically used at concentrations of 0.1% to 0.5%. **1.1.4 Acids and Stabilizers** Acids and stabilizers play significant roles in flavor enhancement and product stability. Citric acid, for instance, is frequently added to provide tartness and is usually present in concentrations ranging from 0.1% to 0.5% (Sullivan, 2019). Additionally, preservatives such as sodium benzoate are incorporated to inhibit microbial growth, typically at levels of no more than 0.1% (WHO, 2021). These ingredients are crucial for extending shelf life and maintaining the quality of soft drinks during storage. **1.1.5 Colors and Preservatives** Coloring agents enhance the visual appeal of soft drinks, with both natural and synthetic options available. Natural colors, such as beet juice concentrate, are often used, typically at concentrations of 0.1% to 0.5% (CIR, 2020). Synthetic dyes, like Red 40, are also common, usually incorporated at levels of about 0.02%. Preservatives are vital for preventing spoilage and ensuring that the product remains safe and appealing to consumers. **1.1.6 Carbonation** Carbonation is a defining characteristic of many soft drinks, providing the effervescence that consumers expect. Carbon dioxide (CO2) is infused into the beverage during processing to achieve a concentration of approximately 2.5 to 3.0 volumes of CO2, with infusion pressures ranging from 2.5 to 4.0 bar (Gomez et al., 2021). This process requires careful management to maintain the desired level of fizziness in the final product. 2. **Operational Condition** **Parameter** **Specification** **Description** -------------------- ----------------------------------------- --------------------------------------------------------------------------------------------- Temperature 60°C to 130°C Optimal range for effective moisture evaporation without degrading sensitive ingredients. Inlet Humidity \>80% for fruit extracts Initial moisture content of feedstock prior to drying; varies by ingredient type. Outlet Humidity 1% to 5% Target moisture level for ensuring product stability and extending shelf life. Operating Pressure Atmospheric or vacuum Standard atmospheric pressure; vacuum conditions may be used for heat-sensitive materials. Flow Rate Variable, based on dryer specifications Adjusted to ensure adequate residence time for effective drying and prevent product damage. Energy Input Steam, hot water, or gas Source of heat; must be controlled to maintain desired drying temperatures consistently. Drying Duration 30 minutes to several hours Time required to achieve the desired moisture content, depending on the feedstock type. *Table 1.1. Operational Conditions* 3. **Operational type: Batch or Continuous** Batch operation is advantageous in the soft drink industry due to its flexibility, quality control, ease of operation, and adaptability to market demands. These benefits make batch systems particularly suitable for producing a variety of products while maintaining high standards of quality and safety. 4. **Material Construction** The materials used in constructing heat exchanger dryers for the soft drink industry are critical to the performance, durability, and safety of the equipment. Given the demanding nature of food processing, particularly the need for hygiene, resistance to corrosion, and efficient thermal transfer, the choice of materials plays a fundamental role. a. Stainless Steel b. Aluminum c. Carbon Steel d. Glass-Lined Steel e. Composite Materials 1. **Properties** **1.4.1a. Stainless Steel** - **Types**: - **Type 316**: - **Tensile Strength**: \~580 MPa - **Yield Strength**: \~290 MPa **1.4.1b. Aluminum** - **Properties**: - **Tensile Strength**: \~70-700 MPa (varies by alloy) - **Yield Strength**: \~30-500 MPa (depends on alloy) - **Elongation**: 10-30% - **Hardness**: Rockwell B: \~40-100 **1.4.1c. Carbon Steel** - **Properties**: - **Tensile Strength**: \~370-700 MPa (varies with carbon content) - **Yield Strength**: \~250-450 MPa (depends on grade) - **Elongation**: 20-30% - **Hardness**: Rockwell B: \~60-90 **1.4.1d. Carbon Steel** - **Properties**: - **Tensile Strength**: \~370-700 MPa (varies with carbon content) - **Yield Strength**: \~250-450 MPa (depends on grade) - **Elongation**: 20-30% - **Hardness**: Rockwell B: \~60-90 **1.4.1e. Composite Materials** - **Properties**: - **Tensile Strength**: Varies widely; \~50 MPa to over 700 MPa depending on formulation. - **Yield Strength**: Typically lower than metals; varies by type. - **Elongation**: Generally low, indicating less ductility. - **Hardness**: Varies; engineered for specific hardness requirements. 2. **Mechanical** **Properties** The effectiveness and longevity of heat exchanger dryers in the soft drink industry are heavily influenced by the mechanical properties of the materials used in their construction. Different materials exhibit unique mechanical characteristics that determine their suitability for various applications, ensuring efficiency, safety, and product quality. **1.4.2a. Stainless steel** One of the most commonly used materials in food processing equipment, particularly in heat exchanger dryers. Its mechanical properties, including tensile strength and yield strength, are vital for its performance. For instance, Type 304 stainless steel has a tensile strength of approximately 520 MPa, while Type 316 offers even greater strength at around 580 MPa. The yield strength for Type 304 is about 210 MPa, and for Type 316, it is approximately 290 MPa. These high strength values contribute to stainless steel\'s durability under high temperatures and pressures, making it ideal for the demanding conditions of food processing. Additionally, stainless steel exhibits good ductility, with an elongation of 40-50%, allowing it to deform without breaking. Its hardness, measured by Rockwell B, typically ranges from 70 to 90, further enhancing its wear resistance. **1.4.2b. Aluminum** Is another important material used in heat exchanger systems, particularly for components that require lightweight and high thermal conductivity. The tensile strength of aluminum alloys can vary significantly, ranging from about 70 MPa to 700 MPa, depending on the specific alloy used. Commonly, aluminum exhibits a yield strength of around 30-500 MPa and an elongation of 10-30%, indicating its capability to deform under stress. While aluminum is lighter than stainless steel, its hardness, measured on the Rockwell B scale, typically falls between 40 and 100, depending on the alloy. This property makes aluminum suitable for applications where weight savings and thermal efficiency are critical. **1.4.2c. Carbon steel** Is often selected for its strength and cost-effectiveness, especially in structural components of heat exchanger dryers. Its tensile strength generally ranges from 370 MPa to 700 MPa, with yield strengths between 250 MPa and 450 MPa, depending on the specific grade. Carbon steel also has an elongation of about 20-30%, providing a reasonable degree of ductility. However, it is important to note that carbon steel has low corrosion resistance, necessitating protective coatings to prevent rust and degradation, particularly in humid environments. **1.4.2d.** **Glass-lined steel** Combines the strength of steel with the chemical resistance of glass, making it suitable for applications where corrosive substances are involved. The tensile strength of the underlying steel is comparable to that of carbon steel, ranging from 370 MPa to 700 MPa. However, the glass lining itself is brittle and offers minimal elongation, which means careful handling is essential to avoid chipping or cracking. The hardness of the glass surface is very high, contributing to its durability against chemical attack. **1.4.2e. Composite materials** are increasingly being used in food processing equipment due to their lightweight and customizable properties. The tensile strength of composites can vary widely, typically ranging from 50 MPa to over 700 MPa, depending on the type of reinforcement used. While composites generally have lower yield strengths than metals, their specific formulations can be engineered to meet particular mechanical requirements. However, they typically exhibit lower ductility compared to metals, which affects their elongation properties. 3. **Corrosion Resistance** **1.4.3a. Stainless Steel** - Types: - Type 316: - Corrosion Resistance: Superior resistance, particularly against chlorides and acidic environments, making it ideal for processing fruit juices and carbonated beverages. - General Resistance: Excellent overall, particularly when properly maintained and cleaned regularly. **1.4.3b. Aluminum** - Corrosion Resistance: - Forms a protective aluminum oxide layer that provides moderate resistance to corrosion. - Vulnerable to corrosion in acidic or alkaline environments; can suffer from localized corrosion (pitting) if the oxide layer is compromised. - Applications: Best suited for non-contact components or areas with limited exposure to harsh conditions. **1.4.3c Carbon Steel** - Corrosion Resistance: - Low inherent resistance; prone to rusting when exposed to moisture and corrosive substances. - Requires protective coatings such as epoxy or galvanization to enhance corrosion resistance. - Common Applications: Primarily used in structural components where direct contact with food products is minimal, and corrosion risk is managed. **1.4.3d. Glass-Lined Steel** - Corrosion Resistance: - The glass lining provides excellent resistance to acids and alkalis, preventing chemical attack from food products. - The underlying steel offers structural strength while the glass ensures non-reactivity. - Considerations: The glass surface can be brittle and may chip, exposing the steel to corrosion if not handled carefully. - Corrosion Resistance: - Generally excellent, with many composites engineered to withstand harsh chemicals and moisture without degradation. - Specific formulations can provide tailored resistance to corrosive environments. - Applications: Ideal for non-structural components and areas prone to chemical exposure. **Chapter 2 Rationale** Food industry is one of the key sectors of the world\'s economy, being an essential support activity for human livelihood and is currently encountering various challenges that require innovative approaches. Rising energy costs, environmental issues, and high consumer demands for quality, safe, and sustainably produced food are compelling important changes in food processing technologies. Traditional methods often are based on inefficient heat transfer mechanisms and waste energy and take up much processing time and may result in degraded products. This aims to design and develop advanced heat transfer systems in order to increase efficiency, save energy, and improve product quality in food processing operations. In addition, an elaborate approach with advanced technologies such as new materials like ceramics and alloys for enhanced thermal conductivity will be used. New means of heat transfer will be developed so that the resultant systems may become more effective and further on, the installation of semiconductor equipment and real-time monitoring will be the cause of only the highest level of production and absolute saving of energy. This would mean a feature at a micro/nano scale together with complexity geometries motivated by natural forms or simply advanced exchangers coupled with better designs. This may also be able to considerably shorten processing times, decrease energy consumption, and minimize waste in products, and create a more sustainable and profitable food production system, by focusing on developing solutions customized to effectively meet these needs, as a consequence of these consolidations. **Innovative Heat Exchanger Dryer Solution in Equipment Design for the Soft Drink Industry** Submitted by: Apelado, Divine Panaligan, Amihan D. **CHAPTER 3: DESIGN** **3.1. Design Summary** +-----------------------------------+-----------------------------------+ | Design Aspect | Details | +===================================+===================================+ | Project Goal | Design heat exchanger dryers that | | | effectively remove moisture from | | | soft drink products while | | | maintaining quality. | +-----------------------------------+-----------------------------------+ | Material Selection | **- Corrosion Resistance**: Use | | | Type 316 stainless steel or | | | similar materials to withstand | | | harsh conditions. | | | | | | **Durability:** Ensure materials | | | can handle long-term operation | | | and cleaning protocols. | +-----------------------------------+-----------------------------------+ | Process Flow | \- **Feedstock Preparation**: | | | Establish protocols for uniform | | | feed introduction. | | | | | | \- **Drying Chamber | | | Configuration**: Design for | | | efficient airflow and moisture | | | removal. | +-----------------------------------+-----------------------------------+ | Corrosion Assessment | \- **Corrosion Rate | | | Calculations**: Monitor corrosion | | | rates and ensure they remain | | | within acceptable limits | | | | | | \- **Pitting Corrosion | | | Preventions**: Evaluate the | | | potential for pitting based on | | | material composition and | | | operating conditions. | +-----------------------------------+-----------------------------------+ *Table 1.2 Design Summary* This table provides a comprehensive overview of the design considerations, focusing on efficiency, material selection, and Corrosion Assessment relevant to heat exchanger dryers in the soft drink industry. **3.2** **Heat Transfer Calculations** **Heat Transfer Rate (Q)** The heat transfer rate can be calculated using the formula: Where: Q = Heat transfer rate (W or kW) m˙ = Mass flow rate of the fluid (kg/s) Cp​ = Specific heat capacity of the fluid (J/kg·K) ΔT = Temperature difference between the inlet and outlet (K) **3.3 Heat Exchanger Area Calculation** **Log Mean Temperature Difference (LMTD)** To calculate the heat exchanger area, first find the Log Mean Temperature Difference (LMTD): **Where:** - [*ΔT*~1~]{.math.inline} [=]{.math.inline} [*T*~*hot*, *in*~ − *T*~*cold*, *out*~ ]{.math.inline} - [*ΔT*~2~]{.math.inline} [=]{.math.inline} [*T*~*hot*, *out*~ − *T*~*cold*, *in*~ ]{.math.inline} Example Data: - Hot fluid inlet temperature [*T*~*hot*, *in*~]{.math.inline} [=]{.math.inline} **80** [℃]{.math.inline} - Hot fluid outlet temperature [*T*~*hot*, *out*~]{.math.inline} [=]{.math.inline} **60** [℃]{.math.inline} - Cold fluid inlet temperature [*T*~*cold*, *in*~]{.math.inline} [=]{.math.inline} **20** [℃]{.math.inline} - Cold fluid outlet temperature [*T*~*cold*, *out*~]{.math.inline} [=]{.math.inline} **30** [℃]{.math.inline} Calculate [*ΔT*~1~]{.math.inline} and [*ΔT*~2~]{.math.inline} : [*ΔT*~1~]{.math.inline} [=]{.math.inline} 80 [--]{.math.inline} 30 [=]{.math.inline} 50 [℃]{.math.inline} [*ΔT*~2~]{.math.inline} [=]{.math.inline} 60 [--]{.math.inline} 20 [=]{.math.inline} 40 [℃]{.math.inline} Now substitute into the LMTD formula: [*ΔT*~lm~]{.math.inline} [=]{.math.inline} [\$\\text{\\ \\ }\\frac{50\\ - 40}{\\ln\\left( \\frac{50}{40} \\right)}\$]{.math.inline} [≈]{.math.inline} [\$\\frac{10}{0.2218}\$]{.math.inline} [≈]{.math.inline} 45.1 [℃]{.math.inline} **Heat Exchanger Area (A)** **Using the LMTD, calculated the required heat transfer area:** Where: - [*A*]{.math.inline} [=]{.math.inline} **Heat exchanger area** [(*m*^2^)]{.math.inline} - [*U*]{.math.inline} [=]{.math.inline} Overall heat transfer coefficient (W/m^2^[⋅]{.math.inline}K) Assume Data: - [*U*]{.math.inline} [=]{.math.inline} 200 W/m^2^[⋅]{.math.inline}K - [*Q*]{.math.inline} [=]{.math.inline} 34.77 kW [=]{.math.inline} 34,770 W Substituting the values: **Overall Heat Transfer Coefficient** [(**U**)]{.math.inline} The overall heat transfer coefficient [*U*]{.math.inline} *can be estimated using the formula:* \ [\$\$\\frac{1}{U}\\ = \\ \\frac{1}{h\_{\\text{hot}}}\\ + \\ \\frac{R\_{f}}{A}\\ + \\frac{1}{h\_{\\text{cold}}}\\ + \\ R\_{w}\$\$]{.math.display}\ Where: - [*h*~hot~]{.math.inline} [=]{.math.inline} Heat transfer coefficient for the hot fluid (W/m^2^[⋅]{.math.inline}K) - [*h*~cold~]{.math.inline} [=]{.math.inline} Heat transfer coefficient for the cold fluid (W/m^2^[⋅]{.math.inline}K) - [*R*~*f*~]{.math.inline} [=]{.math.inline} Fouling resistance (m^2^[⋅]{.math.inline}K/W) - [*R*~*w*~]{.math.inline} [=]{.math.inline} Resistance of the wall (m^2^[⋅]{.math.inline}K/W) Example Values: - [*h*~hot~]{.math.inline} [=]{.math.inline} 500 W/m^2^[⋅]{.math.inline}K - [*h*~cold~]{.math.inline} [=]{.math.inline} 300 W/m^2^[⋅]{.math.inline}K - [*R*~*f*~]{.math.inline} [=]{.math.inline} 0.0005 m^2^[⋅]{.math.inline}K/W - [*R*~*w*~]{.math.inline} [=]{.math.inline} 0.001 m^2^[⋅]{.math.inline}K/W Calculating [*U*]{.math.inline}: \ [\$\$\\frac{1}{U}\\ = \\ \\frac{1}{500}\\ + \\ 0.0005\\ + \\frac{1}{300}\\ + \\ 0.001\$\$]{.math.display}\ Calculating each term: \ [\$\$\\frac{1}{U}\\ \\approx 0.002\\ + \\ 0.0005\\ + \\ 0.0033\\ + \\ 0.001\$\$]{.math.display}\ Thus: \ [\$\$U\\ \\approx \\ \\frac{1}{0.0068}\\ \\approx \\ 147.46\\ W/m2 \\cdot K\$\$]{.math.display}\ **3.4 Corrosion Resistance Limit Calculations for Heat Exchanger Dryers** **Corrosion Rate Solution** The corrosion rate can be calculated using the formula: Where: - K = Constant (usually 8.76 for corrosion rate in mm/year) - W = Weight loss (grams) - D = Density of the material (g/cm^3^) - A = Surface area exposed to corrosion (cm^2^) - T = Time of exposure (hours) Example Calculation: - Assume: - Weight loss [(*W*)]{.math.inline} [=]{.math.inline} 0.5 g - Density [(*D*)]{.math.inline} [=]{.math.inline} 8.0 g/cm^3^ - Surface area [(*A*)]{.math.inline} [=]{.math.inline} 100 cm^2^ - Exposure time [(*T*)]{.math.inline} [=]{.math.inline} 1000 hours Calculating the corrosion rate: To convert to mm/year: Corrosion Rate [≈]{.math.inline} 0.00005475 mm/year A safety factor (SF) is a dimensionless number that provides a margin of safety in engineering design. It is defined as: \ [\$\$\\mathbf{Safety\\ Factor\\ (SF)\\ }\\mathbf{= \\ }\\frac{\\mathbf{\\text{Ultimate\\ Load\\ }}}{\\mathbf{\\text{Design\\ Load}}}\$\$]{.math.display}\ Where: - **Ultimate Load:** The maximum load that a material can withstand before failure. - **Design Load:** The expected load that the material will experience during normal operation. **Rationale for a Safety Factor of 4.0** Here are the key reasons for using a safety factor of 4.0 in food processing materials: - **Corrosion Allowance:** Corrosion rates can vary significantly based on environmental conditions. For example, if the expected corrosion rate is 0.1 mm/year and the expected lifespan. of the equipment is 10 years, the total corrosion could be: \ [Total Corrosion **=Corrosion** **Rate×** **Lifespan** ]{.math.display}\ \ [**=** **0.1** **mm/year** **×** **10** **years**  **=** **1.0** **mm**]{.math.display}\ If the original material thickness is 4 mm, after 10 years, the effective thickness could reduce to 3 mm, which may not meet the design requirements. **Example Calculation** Let\'s consider a simple example of selecting a material thickness for a heat exchanger. - **Design Load (based on operational conditions):** 1000 N - **Ultimate Load (based on material strength):** 4000 N Using the formula for the safety factor: \ [\$\$\\mathbf{\\text{SF}}\\mathbf{= \\ }\\frac{\\mathbf{4000\\ N\\ }}{\\mathbf{1000\\ N}}\\mathbf{\\ = \\ 4}\\mathbf{.0}\$\$]{.math.display}\ **Determining Corrosion Allowance** The corrosion allowance can be calculated based on the expected corrosion rate and the lifespan of the equipment: Formula: \ [Corrosion Allowance**=Corrosion** **Rate×** **Lifespan** ]{.math.display}\ **Assumptions for the Calculation** - **Corrosion Rate**: This varies depending on the material and environment. For example, a common corrosion rate for stainless steel in food processing environments might be around **0.1 mm/year**. - **Lifespan**: The expected lifespan of the heat exchanger could be **10 years**. **Example Calculation** Using the assumed values: - Corrosion Rate: 0.1 mm/year - Lifespan: 10 years **Calculation:** \ [Corrosion Allowance **=** 0.1 *mm*/*year* × 10 *years*  = 1.0*mm*]{.math.display}\ **Interpreting the Corrosion Allowance** - The corrosion allowance of 1.0 mm means that the original thickness of the material should be increased by this amount to ensure that the effective thickness remains above the minimum required thickness after accounting for corrosion over the lifespan of the equipment. - If the heat exchanger is originally designed with a thickness of **4.0 mm**, the effective thickness after 10 years of corrosion would potentially be reduced to **3.0 mm** if no allowance is made. 5. **Pitting Corrosion Limit** The following empirical relationship can be used to estimate the CPT: ***CPT = 0.1*** [**×**]{.math.inline} ***Cr*** [**+**]{.math.inline} ***0.5*** [**×**]{.math.inline} ***Mo*** [**+**]{.math.inline} ***0*** Where: - Cr = Chromium content (%) - Mo = Molybdenum content (%) - N = Nitrogen content (%) Example Calculation: For Type 316 stainless steel: - Chromium Cr [=]{.math.inline} 16% - Molybdenum Mo [=]{.math.inline} 10% - Nitrogen N [=]{.math.inline} 0.1% Calculating the CPT: \ [*CPT* = 0.1 × 16  + 0.5 × 10 + 0.015 × 0.1 = 6.6015 ℃ ]{.math.display}\ 6. **Estimating the Maximum Allowable Corrosion Rate** - T = Initial thickness of the material (mm) - L = Expected service life (years) Example Calculation: - Assume: - Initial thickness (T) [**=**]{.math.inline} 5 mm - Expected service life (L) [**=**]{.math.inline} 20 years Calculating the maximum allowable corrosion rate: **Comparison of Corrosion Rates** **From the previous calculations:** - **Calculated corrosion rate:** 0.00005475 mm/year - **Maximum allowable corrosion rate: 0.25 mm/year** **Since** 0.00005475 mm/year **\< 0.25 mm/year, the material is suitable for the design requirements and will perform adequately over the expected service life.** **Example Sizing Calculation** Heat Load Calculation: - Assume [*ṁ*]{.math.inline} [=]{.math.inline} 0.139 kg/s, [*C*~*p*~]{.math.inline} [=]{.math.inline} 4186 J/kg[⋅]{.math.inline}K, [*ΔT*]{.math.inline} [=]{.math.inline} 60 K: LMTD Calculation: - Assume [*ΔT*~1~]{.math.inline} [=]{.math.inline} 50 [℃]{.math.inline} and [*ΔT*~2~]{.math.inline} [=]{.math.inline} 40 [℃]{.math.inline} [*ΔT*~lm~]{.math.inline} [=]{.math.inline} [\$\\text{\\ \\ }\\frac{50\\ - 40}{\\ln\\left( \\frac{50}{40} \\right)}\$]{.math.inline} [≈]{.math.inline} 45.1 [℃]{.math.inline} Area Calculation: - Assume [*U*]{.math.inline} [=]{.math.inline} 200 W/[*m*^2^⋅]{.math.inline}K Example Calculation: - Assume: - [*ṁ*]{.math.inline} [=]{.math.inline} 500 kg/h [=]{.math.inline} [\$\\frac{500}{3600}\$]{.math.inline} kg/s [≈]{.math.inline} 0.139 kg/s - [*C*~*p*~]{.math.inline} [=]{.math.inline} 4.186 kJ/kg[⋅]{.math.inline}K [=]{.math.inline} 4186 J/kg[⋅]{.math.inline}K - Inlet temperature [*T*~in~]{.math.inline} [=]{.math.inline} 80 [℃]{.math.inline} - Outlet temperature [*T*~out~]{.math.inline} [=]{.math.inline} 20 [℃]{.math.inline} - [*ΔT*]{.math.inline} [=]{.math.inline} [*T*~in~]{.math.inline} [−]{.math.inline} [*T*~out~]{.math.inline} [=]{.math.inline} 80 [--]{.math.inline} 20 [=]{.math.inline} 60 K [*Q* = 0.139 ⋅ 4186 ⋅  60 ≈ 34.77 kW]{.math.inline} **CHAPTER 4: ENERGY, MASS BALANCES AND HEURISTICS** **4.1. Heuristic** A heuristic is a problem-solving strategy or what others called the "rule of thumb", allows researchers to make quick, efficient decisions, especially in situations where complete information is unavailable or impractical to obtain. Heuristics are cognitive shortcuts or mental rules that people use to simplify designs. These are practical strategies that often rely on past experiences, intuition, or common sense rather than exhaustive analysis. **4.1.1. Design Heuristics** Design heuristics provide guidelines regarding dimensions, materials, and configurations that enhance heat transfer and operational efficiency. Key considerations include: - **Heat Exchanger Area Calculation** **A≈**[\$\\frac{\\mathbf{Q}}{\\mathbf{300}}\$]{.math.inline} - where Q is the heat load in kW. This helps in estimating the required surface area effectively. - **Material Selection**: Choose materials with high thermal conductivity, such as stainless steel, to improve heat transfer and resist corrosion. A safety factor of **4.0** should be applied for material thickness to account for wear in food processing applications. - **Configuration Optimization**: Utilize designs that maximize temperature differences (e.g., counterflow configurations) to enhance heat transfer efficiency. - **Diameter**: For tube heat exchangers, a typical tube diameter ranges from **12 to 50 mm**. A common heuristic is: - **Tube Diameter**: Use a diameter of **25 mm** for initial designs. - **Length**: The length of the heat exchanger can often be estimated based on the total number of tubes required: - **Length per Tube**: Assume a tube length of around **1.5 to 3 meters**. - **4.1.2. Operational Heuristics** Operational heuristics focus on managing flow rates, temperatures, and other operational parameters to maximize efficiency and minimize energy consumption: - **Flow Rate Management**: Maintain optimal flow rates between **1 to 3 m/s** for liquid streams to ensure effective heat exchange without excessive pressure drop. - **Temperature Settings**: Establish temperature ranges for the drying process that are effective for specific materials, typically between **60°C to 80°C** for soft drink ingredients, ensuring they do not degrade during drying. - **Airflow Requirements**: For effective moisture removal, estimate airflow at around **1 to 2 m³ of air per kg of product**. This ensures adequate drying and prevents hotspots, thereby achieving uniform moisture content. **4.1.3. Maintenance Heuristics** Maintenance heuristics are crucial for ensuring the longevity and reliability of heat exchangers and dryer systems: - **Routine Inspections**: Conduct regular checks for fouling, leaks, and corrosion. Inspections should be scheduled every **6 to 12 months**, as highlighted in previous discussions. - **Cleaning Protocols**: Implement cleaning schedules to address fouling, using appropriate techniques such as chemical cleaning or mechanical brushing to maintain heat transfer efficiency. - **Performance Monitoring**: Utilize sensors to continuously monitor parameters like temperature, pressure, and flow rates. This allows for quick identification of performance deviations, facilitating timely maintenance actions. **Overall material balance** **Material Balance Equation** 1. **Define Input and Output Streams:** - Input Stream (Inlet Feed): - Mass Flow Rate: [\${\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{in}}}\$]{.math.inline} (kg/s) - Initial Moisture Content: [**w**~in~]{.math.inline} (fraction, e.g., 0.85 for 85% moisture) - Output Stream (Dried Product) - Mass Flow Rate: [\${\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}}\$]{.math.inline} (kg/s) - Initial Moisture Content: [**w**~out~]{.math.inline} (fraction, e.g., 0.05 for 5% moisture) 2. **Material Balance Equation** In a steady-state condition (no accumulation), the mass balance can be written as: \ [\$\${\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{in}}}\\mathbf{\\cdot (1\\ - \\ }\\mathbf{w}\_{\\mathbf{\\text{in}}}\\mathbf{) = \\ }{\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}}\\mathbf{\\cdot (1\\ - \\ }\\mathbf{w}\_{\\mathbf{\\text{out}}}\\mathbf{)}\$\$]{.math.display}\ 3. **Example Calculation:** **Given Data:** - [\${\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{in}}}\$]{.math.inline} [=]{.math.inline} **500 kg/h** [=]{.math.inline} [\$\\frac{500}{3600}\$]{.math.inline} **kg/s** [≈]{.math.inline} **0.139 kg/s** - [**w**~in~]{.math.inline} [=]{.math.inline} **0.85** - [**w**~out~]{.math.inline} [=]{.math.inline} **0.05** **Material Balance Calculation:** Substituting the known values into the material balance equation: \ [\$\$0.139\\ \\mathbf{\\cdot (}1\\mathbf{\\ - \\ }0.85\\mathbf{) = \\ }{\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}}\\mathbf{\\cdot (}1\\ \\mathbf{- \\ }0.05\\mathbf{)}\$\$]{.math.display}\ **Calculating the left side:** \ [\$\$0.139\\mathbf{\\cdot}15\\mathbf{= \\ }{\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}}\\mathbf{\\cdot}0.95\$\$]{.math.display}\ **This simplifies to:** \ [\$\$0.02085\\mathbf{= \\ }{\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}}\\mathbf{\\cdot}0.95\$\$]{.math.display}\ **Now, solving for** [\${\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}}\$]{.math.inline}**:** \ [\$\${\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}}\\mathbf{= \\ }\\frac{0.02085}{0.95}\\mathbf{\\ } \\approx 0.02196\\ kg/s\\ \$\$]{.math.display}\ **To covert to kg/h for:** \ [\$\${\\dot{\\mathbf{m}}}\_{\\mathbf{\\text{out}}} \\approx \\ 0.02196\\mathbf{\\ \\times}3600\\ \\approx 79.06\\ kg/s\\ \$\$]{.math.display}\ **Types of Heat Exchangers** 1. **Shell and Tube Heat Exchanger**: - Composed of a series of tubes, one set carrying the hot fluid and the other the cold fluid. Effective for high-pressure applications. **Heat Transfer Equations for Heat Exchangers** **The overall heat transfer in a heat exchanger can be described by the following equation:** \ [**Q** **=** **U** **⋅** **A** **⋅** *Δ***T**~lm~]{.math.display}\ **Where:** - [**Q=**]{.math.inline} Heat transfer rate (W) - [**U** **=**]{.math.inline} **overall heat transfer coefficient (W/m^2^**[ ]{.math.inline}**K)** - [**A** **=**]{.math.inline} **surface area for heat transfer (m²)** - [*Δ***T**~lm~ **=**]{.math.inline} **log mean temperature difference (LMTD)** **Log Mean Temperature Difference (LMTD)** For counterflow and parallel flow heat exchangers, LMTD is calculated as: [*Δ***T**~lm~]{.math.inline} **~=~** [\$\\frac{\\mathbf{\\mathrm{\\Delta}}\\mathbf{T}\_{\\mathbf{1}}\\mathbf{\\ - \\ \\mathrm{\\Delta}}\\mathbf{T}\_{\\mathbf{2}}}{\\mathbf{ln\\ (}\\frac{\\mathbf{\\mathrm{\\Delta}}\\mathbf{T}\_{\\mathbf{1}}}{\\mathbf{\\mathrm{\\Delta}}\\mathbf{T}\_{\\mathbf{2}}}\\mathbf{)}}\$]{.math.inline} Where: - [*ΔT*~1~]{.math.inline} = Temperature difference at one end of the heat exchanger - [*ΔT*~2~]{.math.inline} = Temperature difference at the other end **Basic Material Balance Equation** **The fundamental equation for a material balance can be expressed as:** **For a steady-state process (where accumulation is zero), this simplifies to:** **Input** [**−**]{.math.inline} **Output = 0** **Application in Heat Exchangers** **Inputs and Outputs** 1. **Inlet Streams:** - **Fluid A:** - **Mass flow rate: (**[\${\\dot{\\mathbf{m}}}\_{\\mathbf{A,in}}\$]{.math.inline}**)** - **Inlet temperature: (**[**T**~**A,in**~]{.math.inline}**)** - **Fluid B:** - **Mass flow rate: (**[\${\\dot{\\mathbf{m}}}\_{\\mathbf{B,in}}\$]{.math.inline}**)** - **Inlet temperature: (**[**T**~**B,in**~]{.math.inline}**)** 2. **Outlet Streams:** - **Fluid A:** - **Mass flow rate: (**[\${\\dot{\\mathbf{m}}}\_{\\mathbf{A,out}}\$]{.math.inline}**)** - **Inlet temperature: (**[**T**~**A,** **out**~]{.math.inline}**)** - **Fluid B:** - **Mass flow rate: (**[\${\\dot{\\mathbf{m}}}\_{\\mathbf{B,out}}\$]{.math.inline}**)** - **Inlet temperature: (**[**T**~**B,** **out**~]{.math.inline}**)** **Material Balance Equations** **For each fluid in the heat exchanger, the material balance can be expressed as follows:** **For Fluid A:** **For Fluid B:** **Fundamental Concepts of Heat Transfer** **Heat transfer occurs through three primary mechanisms:** 1. **Conduction** - **The transfer of heat through a solid material or between materials in direct contact.** - **Governed by Fourier\'s law:** \ [\$\$\\mathbf{Q =} - \\mathbf{k \\bullet A \\bullet}\\frac{\\mathbf{\\text{dT}}}{\\mathbf{\\text{dx}}}\$\$]{.math.display}\ **Where:** - [**Q=**]{.math.inline} **heat transfer rate (W)** - [**k** **=**]{.math.inline} **thermal conductivity (W/m**[ ]{.math.inline}**K)** - [**A** **=**]{.math.inline} **area through which heat is being transferred (m²)** - [\$\\frac{\\mathbf{\\text{dT}}}{\\mathbf{\\text{dx}}}\\mathbf{\\ =}\$]{.math.inline} **temperature gradient (K/m)** 2. **Convection** - **The transfer of heat between a solid surface and a fluid in motion. It can be forced using pumps or fans) or natural (due to buoyancy).** - **Governed by Newtown's law of cooling:** \ [**Q** **=** **h** ** ** **A** ** ** **(T**~**s**~**−T**~**∞**~**)**]{.math.display}\ **Where:** - [**h=**]{.math.inline} **convective heat transfer coefficient (W/m^2^**[ ]{.math.inline}**K)** - [**T**~**s**~ **=**]{.math.inline} **surface temperature (K)** - [**T**~**∞**~ **=**]{.math.inline} **fluid temperature far from the surface (K)** 3. **Radiation** - **The transfer of heat through electromagnetic waves. This is significant at high temperatures.** - **Governed by Stefan-Boltzmann law:** \ [**Q** **=** **ϵ** ** ** **σ** ** ** **A** ** ** **(T**^**4**^~**s**~**−T**^**4**^~**∞**~**)**]{.math.display}\ **Where:** - [**ϵ=**]{.math.inline} **emissivity of the surface (dimensionless)** - [**σ** **=**]{.math.inline} **Stefan-Boltzmann constant (5.67 x** [10^ − 8^]{.math.inline} **W/m^2^**[ ]{.math.inline}**K)** - [**T**~**s**~ **=**]{.math.inline} **surface temperature (K)** - [**T**~**∞**~ **=**]{.math.inline} **fluid temperature far from the surface (K** **CHAPTER 5: NUMERICAL TECHNIQUES, CALCULATED VALUES AND SOLUTIONS** **5.1 Numerical Techniques** 1. Finite Difference Method (FDM): Discretizes differential equations into finite difference equations, making them suitable for solving transient and non-linear heat transfer problems. 2. Finite Element Method (FEM): Divides the system into smaller, simpler elements and analyzes each element individually, allowing for the modeling of complex geometries and boundary conditions. 3. Computational Fluid Dynamics (CFD): Solves the governing Navier-Stokes equations to provide detailed insights into fluid flow, heat transfer, and mass transfer phenomena within heat exchangers. 4. Iterative Methods: Techniques like Newton-Raphson or Gauss-Seidel are used to solve the systems of equations that arise from conservation laws and other governing equations. **5.2 Calculated Values in Heat Exchangers** - **Heat Transfer Rate (Q)**: Calculated using the overall heat transfer equation: Q = U⋅A​⋅[*T*~lm~]{.math.inline} where U is the overall heat transfer coefficient, A is the surface area, and ΔT\_lm is the log mean temperature difference. - **Log Mean Temperature Difference (LMTD)**: For counterflow and parallel flow heat exchangers, LMTD is calculated as: [*ΔT*~lm~]{.math.inline} ~=~ [\$\\frac{\\mathrm{\\Delta}T\_{1}\\ - \\ \\mathrm{\\Delta}T\_{2}}{ln\\ (\\frac{\\mathrm{\\Delta}T\_{1}}{\\mathrm{\\Delta}T\_{2}})}\$]{.math.inline} where ΔT\_1 and ΔT\_2 are the temperature differences at the two ends of the heat exchanger. **5.2. CALCULATED VALUES AND INTERPRETATION** ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- **Calculated Value** **Formula/Equation** **Value** **Interpretation** ---------------------------------------- ----------------------------------- ------------------------ ----------------------------------------------------------------------------------------------------------------------------- Temperature Difference (ΔT\_1) ΔT\_1 = T\_A,in - T\_B,out 60°C Represents the maximum temperature difference achievable in the heat exchanger, indicating the potential for heat transfer. Temperature Difference (ΔT\_2) ΔT\_2 = T\_A,out - TB,in 50°C Indicates the minimum temperature difference, essential for calculating LMTD. Log Mean Temperature Difference (LMTD) \ 55.17°C The effective temperature difference for heat transfer calculations, accounting for the non-linear temperature profile. [*ΔT*~lm~]{.math.display}\ Heat Transfer Rate (Q) Q = U⋅A​⋅[*T*~lm~]{.math.inline} 110,340W(or 110.34 kW) The rate of heat transfer, crucial for evaluating the heat exchanger\'s performance and efficiency. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- The calculated heat transfer rate of 110.34 kW indicates the amount of energy that is being transferred from the hot fluid (Fluid A) to the cold fluid (Fluid B) in the heat exchanger. This value is crucial for evaluating the performance and efficiency of the heat exchanger in the given application. The LMTD of 55.17°C represents the effective temperature difference driving the heat transfer process, accounting for the non-linear temperature profiles of the fluids. This value is essential for calculating the heat transfer rate accurately. The temperature differences ΔT\_1 and ΔT\_2 provide insights into the maximum and minimum possible temperature changes in the heat exchanger, which can be used to assess the overall thermal efficiency of the system. By analyzing these calculated values, engineers can optimize the design and operation of the heat exchanger to ensure efficient heat transfer, meet process requirements, and enhance the overall performance of the system. **Costing** **Material Description** **Quantity** **Unit Cost (PHP)** **Total Cost (PHP)** -------------------------------------------- -------------- --------------------- ---------------------- **Nozzle (stub pipe)** 2 2,000 4,000 **Distributor Fin** 1 15,000 15,000 **Heat Transfer Fin** 1 20,000 20,000 **Shear Plate (support plate)** 1 12,000 12,000 **Spacer Bar (side bar)** 2 3,000 6,000 **316 Stainless Steel (for construction)** 200kg 300 60,000 **Piping (Stainless Steel)** 100 meters 1,100 110,000 **Sensors and Controls** 5 5,500 27,500 **Electrical Wiring and Components** various 16,500 16,500 **Miscellaneous Supplies** \- 27,500 27,500 **Safety Equipment (e.g., alarms)** 1 55,000 55,000 **Labor And Installation of Materials** \- 165,000 165,000 **Total Material Cost** Php 518,500 **Prepared by:** **Apelado, Divine F.** **Panaligan, Amihan D.** **Appendix A: Nomenclature** **Appendix: Nomenclature for Innovative Heat Exchanger Dryer Solution in Equipment Design for the Soft Drink Industry** **Symbols and Terms** --------------------------------------------------------------------------------------------------- **Symbol** **Definition** **Units** ----------------------------- ----------------------------------------------- --------------------- \ Input Flow Stream kg/h [*F*~in~]{.math.display}\ \ Output Flow Stream kg/h [*F*~out~]{.math.display}\ \ Concentration of Input kg solids/kg syrups [*C*~in~ ]{.math.display}\ \ Concentration of Output kg solids/kg syrup [*C*~out~]{.math.display}\ \ Temperature difference °C or K [*ΔT*]{.math.display}\ \ Overall heat transfer coefficient W/m²·K) [*U*]{.math.display}\ \ Surface area of the heat exchanger m^2^ [*A*]{.math.display}\ \ Heat transfer rate W or kW [*Q*]{.math.display}\ \ Safety factor (dimensionless) [SF]{.math.display}\ Corrosion Allowance Additional thickness to account for corrosion mm \ Material thickness mm [*t*]{.math.display}\ Lifespan Expected lifespan of the equipment years Corrosion Rate Rate of material loss due to corrosion mm/year \ Log mean temperature difference °C or K [*ΔT*~lm~]{.math.display}\ --------------------------------------------------------------------------------------------------- **Units of Measurement** **Quantity** **Definition** **Unit** --------------- ------------------------------------------------------------------ -------------------- Flow Rate Volume of fluid kg/h Concentration Amount of substance (solute) present in given volume of solution kg solids/kg syrup Temperature Measure the average kinetic energy of the substance °C or K Heat Transfer Process of thermal energy moving from one object to another W or kW Area Measure the extent of a two dimensional surface m^2^ Thickness Dimension measured between the two surface of an object mm Time A measure of the duration which event occur years **Appendix A: TABLES, GRAPHS AND DIAGRAMS** **AB.1. 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