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Nepal Engineering Council · Registration ExaminationAChE · Ch 5

Chapter 5

Energy and Heat Transfer

ACHE05·6 Sub-topics·78 MCQs

5.1

Energy Sources, Fuels and Combustion

AChE0501

This section covers fossil fuels, combustion and fuel calculations, the different forms of energy including the renewable versus non-renewable and conventional versus non-conventional distinctions, electrochemical cells and water splitting, small hydro power, hydrogen energy and fuel cells, solar thermal and photovoltaic applications, wind, geothermal, biofuels, nuclear energy, and waste to energy including sanitary landfill and gasification.

Classification of Energy Sources • Non-renewable sources exist in a fixed stock and are consumed far faster than they form: coal, petroleum, natural gas and nuclear fuels.

Renewable sources are replenished on a human timescale: solar, wind, hydro, biomass, geothermal and tidal. • Conventional means long established and commercially dominant — coal, oil, gas, large hydro and nuclear; non-conventional means the newer alternatives — solar, wind, biogas, tidal, geothermal and fuel cells.

The two classifications are not the same, which is a favourite trap: large hydro is renewable but conventional, while nuclear is non-renewable yet is often grouped with conventional sources. • Primary energy is taken directly from nature; secondary energy such as electricity or hydrogen must be manufactured from a primary source.

Hydrogen and electricity are energy carriers, not energy sources — an important and frequently examined distinction.

Fossil Fuels and Their Analysis • Coal ranks in order of increasing carbon content and calorific value: peat → lignite → sub-bituminous → bituminous → anthracite.

Anthracite has the highest carbon and calorific value and the lowest moisture and volatile matter; peat the reverse. • Proximate analysis reports moisture, volatile matter, ash and fixed carbon, and is the routine commercial test.

Ultimate analysis reports the elemental composition — C, H, O, N, S and ash — and is what combustion calculations require.

Distinguishing the two is a standard question. • Calorific value: the gross or higher calorific value (GCV/HCV) assumes the water formed is condensed and its latent heat recovered; the net or lower calorific value (NCV/LCV) assumes it leaves as vapour.

GCV is therefore always greater than NCV, and the difference is largest for hydrogen-rich fuels.

A bomb calorimeter measures GCV at constant volume. • Typical values worth carrying: natural gas about 50 MJ/kg, fuel oil about 44, bituminous coal 25-33, dry wood 15-18, and hydrogen about 142 MJ/kg on a gross basis — the highest of any chemical fuel by mass, though very low by volume unless compressed or liquefied.

Combustion and Fuel Calculations • Stoichiometric (theoretical) air is the exact quantity needed for complete combustion.

In practice excess air is supplied to ensure complete burning: typically 5-20 per cent for gaseous fuels, 15-30 for liquid and 20-50 for solid fuels. • Too little air leaves carbon monoxide and unburnt carbon; too much air carries heat out with the flue gas and lowers efficiency — the optimum is a balance between the two losses, found in practice by monitoring flue-gas oxygen. • Key stoichiometry to memorise:

C + O₂ → CO₂ requires 32/12 = 2.67 kg O₂ per kg C;

2H₂ + O₂ → 2H₂O requires 8 kg O₂ per kg H₂;

S + O₂ → SO₂ requires 1 kg O₂ per kg S. • The standard formula for theoretical oxygen, allowing for oxygen already present in the fuel, is O₂ required = 2.67C + 8(H − O/8) + S kg per kg of fuel, and since air is 23.2 per cent oxygen by mass (21 per cent by volume), the theoretical air = O₂ required / 0.232. • Flue gas analysis by Orsat apparatus gives CO₂, O₂ and CO on a dry volume basis, absorbed successively in potassium hydroxide, alkaline pyrogallol and ammoniacal cuprous chloride — in that order.

The reported analysis is dry, because water vapour condenses in the sampling line. • Flame temperature: the adiabatic flame temperature is the maximum attainable, with no heat loss and complete combustion; it falls as excess air increases, because the extra nitrogen must be heated too.

Renewable and Non-conventional Sources Source Principle Strengths Limitations Solar thermal Concentrating or flat-plate collectors convert radiation to heat Simple, good for water and process heat Intermittent; needs storage; area intensive Solar PV Photovoltaic effect in a semiconductor junction generates DC directly No moving parts, modular, falling cost Commercial module efficiency typically 15-22 per cent; intermittent Wind Aerodynamic lift turns a rotor driving a generator Low running cost; mature technology Site specific, variable;

Betz limit caps efficiency at 59.3 per cent Hydro (including small and micro) Potential energy of falling water drives a turbine High efficiency (80-90 per cent), dispatchable, long life Site specific; seasonal flow variation; sediment handling Geothermal Heat extracted from hot rock or fluids underground Continuous base load, small footprint Limited to suitable geology; scaling and dissolved gases Biomass and biofuels Combustion, digestion or fermentation of organic matter Storable, carbon neutral in principle, uses wastes Land and water use, food competition, seasonal supply Nuclear fission Heat from splitting heavy nuclei raises steam Very high energy density, no combustion emissions Waste management, capital cost, safety and proliferation Waste to energy Incineration, gasification, digestion or landfill gas recovery Reduces waste volume and recovers energy Emission control, variable feed, public acceptance • Hydro turbine selection by head is a standard question:

Pelton (impulse) for high head, Francis (reaction, mixed flow) for medium head, and Kaplan (reaction, axial flow) for low head and high flow.

Small, mini and micro hydro are classified by capacity, and micro-hydro is of particular importance for rural electrification in mountainous terrain. • Biofuels are grouped as solid (wood, charcoal, briquettes), liquid (bioethanol from fermentation of sugars or starch, biodiesel from transesterification of oils with methanol) and gaseous (biogas from anaerobic digestion, roughly 50-70 per cent methane and the balance mainly carbon dioxide; producer gas and syngas from gasification). • Generations of biofuel: first from food crops, second from lignocellulosic residues, third from algae — the progression being driven by the food-versus-fuel objection. • Gasification converts a solid fuel with a controlled, sub-stoichiometric supply of air, oxygen or steam into a combustible gas, chiefly CO, H₂ and CH₄.

It differs from combustion precisely in being oxygen starved, and from pyrolysis in that pyrolysis uses no oxygen at all. • Sanitary landfill places waste in lined, compacted cells with daily cover, leachate collection and treatment, and gas extraction.

Landfill gas is roughly half methane and half carbon dioxide, and since methane is a far more potent greenhouse gas than carbon dioxide, capturing and burning it is beneficial even when the energy is not used.

Electrochemical Cells, Water Splitting and Fuel Cells • A galvanic (voltaic) cell converts chemical energy to electrical energy spontaneously; an electrolytic cell does the reverse, consuming electrical energy to drive a non-spontaneous reaction.

In both, oxidation occurs at the anode and reduction at the cathode — but the sign convention reverses: the anode is negative in a galvanic cell and positive in an electrolytic cell, which is a classic point of confusion. • Water splitting (electrolysis):

2H₂O → 2H₂ + O₂, with hydrogen released at the cathode and oxygen at the anode in a 2:1 volume ratio.

The theoretical decomposition voltage is 1.23 V, but practical cells need 1.8-2.0 V because of overpotentials and resistance.

Routes include alkaline, PEM and solid-oxide electrolysis, and the colour convention — green hydrogen from renewable electricity, blue from natural gas with carbon capture, grey from natural gas without it — is worth knowing. • A fuel cell converts chemical energy directly to electricity without a combustion step, so it is not limited by Carnot efficiency — the single most examined fact about fuel cells.

Practical efficiencies of 40-60 per cent electrical, and up to 85 per cent in combined heat and power, are achieved. • The hydrogen-oxygen fuel cell has the overall reaction 2H₂ + O₂ → 2H₂O, producing only water as a by-product.

Principal types are the PEM (proton exchange membrane, low temperature, used in vehicles), alkaline (used in spacecraft), phosphoric acid, molten carbonate and solid oxide (high temperature, tolerant of carbon monoxide and suitable for stationary power).

5.2

Conduction

AChE0502

This section covers the Fourier conduction equation, thermal conductivity, heat conduction through composite walls, cylinders and spheres, insulation and its optimum or critical thickness, extended surfaces and fins, and steady state and unsteady state conduction.

Fourier's Law and Thermal Conductivity • Fourier's law: q = −kA (dT/dx).

The negative sign expresses the second law — heat flows down the temperature gradient, from hot to cold. • Thermal conductivity k, in W/(m·K), is a property of the material.

The ordering is pure metals (silver 420, copper 385, aluminium 205) ≫ alloys > non-metallic solids > liquids (water 0.6) > gases (air 0.026) > evacuated insulation. • Temperature dependence: conductivity decreases with temperature for most pure metals, increases for most gases, and increases for most insulating solids; it is usually written k = k₀(1 + βT). • Why insulation works: almost all common insulants — glass wool, expanded polystyrene, cork, asbestos substitutes — are effective because they trap still air in small pockets, and still air is among the poorest conductors of all.

Once convection is allowed within the pores the insulation fails, which is why moisture ingress is so damaging. • The general conduction equation is ∇²T + q̇/k = (1/α)(∂T/∂t), where α = k/(ρcp) is the thermal diffusivity in m²/s — the ratio of the ability to conduct heat to the ability to store it.

A high diffusivity means the material responds quickly to a change in thermal conditions.

Steady Conduction and the Resistance Analogy Geometry Heat flow Thermal resistance Temperature profile Plane wall q = kA(T₁ − T₂)/L R = L/kA Linear Hollow cylinder q = 2πkL(T₁ − T₂)/ln(r₂/r₁) R = ln(r₂/r₁)/(2πkL) Logarithmic Hollow sphere q = 4πk r₁r₂(T₁ − T₂)/(r₂ − r₁) R = (r₂ − r₁)/(4πk r₁r₂) Hyperbolic Convective film q = hA(Ts − T∞) R = 1/hA — • The electrical analogy is the organising idea of the whole section: q corresponds to current, ΔT to voltage and R to resistance.

Resistances in series add directly, and for parallel paths the conductances add. • Composite wall: q = ΔToverall/ΣR = ΔT/(L₁/k₁A + L₂/k₂A + … + 1/h₁A + 1/h₂A).

The largest resistance dominates and is where any improvement must be made; correspondingly, the largest temperature drop occurs across the largest resistance — an inference examined frequently. • Contact resistance arises at the interface between two solids because real surfaces touch only at asperities, the gaps being filled with a poorly conducting gas.

It is reduced by higher contact pressure, smoother surfaces and thermal interface materials or greases. • Overall heat transfer coefficient U is defined by q = UAΔT with 1/UA = ΣR.

Because A differs between the inside and outside of a tube, U must always be quoted with the area on which it is based.

Critical Thickness of Insulation • Adding insulation to a cylinder or sphere has two opposing effects: it increases the conduction resistance but also increases the outer surface area, which reduces the convection resistance. • Critical radius rc = k/h for a cylinder and 2k/h for a sphere, where k is the conductivity of the insulation and h the outside convection coefficient. • The consequence: if the bare outer radius is less than rc, adding insulation increases the heat loss until rc is reached, and only reduces it thereafter.

If the bare radius already exceeds rc, any added insulation reduces loss immediately. • Practical significance: for large pipes and vessels the critical radius is tiny and irrelevant; for small-diameter electrical wires it is exactly what is wanted — the plastic sheathing helps dissipate heat while providing insulation.

For a plane wall there is no critical thickness, since the area does not change. • Economic (optimum) thickness is a different quantity altogether: the thickness at which the total of the annualised insulation cost and the cost of the heat lost is a minimum.

It always lies well beyond the critical radius.

Extended Surfaces (Fins) • Fins increase heat transfer by increasing the surface area available, and are used where h is low — which is why they are almost always placed on the gas side rather than the liquid side of an exchanger. • For a uniform fin, the temperature falls along its length, so the fin is not fully effective.

Two measures are defined and are commonly confused: • Fin efficiency ηf = actual heat transferred / heat that would be transferred if the whole fin were at the base temperature.

It is always less than one and falls as the fin is made longer. • Fin effectiveness εf = heat transferred with the fin / heat transferred from the same base area without it.

Fins are justified only when the effectiveness is comfortably greater than one, and a value of at least 2 is the usual criterion. • Fins are most beneficial when hδ/k is small — that is, for a high-conductivity, thin fin in a low-coefficient fluid.

Adding fins to a surface where h is already very high can actually reduce heat transfer, because the fin's own conduction resistance and the blockage of flow outweigh the added area.

Unsteady-State Conduction • Biot number Bi = hLc/ksolid, where Lc = V/As is the characteristic length.

It compares the internal conduction resistance with the external convection resistance. • Lumped capacitance method applies when Bi < 0.1, meaning the internal resistance is negligible and the body may be taken as uniform in temperature.

Then (T − T∞)/(Ti − T∞) = exp(−t/τ) with the time constant τ = ρVcp/(hAs) — an exponential approach to the surrounding temperature. • Fourier number Fo = αt/Lc² is the dimensionless time, measuring how far a thermal disturbance has penetrated.

Heisler charts present the solution for Bi greater than 0.1 in terms of Bi and Fo. • The semi-infinite solid solution, involving the error function, applies for short times before the disturbance reaches the far boundary, and gives the classic result that the penetration depth grows as the square root of time.

5.3

Convection

AChE0503

This section covers Newton's law of cooling, heat transfer in laminar and turbulent flow inside tubes, heat transfer by external flow across cylinders, tube banks and spheres, natural convection, and convection with phase change in boiling and condensation.

Newton's Law of Cooling and the Dimensionless Groups • q = hA(Ts − T∞), which defines the convective heat transfer coefficient h in W/(m²·K). h is not a property of the fluid but of the whole situation — geometry, flow regime, velocity and fluid properties all enter it, which is why correlations rather than tables are needed. • Convection is classified as forced (motion driven by a pump or fan) or natural/free (motion driven by density differences arising from heating), and as with or without phase change.

Group Definition Physical meaning Nusselt, Nu hL/kfluid Ratio of convective to conductive heat transfer at the boundary; the dimensionless coefficient Prandtl, Pr cpμ/k = ν/α Ratio of momentum to thermal diffusivity; a fluid property alone Reynolds, Re ρvD/μ Inertial to viscous forces; sets the flow regime Grashof, Gr gβΔT L³/ν² Buoyancy to viscous forces; the natural-convection analogue of Re Rayleigh, Ra Gr × Pr Governs the onset and intensity of natural convection Stanton, St Nu/(Re·Pr) = h/(ρvcp) Heat transferred to thermal capacity of the stream Peclet, Pe Re × Pr Bulk to diffusive heat transport • Prandtl number values are worth carrying: liquid metals about 0.01 (thermal boundary layer much thicker than the velocity layer), gases about 0.7, water about 7 at room temperature, and heavy oils in the hundreds or thousands.

When Pr = 1, the velocity and thermal boundary layers have the same thickness. • The general forms: forced convection gives Nu = f(Re, Pr); natural convection gives Nu = f(Gr, Pr) = f(Ra).

Recognising which applies is the first step in every convection problem.

Forced Convection Inside Tubes • Flow regime: laminar below Re = 2100, transitional to 4000, turbulent above. • Laminar, fully developed with constant wall temperature:

Nu = 3.66; with constant wall heat flux:

These are constants — h is independent of velocity in fully developed laminar flow, a result that surprises candidates and is often tested. • Laminar with entrance effects: the Sieder-Tate (Hausen) relation applies, and h is higher near the entrance because the boundary layer is still thin. • Turbulent: the Dittus-Boelter equation Nu = 0.023 Re0.8Prn, with n = 0.4 for heating and 0.3 for cooling of the fluid.

It is valid for Re > 10 000, 0.7 < Pr < 160 and L/D > 10, with small temperature differences. • The practical consequence of the 0.8 exponent: since h ∝ v0.8D−0.2, doubling the velocity raises h by only about 74 per cent while raising the pressure drop roughly four-fold — the central economic trade-off in exchanger design. • Sieder-Tate equation adds the viscosity correction (μ/μw)0.14, needed when the fluid viscosity changes sharply between bulk and wall, as with viscous oils.

External Flow and Natural Convection • Flow across a cylinder or sphere follows correlations of the form Nu = C RemPr1/3, with C and m depending on the Reynolds range (the Hilpert, Zukauskas and Whitaker correlations).

The local coefficient varies sharply around the circumference, falling to a minimum at the separation point and then rising again in the wake. • Tube banks: staggered arrangements give higher heat transfer than in-line arrangements because of better mixing, at the cost of a higher pressure drop.

The coefficient increases through the first few rows and becomes essentially constant after about the fifth. • Natural convection is driven by buoyancy, so the Grashof number replaces the Reynolds number.

The general correlation is Nu = C(Gr·Pr)n = C Ran, with n = 1/4 for laminar and 1/3 for turbulent conditions.

Since n = 1/3 makes the characteristic length cancel, the turbulent natural-convection coefficient is independent of the size of the surface. • Coefficients are far lower in natural than in forced convection — typically 5-25 W/(m²·K) for gases and 50-1000 for liquids, against 10-500 and 100-15 000 respectively for forced convection. • Orientation matters: a hot plate facing upwards loses heat faster than one facing downwards, because the buoyant plume can rise freely.

Boiling • The pool boiling curve, plotting heat flux against excess temperature ΔTe = Ts − Tsat, has four regions that must be known in order: • 1.

Free convection boiling (small ΔTe): liquid is superheated and evaporates at the free surface; no bubbles form on the surface. • 2.

Nucleate boiling: bubbles form at nucleation sites and detach, stirring the liquid vigorously.

This is the desirable industrial regime, giving very high coefficients with a modest temperature difference. • 3.

Transition (partial film) boiling: bubbles merge into an unstable vapour film.

The heat flux falls as ΔTe increases — an unstable region that cannot be held in a heat-flux-controlled system. • 4.

Film boiling: a stable insulating vapour blanket covers the surface; transfer is poor and increasingly radiative. • The critical heat flux (burnout point) is the peak of the curve, at the end of nucleate boiling.

In a heat-flux-controlled system such as an electrically heated element or a nuclear fuel rod, exceeding it causes the surface temperature to jump by hundreds of degrees, often destroying the equipment — hence the name burnout.

This is the most examined point of the whole topic. • The Leidenfrost point is the minimum of the curve, at the start of stable film boiling; it is why a water droplet skitters on a very hot plate instead of evaporating at once.

Condensation • Filmwise condensation: the condensate wets the surface and forms a continuous film that must be conducted through, so the film itself is the main resistance.

This is the normal industrial case, and it is the basis of Nusselt's analysis, which gives h ∝ (1/L)1/4 for a vertical plate and h ∝ (1/D)1/4 for a horizontal tube. • Dropwise condensation: the surface is non-wetting, so droplets form, grow and roll off, repeatedly exposing bare surface.

It gives coefficients some five to ten times higher than filmwise, but is very difficult to sustain, because the promoters or coatings needed are eroded or oxidised away, so equipment is always designed on the conservative filmwise assumption. • Horizontal tubes give higher coefficients than vertical ones of the same size, because the condensate film is shorter and thinner, which is why condensers are usually built with horizontal tubes. • Non-condensable gases are extremely damaging: even a small percentage of air accumulating at the condensing surface can reduce the coefficient dramatically, because the vapour must then diffuse through the gas layer.

This is why condensers are fitted with vents.

5.4

Radiation

AChE0504

This section covers the theories of radiation, the electromagnetic spectrum, thermal radiation and spectral emissive power, surface emission and the basic equations, emissivity and absorption, black and grey bodies, thermal radiation exchange between two surfaces, and radiation shields.

Nature of Thermal Radiation • Radiation is energy emitted as electromagnetic waves (or photons) by virtue of a body's temperature.

It requires no medium and travels fastest through a vacuum — the property that distinguishes it fundamentally from conduction and convection. • Thermal radiation occupies roughly 0.1 to 100 μm of the electromagnetic spectrum, spanning part of the ultraviolet, the whole of the visible (0.4-0.7 μm) and the infrared. • Radiation is emitted from the surface of opaque solids and liquids, but throughout the volume of gases and semi-transparent media.

Gases radiate selectively, in bands rather than continuously: carbon dioxide and water vapour are significant radiators and absorbers, while the symmetrical diatomic gases oxygen and nitrogen are essentially transparent to thermal radiation — an important fact for furnace design and for the greenhouse effect.

The Basic Laws • Stefan-Boltzmann law:

Eb = σT⁴, the total emissive power of a black body, with σ = 5.67 × 10−8 W/(m²·K⁴).

The fourth-power dependence, with T in absolute units, is the single most important fact of the topic: doubling the absolute temperature raises emission sixteen-fold. • Planck's law gives the spectral distribution of black-body emissive power with wavelength, and its integral over all wavelengths yields the Stefan-Boltzmann law. • Wien's displacement law: λmaxT = 2898 μm·K.

The wavelength of peak emission shifts to shorter values as temperature rises, which is why a heated body glows first dull red, then orange, then white.

The sun at about 5800 K peaks at roughly 0.5 μm, in the visible; a body at room temperature peaks near 10 μm, in the far infrared. • Kirchhoff's law: at thermal equilibrium, the emissivity of a surface equals its absorptivity, α = ε.

A good emitter is therefore necessarily a good absorber — and a poor emitter, such as polished metal, is a good reflector. • Lambert's cosine law: for a diffuse surface, the intensity of radiation in a direction varies as the cosine of the angle from the normal.

Surface Properties • Incident radiation is disposed of in three ways, so that α + ρ + τ = 1, where α is absorptivity, ρ reflectivity and τ transmissivity.

For an opaque body τ = 0, so α + ρ = 1. • Black body: α = ε = 1, ρ = τ = 0 — a perfect absorber and a perfect emitter, and the standard against which all real surfaces are compared.

A small hole in a large isothermal cavity is the practical realisation. • White body reflects all incident radiation (ρ = 1); a transparent or diathermanous body transmits it all (τ = 1). • Grey body: a surface whose emissivity is constant with wavelength, though less than one.

Real surfaces are not exactly grey, but the assumption makes calculation tractable and is used almost universally. • Typical emissivities: polished aluminium or silver 0.03-0.05; oxidised steel 0.8; brick, concrete and most paints 0.85-0.95; lamp black about 0.95; water 0.96.

Note that a white paint can have a very high infrared emissivity despite its low absorptivity for visible sunlight — colour in the visible range says little about behaviour in the infrared, which is the principle of solar-selective and cool-roof coatings.

Radiation Exchange Between Surfaces • View (shape, configuration) factor F12 is the fraction of the radiation leaving surface 1 that is intercepted by surface 2.

It is purely geometric, independent of temperature and surface properties. • Key relations: the reciprocity rule A₁F₁₂ = A₂F₂₁, and the summation rule ΣFij = 1 over all surfaces seen by i, including itself.

For a flat or convex surface F₁₁ = 0, since it cannot see itself; for a concave surface F₁₁ is greater than zero.

A completely enclosed body has F₁₂ = 1 with respect to its enclosure. • Two black surfaces:

Q₁₂ = A₁F₁₂σ(T₁⁴ − T₂⁴). • Two grey surfaces: the same expression multiplied by a grey-body factor.

Two cases recur constantly: • Large parallel plates:

Q = σA(T₁⁴ − T₂⁴)/(1/ε₁ + 1/ε₂ − 1). • Small body of area A₁ completely enclosed by a much larger surface:

Q = ε₁A₁σ(T₁⁴ − T₂⁴) — the emissivity of the large enclosure drops out entirely, because almost all radiation reflected from it is eventually reabsorbed.

This simplification is very often examined. • Radiation network method treats the problem as a circuit: the surface resistance (1 − ε)/(εA) and the space resistance 1/(A₁F₁₂) in series, driven by the difference in σT⁴.

Radiation Shields • A radiation shield is a thin sheet of low emissivity placed between two surfaces.

It works by adding two more surface resistances and one more space resistance to the network, without removing or adding heat itself. • For n shields of the same emissivity as the two original surfaces placed between large parallel plates, the heat transfer is reduced by a factor of (n + 1).

So a single shield halves the radiant exchange, two shields reduce it to a third, and so on.

This 1/(n + 1) result is a standard examination question. • With a low-emissivity shield the reduction is far greater still, which is the principle of multilayer (superinsulation) blankets in cryogenic vessels and spacecraft, and of the aluminised sheets in a vacuum flask. • A shield placed in front of a radiation pyrometer or thermocouple reduces radiation error in temperature measurement, which is the other common application.

5.5

Heat Exchangers

AChE0505

This section covers the types of heat exchanger, their constructional details and internal components and the function of each, condensers, double pipe, shell and tube, air-cooled, plate type and compact exchangers, the LMTD and effectiveness-NTU design methods, and the fouling of heat exchangers.

Classification and Types Type Construction Advantages Limitations Double pipe (hairpin) One pipe inside another; true counter-current Simple, cheap, easy to add sections; high pressure capability Small area per unit; uneconomic above about 50 m² Shell and tube Tube bundle inside a cylindrical shell with baffles Very large area, rugged, wide range of duties, well standardised (TEMA) Bulky and heavy; not true counter-current with multiple passes Plate and frame Corrugated plates in a frame with gaskets Very high U, compact, easy to clean and to extend Limited pressure and temperature by the gaskets Spiral Two long sheets rolled into concentric passages Self-cleaning, ideal for slurries and fouling fluids Difficult to repair; limited pressure Air-cooled (fin fan) Finned tube bundle with forced-draught or induced-draught fans No cooling water needed; low operating cost Large area; performance depends on ambient air temperature; noisy Compact (plate-fin, printed circuit) Very high surface area density, above 700 m²/m³ Extremely compact; suitable for gas-gas duties Easily fouled; hard to clean; expensive • Shell-and-tube internals and their functions are asked directly: • Baffles — direct the shell-side fluid across the tubes, increasing velocity and turbulence and hence the coefficient, and also support the tubes against sagging and vibration.

The commonest form is the segmental baffle, usually with a 25 per cent cut. • Tube sheets hold the tubes and separate the shell-side from the tube-side fluid. • Tie rods and spacers hold the baffle assembly at the correct pitch. • Impingement plate protects the first row of tubes from erosion by the entering shell-side stream. • Floating head or expansion bellows accommodate differential thermal expansion between the tubes and the shell, which would otherwise buckle the tubes or pull them out of the tube sheet.

A fixed tube-sheet design is the cheapest but cannot accommodate this expansion and does not allow mechanical cleaning of the shell side; a U-tube design allows free expansion but its bent tubes cannot be cleaned mechanically. • Tube pitch and layout: a triangular pitch gives more tubes and a higher coefficient in a given shell; a square pitch gives cleaning lanes and is used for fouling service. • Which fluid goes where: put the corrosive, fouling, high-pressure or scaling fluid inside the tubes, since tubes are easier to clean and cheaper to build in exotic alloy; put the viscous or low-coefficient fluid, and a condensing vapour, on the shell side.

The LMTD Method • q = UA(ΔT)lm, where the logarithmic mean temperature difference (ΔT)lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂), with ΔT₁ and ΔT₂ the terminal differences at the two ends. • The LMTD is always less than the arithmetic mean of the two terminal differences, and the two become equal when ΔT₁ = ΔT₂ — in which case the logarithmic form is indeterminate and the arithmetic value is used. • Counter-current versus co-current: for the same four terminal temperatures the counter-current LMTD is always larger, so counter-current flow needs less area for the same duty.

Moreover, counter-current flow can cool the hot stream below the outlet temperature of the cold stream — a temperature cross that co-current flow can never achieve.

For these reasons counter-current is the standard arrangement; co-current is used only where a limit must be placed on the wall temperature, or where a rapid initial temperature change is wanted. • Correction factor F: for multi-pass and cross-flow exchangers the flow is neither purely counter- nor co-current, so q = UA F (ΔT)lm,counter-current.

F is always less than 1, and a design giving F below about 0.75-0.8 is considered unacceptable because performance then becomes very sensitive to small errors. • Overall coefficient:

1/UoAo = 1/hiAi + Rfi/Ai + ln(ro/ri)/(2πkL) + Rfo/Ao + 1/hoAo.

The smallest coefficient controls U, so improving the good side is a waste of effort — which is why fins are put on the gas side.

The Effectiveness-NTU Method • Effectiveness ε = actual heat transfer / maximum possible heat transfer = q/[Cmin(Th,in − Tc,in)], where C = ṁcp is the capacity rate and Cmin is the smaller of the two. • NTU = UA/Cmin, the number of transfer units, a dimensionless measure of exchanger size, and Cr = Cmin/Cmax. • When to use which method:

LMTD is convenient when all four terminal temperatures are known (a rating or sizing calculation); the effectiveness-NTU method avoids the trial and error that LMTD would require when the outlet temperatures are unknown.

That is the practical distinction the examination looks for. • Two limiting cases worth remembering: when one fluid undergoes a phase change its temperature is constant, so C = ∞ and Cr = 0, giving ε = 1 − exp(−NTU) for every configuration; and a balanced counter-current exchanger (Cr = 1) has a constant temperature difference along its length.

Condensers and Fouling • Condensers are classified as surface condensers, in which the coolant and vapour are separated by a wall, and direct-contact (jet or barometric) condensers, in which they mix.

A barometric condenser discharges through a leg tall enough — about 10.4 m — for the column of water to balance atmospheric pressure, allowing operation under vacuum without a pump. • Fouling is the accumulation of deposits on the heat transfer surface, and it is quantified by the fouling factor or dirt resistance Rf, in m²·K/W, added as an extra resistance in series. • Mechanisms: crystallisation or scaling (inverse-solubility salts such as calcium carbonate and calcium sulphate depositing on the hot surface), particulate deposition, chemical reaction and coking, corrosion product build-up, and biological fouling. • The design consequence: fouling reduces U and therefore the duty, and increases pressure drop by narrowing the flow passage.

Exchangers are deliberately oversized at the design stage by including fouling factors, so a new exchanger initially over-performs and must be throttled. • Control is by maintaining adequate velocity (low velocity is the commonest cause of fouling), treating the water chemically, using square pitch and removable bundles for cleanability, and scheduling regular mechanical or chemical cleaning.

5.6

Evaporators and Reactor Heating and Cooling Systems

AChE0506

This section covers the classification of evaporators, single and multiple effect operation, evaporator performance in terms of capacity and economy, methods of feeding, and reactor heating and cooling systems including the time required for heating and cooling agitated batch reactors, helical cooling coils and jacketed vessels.

Evaporator Types Type Description Best suited to Horizontal tube Steam inside horizontal tubes, liquor outside Non-viscous, non-scaling liquids; small duty Short-tube (calandria) vertical Short vertical tubes with a central downcomer; natural circulation Mildly scaling liquids; sugar industry Long-tube vertical (LTV), rising film Liquid rises as a film driven by the vapour generated Clear, non-scaling liquids; large duty; low residence time Falling film Liquid fed at the top flows down the tube walls as a film Heat-sensitive liquids; small temperature difference; dairy and juice Forced circulation A pump drives the liquid through the tubes at high velocity Viscous, scaling and crystallising liquids; highest coefficient Agitated thin film (wiped film) Rotating blades spread a thin film on a heated wall Very viscous and highly heat-sensitive products Capacity and Economy • Capacity is the mass of water evaporated per unit time, in kg/h. • Economy (steam economy) is the mass of water evaporated per unit mass of steam supplied, and is dimensionless.

Steam consumption = capacity / economy.

Confusing these two definitions is the single commonest error in this section. • A single-effect evaporator has an economy slightly below 1 — roughly 0.8-0.9 in practice — because some steam is used to raise the feed to its boiling point and there are heat losses.

It is below rather than at 1 despite the latent heats being similar. • In an N-effect system the economy is approximately 0.8N, so a triple effect gives about 2.4 and a quadruple about 3.2.

The economy rises roughly in proportion to the number of effects, but the capacity does not increase at all. • Why capacity does not rise: adding effects divides the same overall available temperature difference among more units, so each effect has a smaller ΔT and a correspondingly smaller capacity — and N effects each with ΔT/N and area A evaporate about the same total as one effect with the full ΔT.

Multiple effects therefore buy steam economy with capital cost, not throughput, and this is a very frequently examined point. • Boiling point elevation reduces the useful temperature difference further, because the solution boils above the saturation temperature of the vapour it produces.

Dühring's rule — that the boiling point of a solution is a linear function of the boiling point of pure water at the same pressure — is the standard way of estimating it.

Methods of Feeding Arrangement Flow of feed and steam Advantages Limitations Forward feed Feed and steam both enter the first effect and move in the same direction Simple, needs no pumps between effects, safe for heat-sensitive material Coldest feed meets hottest steam; the most concentrated, most viscous liquor sits in the coldest effect, so U is low there Backward feed Feed enters the last (coldest) effect and moves counter to the steam Most concentrated liquor meets the hottest steam, giving higher U for viscous liquids Needs a pump between every effect; unsuitable for heat-sensitive products Mixed feed Feed enters an intermediate effect, then finishes in the hottest Combines the advantages of both More complex piping and control Parallel feed Fresh feed enters and product leaves every effect separately Essential where a crystallising solid is produced No counter-current advantage; used for crystallising evaporators such as salt • Improving economy further: vapour recompression raises the pressure of the vapour leaving an effect so that it can be reused as the heating medium.

Mechanical vapour recompression (MVR) uses a compressor and thermal vapour recompression (TVR) a steam ejector; both can give economies equivalent to many effects at lower capital cost.

Vapour bleeding — drawing vapour from an effect for use elsewhere in the plant — is the other common measure.

Batch Reactor Heating and Cooling • Batch vessels are heated or cooled through a jacket or an internal helical coil.

The vessel contents are agitated and therefore essentially uniform in temperature, which makes the analysis an unsteady-state energy balance on a well-mixed batch. • Case 1 — isothermal medium (condensing steam or boiling refrigerant), batch heating: the medium stays at T1 and the result is • ln[(T₁ − t₀)/(T₁ − t)] = UA ttime/(M cp), so the batch temperature approaches the medium temperature exponentially and, in theory, never quite reaches it — which is why heating times are quoted to a specified approach. • Case 2 — non-isothermal medium (cooling water rising in temperature as it passes through the coil) gives the same logarithmic form but with a factor K = exp[UA/(ṁccc)] accounting for the change in the medium, the group (K − 1)/K replacing unity. • The practical readings of the formula: the time is proportional to the mass and specific heat of the charge and inversely proportional to UA; doubling the heat transfer area halves the heating time; and, because the driving force decays, the last few degrees take disproportionately long.

Jackets Versus Coils Feature Jacket Internal helical coil Heat transfer area Limited to the vessel wall Much larger area can be installed in the same vessel Coefficient Lower; velocity in the jacket is low unless baffled or spiral Higher; good velocity is easily maintained inside the coil Cleaning and fouling Vessel interior remains clear and easy to clean Obstructs the vessel; harder to clean; interferes with agitation Pressure capability Limited by the jacket design High pressure easily contained in small-bore tube Typical use General service, clean products, sterile and pharmaceutical duty High duty, large temperature change, where jacket area is insufficient • Jacket variants: the plain (conventional) jacket, the dimple jacket and the half-pipe coil jacket welded spirally to the outside — the last gives higher velocity, a better coefficient and greater pressure capability, and permits zoning of the jacket. • The vessel-side coefficient is correlated against the impeller Reynolds number ρNDa²/μ, so faster or larger agitation raises it — the practical route to improving heat transfer in a batch reactor when the area is fixed. • The scale-up problem: as a vessel is scaled up, the volume increases as the cube of the linear dimension but the jacket area only as the square, so the area per unit volume falls.

This is why temperature control becomes progressively harder on scale-up, and why large exothermic batch reactors need internal coils, external circulation loops through an exchanger, or reflux cooling.

It is a central safety consideration in process scale-up.