Gate XE Notes (Food Eng) PDF
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These notes cover various food engineering concepts including Fick's law, fungal cell wall characteristic, and mycotoxins. They also include topics like Gate 2023 missed concepts, extrusion steps, amylose, amylopectin, and more.
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# Important Points Gate XL-2024 ## **Important Points Gate XL-2024** ### **Fick's law for molecular diffusion** - $J = -D \frac{dc}{dx}$ where, J = diffusion flux D = Diffusion coefficient (m<sup>2</sup>/s) dc/dx = concentration gradient ### **Characteristics of fungal cell wall** - Histone...
# Important Points Gate XL-2024 ## **Important Points Gate XL-2024** ### **Fick's law for molecular diffusion** - $J = -D \frac{dc}{dx}$ where, J = diffusion flux D = Diffusion coefficient (m<sup>2</sup>/s) dc/dx = concentration gradient ### **Characteristics of fungal cell wall** - Histone proteins = framework/rigidity - β-glucans = polymer of glucans - Chitin = N-acetyl glucosyl amine ### **HFCS from corn starch** - Amylase = starch to glucose (hydrolysis) - Glucoamylase = starch to glucose - xylose isomerase = glucose to fructose (β-(1-4) (1-6) bonds broken) ### **Mycotoxins** - Aflatoxin = wheat common fungi/carcinogenie - Ochratoxin = Aspergillus niger and ochraceus (grains and coffee) ### **At a given temperature drying (desorption) exhibits higher adsorption than adsorption.** - EMC = Water binding. - Critical limit = Interaction blw surface and adsorbing substance. - HACCP = Food safety. - CCP = Control point. - Monitoring = corrective action - Record keeping = Verification ### **Gate 2023 Missed Concepts** - **Extrusion steps** - Feeding - Kneading - Cooking = expansion - **Amylose (α(1-4))** - contributes to gelatin property. - linear structure - glycosydic linkage - D-glucose units - less soluble than amylopectin. - affinity to granules ### **Amylopectin** - α-D glucose linkages in chains and α(1-6) linkages at branch points. - Viscosity and thickening property of starch. - More soluble as it is branched (70-80% of starch) - H<sub>2</sub> bonding with water ### **Under standard assay conditions** - 1U = 1 μmol/minute ### **Thermo-sin** - Cheese manufacturing - Coagulation of milk during cheese production ### **Thermolysin** - Aspartame synthesis - Acyl glycerol restructuring ### **Vinegar** - Acetobacter aceti ### **Citric Acid** - Aspergillus niger ### **Lysine** - Corynebacterium glutamicum - E. coli ### **Prolonged fermentation of cocoa seeds leads to ‘off-flavor’ due to the release of SCFAs.** ### **Gate Food Technology (Mock) (Cav-India)** - 36 chapter test - 545 questions ### **Iodine test is used to detect starch as an adulterant in milk and milk products. ** ### **Carbonyl group + a free amino acid to form an aldehyde. ** - Strecker degradation ### **Pyranose and furanose rings open up by: ** - Pyrolytic reaction to form furfural derivatives. - (caramelization). ### **An L-isomer of monosaccharide formed in the body is xylulose (Pentose).** ### **Pentose sugar** - Ribose and deoxy-Ribose - Trehalose = two units of glucose. (α-D glycosidic α(1-1) linkage) ### **Cellobiose/maltose** - Disacaccharide - (β-D glycosidic α(1-4) linkage) ### **Hyaluronic acid** - Heteropolysaccharide ### **Haltose** - α-D glucose units - α(1-4) linkages ### **During gelatinization** - Loss of organized structure. - Increased viscosity - Increased susceptibility to digestion - Increased permeability of water. ### **Retrogradation occurs due to crystallization of amylose occurring quicker than amylopection.** ### **α-D and β-D glucose are anomers.** - Anomeric carbon. ### **Cellulose** - Trees - β-D glucopyranose (β-1-4) linkage ### **Lignin** - Stores of fruits/cereals. ### **Inulin** - Chicory ### **Glucose + Galactose (β-(1-4)) - Lactose** ### **Melibiose** - α-(1-6) disaccharide - (Glucose) + (Galactose) ### **Non-reducing sugars** - Trehalose - Stachyose - Raffinose - Verbaskose - α-glucose (α(1-1) bond) - Tetrasaccharide - Pentasaccharide ### **Papain** - Protease ### **Rennin** - Aspartic protease ### **Lactase** - Glucoamylase ### **Aspergillus niger** - Enzymes were discovered in Yeast – fermentation. ### **Co-factors:** - Inorganic Ions (Mg<sup>+2</sup>/Zn<sup>+2</sup>) - Organic molecules. (NAD<sup>+</sup>/FAD) ### **[S] = Substrate concentration.** - Much higher in the beginning compared to product. - Can be treated as constant. ### **Types of inhibitors and their effect** - **Competitive** - [Km] ↑ (Vm) ↓ - **Non-competitive** - [Km] cons. (Vm) ↓ - **Uncompetitive** - [Km] ↓ (Vm) ↓ - **Mixed** - [Km] ↑ ↓ (Vm) ↑ ↓ ### **Biopolymers can be microbiologically produced and act as gelling agents.** - Xanthan gum/Alginate/Chitosan ### **Amyloglucosidase can catalyze both α(1-4) and α(1-6) linkages.** ### **Lipoxygenase** - Capable of catalyzing FFA and monoglycerides. ### **[S] = [2 X 10<sup>-5</sup>] [K]m = [5 X 10<sup>-3</sup>] [S] < [0.004] < 0.01 first order reaction.** - 10 Inz = kT 0.693 = k 0.115 /min T 6 ### **Enzymes** - Epoylase/Hexokinase/Glucose-6-phosphatase - Cofactor (Mg<sup>+2</sup>) - Glutathione peroxidase ### **JFHAC-** ### **Microbial enzyme** - Glucoamylase - Protease - Xylanase - Glucose isomerase - Catalase - Asparaginase - Thermolysin ### **Applications** - HFCS/beer production - Softening of doush/meat tenderization. - Clarification of fruit juice. - PIFCS = prior to cheese production. - removal of H2O2 from milk (baking). - Reduction in formation of acrylamide. - Aspartame. ### **Enzymatic browning** - also takes place in seafood. ### **Naringinase** - Debittering enzyme used in citrus fruit juices. ### **Animal fat is rich in saturated fatty acids and poor in Poly-unsaturated fatty acids. ** ### **Simple lipids** - Fats/waxes/Isoprenoids. - Fatty acids - Derived lipids. ### **Complex lipids** - phospholipids - Glycolipids (Glycosphingolipids) ### **CH<sub>3</sub> at left (C9-10) (C01) -- Lipid** ### **Derived Lipids** - Ketone bodies - Steroids - Lipid-soluble vitamins ### **BHA** - prevents rancidity and off odour. ### **Calcium propionate** - mold and bacterial growth. ### **Oxidation in fats and oils are prevented by** - Propyl gallate ### **Melting point of fats increase with chain length and decrease with degree of unsaturation.** ### **Principal antioxidants in vegetable oil** - Soybean oil = tocopherol and vitamin E. - Inherently present: - Diterpenoid = Retinol - Tetra-terpenoid = Carotenoid ### **Saponification number:** - ¼ Avg mol wt of fatty acids present. - SCPA in fat in a sample. - L = number of 1g KOH required - LMFA = Free fa in sample. - Acid number = ### **Hydrolytic rancidity. ** - This hydrolyzed = fat + glycerol. - No enzyme involved. ### **Avidin & pyrithiamine = Anti-vitamin** ### **Total calcium in kgus = (lky)** ### **Chemical score of milk protein is (CS)** ### **Functional Food = Nutraceuticals (example: iodised table salt)** ### **[bacteria] can be estimated by Lactobacillus leichmanni.** ### **Dietary guidelines are used to lesser the incidence of chronic killer diseases.** ### **DRI = Dietary reference intake = Diet planning.** ### **Most common vitamin deficiency = Folic acid (vit -B-9) (Digestive-U/F) (D - Fecal).** ### **BV% = % of ingested protein/nitrogen in the body x 100% of the protein.** ### **Fenugreek seeds are rich source of saponins, yamogenin/gitogenin/figogenin** ### **Bowman Birk trypsin inhibitor = ** soy bean. - Inhibits only trypsin. - Kunitz type. - Inhibits both trypsin and chymotrypsin. ### **Betalains =** plant pigments from tyrosine ### **Catalase & hemo grubin =** both have porphyrin ring ### **Largest known protein =** Titin (human body) - Most abundant = Collagen (1) Keratin (2) ### **Disulfide bonds** = stabilize extracellular protein. ### **Gelatin =** hydrolyzed protein. - Fibrils = peptides ### **Veri green process =** vegetable blanching - 2 nt2/cu ions used = greener ### **Hemoglobin (Both proteins)** - 8 alpha helix - Muscle cells ### **Myoglobin** - 8 alpha helix - monomer - 0<sub>2</sub> storage ### **Tetratrame (2 α,2β)** - 0<sub>2</sub> transport - 4 O<sub>2</sub> binding sites - 1 O<sub>2</sub> binding site. ### **Frozen Foods** - must contain less amylose and more amylopectin. - Quality loss, if high amylose - gel formation = syneresis when reheated. ### **When a fined mass of air-water vapor mixture is heated at constant pressure** - const (not net addition). - RH = Specific Humidity. ### **During sensible cooling of air with 60% relative humidity ratio remains constant (cooling without changing me).** - Moist air enters at 3 kg/s. at 10<sup>o</sup>C 80% RH. heated exit at 30<sup>o</sup>C. - (PV) = 0.01228 bar. - (0.622) × 0.009824 = 0.00617 kg/Kg dry air. - (0.8) × 0.01228 = 0.009824 bar. - H<sub>1</sub> = [283.1 + (1) (254.8)×(8) ] / [ 303.2 + 0.00617 (2556.3) ] = 895.95kW. - H<sub>2</sub> = 956.91k00. - Heat added = 60.967 kW ### **Humidity Rate = (mw/ma) Cooling = dehumidifying (usually).** ### **Aspergillus Oryzae = Koji** - Mw = 20 - H<sub>2</sub>0 = 18 - Amino acid = 30 - Peptide = (30+20) - (H<sub>2</sub>0 ) = (32). ### **Pectin is a structural polysaccharide. Starch is a storage polysaccharide.** ### **Murin content in gram (tre) bacteria = 70% (Peptidoglycan).** ### **Diameter of mycoplasma = 0.05-0.3 μm.** ### **Diameter of fimbriae 3 - 10 nm** - Found in gram +ve bacteria - hair like appendages ### **Toxin in groundnut kernel = Aflatoxin.** ### **Psychrophiles** - (-20 - 20 °C) - Optimum (R) as low as 0<sup>o</sup>C ### **Thermophilus** - (40 - 50 °C) - Optimum (80-60 °C) ### **(t) (g) (6/8) = (3.3)10<sup>g</sup> (1.07/10<sup>5</sup>) (10<sup>9</sup>) x (5) Integration = (generation time) (t) = 19 min.** ### **Aerobic colony count (SPC)** - Aerobic plate count / Standard plate count. - total viable count (TVC) ### **Non carbonated coins = still coins.** ### **Gram staining = Differential staining** ### **Rhizopus = Tempeh starter** ### **Gurm = heat substitute** ### **Yeast and mold determination = potato glucose agar** ### **Fat rich foods most stable at (0.13 - 0.9 aW).** ### **Water activity of distilled water = (1-0)** ### **Stachybotrys chartarum = black mold.** ### **Psychotrophic** - gum (-ve) - Acineto backer ### **Cell membrane** - Separates interior of all cell walls from outside environment.  ### **Cell wall** - Shape to the cell. ### **Gram (+ve) bacteria = Cytoplasmic lipid membrane** ### **Oligotroph:** - Low nutrient availability ### **Osmophile:** - High conc. of (Sugar/salt) (0.6-0.85) ### **Xenophile:** - Dry conditions (a<sub>w </sub>< 0.8) (<0.6) some cases. ### **Thermal death time =** Time taken to kill specific bacteria at specific temperature. ### **F= (TDT) X 10<sup>T-To</sup> = Thermal death time. (121.1<sup>o</sup>C)** ### **Percentage of acetic acid in vinegar = 5-20%.** ### **Sauerkraut contains Lutein & Zeaxanthin.** ### **Traditional Korean sausage = Sundae.** ### **DNA = first product human use (Rennin)** ### **Ropines in wine = Leuconostoc mesenteroide.** ### **Rum = distilled liquor.** ### **Barley flavor is influenced by both adjuncts and malt.** ### **Hops** - Bitterness and aroma - Antimicrobial ### **Blue cheese starters (Lactis)** - *P. roqueforti)* ### **Soy Sauce** - Aspergillus oryzae - Aspergillus sojae ### **Common inoculum for pickle and sauerkraut = *L. plantarum*.** ### **Grape Juice Fermentation** - *Candida picha* - *S. cerevisiae* ### **Hepatitis A = Food Borne** - Blood/semen. ### **Most spoilage bacteria grow at neutral pH (5-8).** ### **Salmonellosis = food infection** ### **Chilled shrimp spoilage = Achromobacter** - (Salmonella - live (Gram +ve)) ### **Folder method of pasteurization** - Temp = 62.5<sup>o</sup>C - Time = 30 min ### **Z value = 10<sup>o</sup>T or D value = 10-fold down (1 log cycle).** ### **Indicator bacteria for milk pasteurization** - *Coxiella burnetii* ### **Belt speed for grain transport = (2.5-2.8 m/s)** ### **Sporogenes more heat resistance than Clost. (A) type.** - *Stearo thermophilus* > *C. Sporogenes* > *C.BA* > *B. coagulans* ### **HTST also called flash pasteurization (72°c [155°F]). Target milk (Coxiella burnetti) 30s.** ### **Blanching is used for: ** - Both vegetables and meat - (mostly for vegetables) ### **[Milk is added in water (H<sub>2</sub>O). Butter is water in oil (BW).** ### **The vast majority of plasticizers = Estors of thalic acid.** ### **F<sub>0</sub> value = when ≥ 121.1<sup>o</sup>C** - Heat to preserve. - Acidity - Salt and sugar ### **Common hurdles used in food preservation** - Bactos - 155<sup>o</sup>C - (Standard) - Coxiella burnetti flash pasteurization ### **Heat treatment used to inactivate = fruit juices** - pectin methyl esterase - Polygalacturonase - α amylase X - β amylase X ### **Earthy flavor = Spoiled meat = Actinomycetes** ### **Egg yolk = Emulsifier = depends on lecithin content.** ### **Fermented fish product = Bagoong** ### **Nitrates in meat prevent = botulinum spore germination.** ### **Clostridium = usually all from G(TUI).** ### **Bacon = pork belly = (Ham = legs). Cured meat.** ### **Quality of eggs judged by candling.** ### **Parboiled rice also known as converted rice.** ### **Rice bran oil = rich in γ-oryzanol** - Hull, Bran, Germ. ### **Milling of rice removes endosperm intact.** ### **Parboiling leads to loss of antioxidants.** ### **Salt used in bread making =** - An antioxidant. - Heightening gluten structure. - Dough strength. ### **Durum/wheat → pasta wheat = yellow endosperm. Milled → endosperm ground → semolina**  - (Pasta color) ### **Glutenin = dough elasticity. Gliadin = bread rising** ### **Wheat kernel =** - Endosperm - Bran - Germ - Husks removed earlier. ### **Density of butter = (911 g/L)** ### **% of PUFA in butter = (3%)** ### **Max moisture in whole milk powder = (4-6%)** ### **Whipping quality = foam production.** ### **Neutralizen in butter = NaHCO3 (Ca(OH)2)** ### **Eyes in swiss cheese = Propionibacterium** ### **White pepper (color) = matured berries.** ### **Astringency in tea = poly phenols.** ### **Selected coconut = alkaline compound (elevated temp)** - Dutch processing ### **Conching =** - Intense mixing/kneading - Viscosity of chocolate (fats adjusted with addition of fats like cocoa butter/emulsifiers = Standardization. ### **Crystal form** - α crystals (1) = low melting point - smooth texture. - β crystals (II) = moderate to low - coarse texture - less desirable. - β crystals (III) = larger more stable - coarse texture - Mixed crystals = both α and β form characteristics - γ crystals = Less common in food. - δ crystals = very high melting points. ### **White tea = wilted un-oxidized** ### **Green tea = un-wilted un-oxidized** ### **Black tea = wilted fully oxidized** ### **Cardamom =** - α-terpencol - limonene - menthone ### **Decaffeination of coffee =** - Super critical CO<sub>2</sub> - Dichloromethane - Ethyl acetate. ### **Product of enzymatic browning = quinones (PPO causes it)** ### **Pectin** - Apples (citrus fruits - high amt of pectin). - Contains = galacturonic acid. - Pectin reduces syneresis. ### **Redness in apple = Anthocyanin.** ### **Fruit squash = PFA limit for fruit juice = 12.5 %** ### **FSSAI logo for fortified soy with (FT)** ### **Emulsifier preservative (E200-249) Emulsifiers/stabilizers etc (E 400-499)** ### **Cop = Jhald (Refrigeration?) Cold = Hot-tool**  - Heat absorbed or rejected. - work done ### **Directly from temp (Ideal) = (Bideal) / (Breal) = Hardening of fats** ### **Refrigeration =** - Decomposition of colloidal system. - F<sub>sc</sub> = cooling ### **MCP = (30+5) + (m)** - Cooling - Heat out - Condensation - Evaporation. - Working - Heating ### **EA = - (T<sub>2</sub>-T<sub>1</sub>) / 2.303R (T<sub>1</sub>T<sub>2</sub>)**  - 2nk = lnA - (EA/RT<sub>1</sub>). - -δ = lnA - (EA/RT<sub>1</sub>) - -9 = lnA - (EA/RT<sub>2</sub>) - 1 = (EA/R) ( T<sub>2</sub>-T<sub>1</sub>/ T<sub>1</sub>T<sub>2</sub>) - 1 = (EA/8.314 J/mol) ( 2 X 153 - 1 X 163 / 8.314 X 153) ### ** (T<sub>1</sub> / T<sub>2</sub>). ## Rate of change of a biological or chemical process with 10<sup>e</sup> Change in temp** ### **Probability of spoilage = (Y<sub>0</sub>)** - If given, directly = (Ton)<sup>-1</sup> = (1/Ton) - If given, 10h<sup>-1</sup> = (ton)<sup>-1</sup>= (1/10<sup>7</sup>). - (0.8)(10<sup>-x</sup>)(10<sup>-x</sup>)(-20)(1-10<sup>-x</sup>)/ (10<sup>-x</sup>)(1-10<sup>-x</sup>)(2(10<sup>-x</sup>) = ff / (ff<sup>2</sup> / 0<sup>2</sup> ) ### **Separation factor =** - √(x<sup>2</sup> + 1). ### **Efficiency of centrifugal separator = (Centrifugal force/Gravity force).** ### **g = [V<sup>2</sup> / (r)] = (2/g) (ω<sup>2</sup> x r) - V = [(2/g) ( ω<sup>2</sup> x r) x (ρ<sub>s</sub> - ρ<sub>l</sub>) r] / [ μ ] = (ω<sup>2</sup> D<sup>2</sup> L<sup>2</sup> ) / (ω<sup>2</sup>. D<sup>2</sup> . L<sup>2</sup> + (2/g) ( ω<sup>2</sup> x r) x (ρ<sub>s</sub> - ρ<sub>l</sub>) r + μ] ### **During falling rate period, when falling rate > constant rate, the moisture content reduces.** - Surface = Free moisture. - Second falling rate = interstitial water. - Falling rate = Free water. ### **Microwave drying = dielectric drying.** ### **q<sub>w</sub> = (ERH) = 65 = (0.65) / 100.** - 100 ### **500 x 0.8 = 400 kg/hr (remind) = (P)(0.4)** - (1)x 0.5 - 100 = (100+x) = P - (100)(0.5) + 2 x 0.01 = (P)(0.4) - 50 + 0.1x = 40 +0.4x - 10 = 0.3x - x = 33.33 - Total P= (100+ 33.33) = 133.33 kg/hr - (2)(0.4) - (0.5) - 500 → 61 → 52 → (y)(0.1) - Evaporator (2 Stages) ### **Rehydration Ratio = (Rehydrated) / (wd) 75 = (6:1)** - 15 ### **Ф = 1 Strue 0.9 = 1 - Phulk. Strue** ### **Ev spherical diameter = 4/3πdL<sup>3</sup> d<sub>e</sub><sup>3</sup> = (4/3π)dL d<sub>e</sub><sup>2</sup> = [(4/3π)dL)<sup>1/3</sup>** ### **Sphoricity of grain = p = (lxbxh)<sup>1/3</sup> / d<sub>e</sub>** ### **Porosity (ε) = [V<sub>v</sub> / V<sub>s</sub>]. ### **de = side<sup>3</sup> = de = (x) P=6(A<sub>s</sub> / A<sub>p</sub>) = (6 / πα<sup>2</sup>) (πd<sup>2</sup> / 6) = (d/2a).** ### **Φ<sub>wv</sub> = (1/Σmi ) = mass fraction** ### **Shear-thinning common for liquids but may occur in solids.** ### **Velocity of falling film = V = (ρgδ<sup>2</sup> / (2μ)) (g<sup>2</sup> - S<sup>2</sup>) - V<sub>avg</sub> = (1/δ) ∫ (ρgδ<sup>2</sup>/ (2μ)) (g<sup>2 </sup>- S<sup>2</sup>) dδ = (1/δ) (ρgδ<sup>2</sup> / (2μ)) ∫ (g<sup>2 </sup>- S<sup>2</sup>) dδ = (1/δ)(ρgδ<sup>2</sup>/(2μ))[ (g<sup>2 </sup>δ ) - (S<sup>2</sup>δ / 3) ] = [ ( ρg / 2μ ) (δ<sup>2</sup>/3) ] ### **Time to fill the tank = (Food Eng) Volume = (πd<sup>2</sup>h) A<sub>v</sub> = (g) t = (V / A<sub>v</sub>)** - (no formula needed) - Ignore viscosity data. - (M<sub>a</sub> = T / (du / day) - M<sub>a</sub> = (M) (du / day) - n = 0.4 - n - 1 = (0.6) - T = (25)(4) - M<sub>a</sub> = (2.5)4<sup>-0.6</sup> - 1.05 / 2.5 = 0.42 - 4 = (h)(g) = 9.0. - 2.5 / 1.05 = (9.0)(2) - 4 = 4.245 ### **Turbulent flow fanning friction AP = [(g/√g) (v<sup>2</sup> / D)]<sup>0.25</sup>= [(0.079) (Re)<sup>-0.25</sup>]**  - AP = (4 fL v<sup>2</sup>/ 2Dg) - Not laminar. ### **L<sub>2</sub>/(1-ε^2) = [ total v / Void v = Total v - Void v ]** - L<sub>1</sub>/ (1 - ε<sup>1</sup>) = more filled = Void fraction - ε = (1-X) / (1-0.7) = ε ### **Rheotropic = α↓ with time (with constant conditions).** ### **Thixotropic = α↑ with time.** - The same as dilatant. ### **Fourier's law of conduction = Q= (KA / Δx) dT** ### **Heat flow through a cylinder = Q = (2πL)KAT / ln(r<sub>2</sub>/r<sub>1</sub>)** ### **Nu number = (2 conduction / (conduction + convection)) = (2hL/K) / (2hL/K + 2πL/K)**  ### **In series: (18-(-18) 21+12+13 K<sub>1</sub>A<sub>1</sub> K<sub>2</sub>A<sub>2</sub> K<sub>3</sub>A<sub>3</sub> Thermal resistance** - Q = (ΔT / [(1 / K<sub>1</sub>A<sub>1</sub>) + (1 / K<sub>2</sub>A<sub>2</sub>) + (1 / K<sub>3</sub>A<sub>3</sub>)]) = (Q / (1 / K<sub>1</sub>)) = (Q * K<sub>1</sub>) = (ΔT / A/h<sub>1</sub>/K<sub>1</sub> ) - Q = (Q/ (1 / K<sub>2</sub>)) = (Q* K<sub>2</sub> ) = (ΔT / (A/h<sub>2</sub>)/K<sub>2</sub> - Q = (Q/ (1 KK<sub>3</sub>)) = (Q* K<sub>3</sub>) = (ΔT/ (A/h<sub>3</sub>)/ K<sub>3</sub>) ### **Bi = [ (hL / K) / (1) ] = (hL/k). ** ### **R = (Q / (ΔT)) = (1 / K<sub>1</sub>) + (1 / K<sub>2</sub>) = ((2πrL) / K<sub>1</sub> ln(r<sub>2</sub>/r<sub>1</sub>) + (2πrL) / K<sub>2</sub> ln(r<sub>2</sub>/r<sub>1</sub>) ) ** - Q = (ΔT(K<sub>1</sub>ln(r<sub>2</sub>/r<sub>1</sub>) / (2πrL)) + ( ΔT(K<sub>2</sub>ln(r<sub>2</sub>/r<sub>1</sub>)) / (2πrL) )). - Q = ( ΔT / [( 2πrL / K<sub>1</sub>ln(r<sub>2</sub>/r<sub>1</sub>)). + (2πrL / K<sub>2</sub>ln(r<sub>2</sub>/r<sub>1</sub>)) ] - R = ( ΔT / (K<sub>1</sub>ln(r<sub>2</sub>/r<sub>1</sub>) / (2πrL) + K<sub>2</sub>ln(r<sub>2</sub>/r<sub>1</sub>) / (2πrL) ) = ( ΔT / [1/ 2πrL ( (K<sub>1</sub>ln(r<sub>2</sub>/r<sub>1</sub>) + K<sub>2</sub>ln(r<sub>2</sub>/r<sub>1</sub>) )] ) - K<sub>1</sub> and K<sub>2</sub> are heat transfer coefficients. ### **f<sub>f</sub> = Fouling factor, U<sub>d</sub> = 2.22 x 10<sup>-4</sup> U<sub>d</sub> = U<sub>c</sub> x e<sup>=0.015</sup> = (900) W/m<sup>2</sup>.K Therefore, of = 2.22 x 10<sup>-4</sup> = (1500) W/m<sup>2</sup>.K. ** ### **U<sub>f</sub> = Heat transfer coeft under fouling condition (W/m<sup>2</sup>.K) ΔT<sub>1</sub> = ΔT<sup>2</sup> LMTD = ΔT<sub>1</sub> - ΔT<sub>2</sub>. UA(ΔT) = (m) C<sub>p</sub>ΔT ΔT<sub>1</sub> + ΔT<sub>2</sub> Fluid which is of constant not counter current 2 (m) (C<sub>p</sub>) (200kJ/s) (LMTD) = (600) J/sm Counter flow/co-flow mentioned = LMTD needed (4.14 - 1) #### **Find LMTD T<sub>hi</sub> = 10 T<sub>ci</sub> = 12 T<sub>he</sub> = 22 T<sub>ce</sub> = 85** - [ (10-85) - (22-12) ] / ln [ (10 -85) / (22-12) ] = 22.32 <sup>o</sup>K ### **Peclet No. = Convective transport / Diffusive transport** - Bird Peck - (time) Related - Oscillate = LU - (time) - LU / D ### **Sherwood number = (km) L / D = convective mass transfer. Dittorre = (time)** ### **(Le) = law's no: [(α / D) / (ν /D)]<sup>1/2</sup>** ### **Log mean pressure value if vapor pressure = P<sub>i</sub>** - P<sub>B1</sub>= P<sub>atm</sub> - P<sub>i</sub> - P<sub>B2</sub>= P<sub>atm</sub> - P<sub>0</sub> - ΔP<sub>m</sub> = (P<sub>B1</sub> - P<sub>B2</sub>) / ln(P<sub>B1</sub> / P<sub>B2</sub>) ### **Sherwood number in mass transfer = Nussdt no. in heat transfer** ### **Degree of homogeneity depends on mixing time in a mixing/stirred tank** ### **Reynolds no. = Forced convection. ** - As porosity increases thermal conductivity decreases. ### **Granshof no. = Free convection** ### **Most bioprocessing fluids = pseudoplastic** ### **Gate 2016 (Missed) (Triple effect evaporator)** - (N) = [U<sub>1</sub>AT<sub>1</sub> ∪<sub>2</sub>AT<sub>2</sub> + U<sub>3</sub>AT<sub>3</sub>] - ΔT = ΣΔT = (ΔT<sub>1</sub> + ΔT<sub>2</sub> + ΔT<sub>3</sub>) = (T<sub>S</sub> - T<sub>1</sub>) - = (ΣΔT) / [ (Y(U<sub>1</sub>) / (Y(U<sub>1</sub>) + (Y(U<sub>2</sub>) + (Y(U<sub>3</sub>))) = (121-65) X (2760) / (2760) + (11875) + (11250) = 108.80