Fundamentals of Heat & Mass Transfer -Basic to Advance Level

Explore the heat diffusion equation in Cartesian coordinates, derived from energy balance and Fourier's law, covering energy storage and generation, steady-state vs transient, and one-dimensional heat transfer.

Explore the heat diffusion equation in cylindrical coordinates, with r, z, and phi axes, and analyze radial, axial, and circumferential temperature variations, including one-dimensional radial cases.

Explore the heat diffusion equation in spherical coordinates, noting that a temperature depending only on radius reduces to one-dimensional radial heat transfer. Understand r, phi, and theta as angular coordinates.

Apply the heat diffusion equation to conduction problems in Cartesian and cylindrical coordinates, addressing steady-state radial conduction with and without internal heat generation, and determine heat transfer per unit length.

One-dimensional steady heat diffusion in a 40 mm isotropic wall with uniform generation and dual-face convection yields a quadratic temperature profile, heat flux, and the zero-flux location.

Explore numerical solutions to heat diffusion problems, including one-dimensional steady-state conduction with boundary convection and insulation, and cylindrical radial conduction with logarithmic temperature distributions, using energy balance and boundary conditions.

Derive the one-dimensional steady-state temperature distribution in plain walls, cylinders, and spheres. Use the thermal network analogy to analyze conductive, convective, radiative resistances, fins, and their series or parallel arrangements.

derive radial heat conduction in a cylinder under steady state, yielding a logarithmic temperature distribution in r and the cylindrical conductive resistance log(R2/R1)/(2πkL).

Derives spherical conductive resistance and links heat flow to electrical current, showing how temperature difference drives heat and presenting the spherical expression 1/(4 pi k) (1/ri - 1/ro).

Apply thermal-network methods to surface thermal resistance problems. Determine inner and outer surface temperatures and heat flux per unit area for a 4 mm glass pane with inner and outer convection, including defogging scenarios.

Explore heat transfer through extended surface fins that increase convection area and derive the fin temperature distribution along the base-to-tip using energy balance.

Examine three fin cases: general, insulated tip, and long fin, and apply base and tip boundary conditions, Fourier conduction, and convection to derive fin temperature distributions.

Derive the temperature distribution for case a fin with convective tip, solving for C1 and C2 to obtain theta(x) and the fin heat transfer rate under steady state.

Derive insulated-tip fin temperature distribution by solving the differential equation and applying the base and insulated-tip boundary conditions to determine C1 and C2, and compute the fin heat transfer rate.

Derive the temperature distribution theta(x) and fin heat transfer rate for Case C, a very long fin, using boundary conditions and an insulated tip with the fin parameter m.

Study solar radiation components, including direct beam, diffuse, and ground-reflected albedo, and the solar spectrum across visible light. Explore radiosity, and emission governed by emissivity and sigma t^4.

Master radiation intensity as the portion leaving a body and incident on a second body, defined per solid angle omega (steradians) and per unit projected area to analyze heat transfer.

Understand spectral emissive power, the energy a black body emits per unit time, area, and wavelength at temperature t, and how spectral power yields total emissive power through wavelength integration.

Learn how spectral emissive power depends on wavelength and temperature, how hotter bodies emit more and shift toward shorter wavelengths, and how emission and reflection govern visible perception.

Calculate the sun’s visible-band fraction by subtracting F(0 to λ1) from F(0 to λ2) using the blackbody table, with λ in micrometers and T in kelvin, yielding about 0.37.

Explore spectral quantities and how emissivity, absorptivity, reflectivity, and transmissivity vary with wavelength. Integrate a spectral quantity over all wavelengths to obtain the total quantity, such as total emissive power.

Kirchhoff's law explains that a small body in a large isothermal enclosure reaches thermal equilibrium by absorbing and emitting radiation. It yields that emissivity equals absorptivity, epsilon equals alpha.

Show how the greenhouse effect traps radiation in a car: short-wavelength sun passes through glass while longer wavelengths are trapped, warming the interior and illustrating global warming.

Compute total emissive power by integrating spectral power over wavelength, yielding 2000 W/m^2, with emission only from 5 to 20 micrometers, indicating infrared, hence lower temperature.

Explore the view factor concept, its geometric basis, and key relations, reciprocity, summation, and symmetry, and apply them to radiation exchange between surfaces with charts and examples.

Explore radiation heat transfer between two black surfaces, focusing on radiosity, two-way energy exchange, and net heat transfer governed by fractions F12 and F21 and the Stefan–Boltzmann law.

Describe how a diffuse grey surface radiosity, j = epsilon plus rho times G, combines emitted and reflected radiation for opaque surfaces, with alpha equals epsilon per Kirchhoff's law.

Learn how net radiation to or from a surface is the difference between leaving radiosity and incident radiation, and how surface resistance governs this transfer, vanishing for black bodies.

describe reradiating surfaces in adiabatic bodies with insulated backsides, where front-side heat transfer is negligible. at steady state the surface radiates as much energy as it gains, maintaining its temperature.

Explore net radiation heat transfer between two surfaces using radiosities J1 and J2, reciprocity of view factors F12 and F21, and the concept of surface and space resistances. Demonstrate how the net transfer equals the difference J1 minus J2 divided by the space resistance, illustrating the two-surface network.

Model a three-surface enclosure to analyze radiation heat transfer by defining surface and space resistances, using reciprocity and F factors to solve for J1, J2, J3.

Block unwanted radiation with a thin, high reflectivity surface called a radiation shield, enabling accurate temperature measurement by managing emissivity and surface resistances such as A1F13.

Solve a three-surface radiative heat transfer problem in a circular furnace using a thermal network, with emissivities 0.4, 0.5, 0.8 and temperatures 400, 500, 800 kelvin, deriving q1, q2, q3.

Understand convection fundamentals: natural and forced flow, external and internal convection, boundary layer concepts, dimensionless numbers, convection heat transfer coefficients, and the governing mass, momentum, and energy equations.

Explain laminar versus turbulent with Reynolds number, steady versus transient, and 1D–3D flow, alongside classifications viscous/inviscid, internal/external, and compressible/incompressible.

Examine velocity and thermal boundary layers on a surface, the growth of boundary-layer thickness with x, no-slip effects, and laminar-to-turbulent transition.

Explore turbulent flow and eddy-driven mixing that boosts heat transfer compared to laminar flow, and learn how velocity fluctuations equal mean plus a fluctuating component.

Compare laminar and turbulent velocity boundary layer, showing laminar flow has a larger velocity gradient across y, while turbulent flow mixes and averages velocity, reducing the gradient.

Learn Reynolds number, the ratio of inertial to viscous forces, Re = rho v L / mu, and critical Reynolds number for flow over a plate is five exponent five.

Explore how the Nusselt number quantifies convection versus conduction by comparing convective to conductive heat transfer; Nu greater than one indicates bulk motion enhances heat transfer.

Prandtl number expresses the ratio of momentum diffusivity to thermal diffusivity, indicating the relative thickness of velocity and thermal boundary layers, with metals yielding small values and oils large.

Explore local and average heat transfer coefficients, showing how H varies along a plate; learn to compute Hbar by integrating H over length or surface, for laminar and turbulent flows.

Derive the differential convection equations: conservation of mass, momentum, and energy, for flow over a plate using a differential element with unit depth and free stream velocity and temperature.

derive the two-dimensional conservation of mass for a differential element by equating inflow and outflow of density times velocity, yielding w_yx + ∂v/∂y = 0.

Derive the two-dimensional conservation of momentum equation from Newton's second law, including surface and body forces, and apply boundary layer approximations to show constant pressure along a flat plate.

Examine the conservation of energy equation, deriving energy balance from heat, mass, and work terms, and link temperature, density, cp, and velocity components to x and y flow.

Explore boundary layer similarity through normalized, dimensionless boundary layer equations and dimensionless variables X*, Y*, U*, P*, T*. Learn how similarity, geometry, and Reynolds number govern the solutions.

Present the functional form of the solutions for velocity and temperature, with u star and t star as functions of x star, y star, Reynolds number, and Prandtl number.

Examine boundary layer analogies by linking u* to X*, y*, and ensemble, and temperature to X*, y*, nodal number, and Prandtl number, with coefficient of friction relating to Reynolds number.

Explore the empirical method to determine the convection coefficient h, covering isothermal and constant heat flux plate cases, unheated starting length, and flow over cylinders and spheres with Nusselt correlations.

Explain laminar flow over a flat plate, derive local and average Nusselt numbers, boundary-layer thickness, and friction; then address turbulent and mixed regimes with Reynolds and Prandtl numbers.

Explore the unheated starting length on a flat plate, where the thermal boundary layer develops after a distance zeta, and note how laminar and turbulent Nusselt expressions guide heat transfer.

Analyze flow over a flat plate with constant heat flux, where wall temperature varies along the surface while heat transfer rate stays constant, using laminar and turbulent Nusselt number correlations.

Master convection calculations by selecting correlations for flat plate, cylinder, or sphere geometry, determining the reference temperature and fluid properties, and choosing between local or surface-averaged heat transfer coefficients.

Explore cross-flow over a cylinder, detailing laminar and turbulent boundary layers, separation and wake, drag trends with Reynolds number, and Nusselt correlations for heat transfer.

Explore external flow Nusselt number correlations for laminar and turbulent regimes, including flat plates, cylinders, and spheres, with properties evaluated at film temperature and relevant Reynolds and Prandtl numbers.

Explore numerical heat transfer problems in internal flow, including laminar, transition, and turbulent regimes over flat plates, to identify maximum heat transfer and heater locations.

Analyzes numerical problems on heat transfer in internal flow over flat plates, computing Reynolds and Nusselt numbers, film temperature, and heat-transfer rate for laminar and constant-heat-flux cases.

Study pipe flow from hydrodynamic entry length to fully developed profiles. Explore Reynolds regimes, boundary layer growth, and energy balances for temperature or heat flux in circular and noncircular ducts.

Explore how thermal boundary layers develop in internal flow, distinguishing thermal from hydrodynamic entry lengths and illustrating heating and cooling effects on temperature and velocity profiles.

Determine laminar and turbulent entry lengths: laminar hydrodynamic 0.05 Re D and laminar thermal 0.05 Re Pr D; turbulent lengths are about 10D and similar.

In internal pipe flow, use the bulk mean temperature TM, not Ts, and note that TM changes along x while the dimensionless ratio (T−T∞)/(Ts−T∞) remains constant in thermally developed region.

Apply energy balance to a differential element under constant heat flux, showing mean temperature varies linearly with x in fully developed flow, and introduce lmtd for the constant temperature case.

Explore laminar flow in circular tubes, where the fully developed region yields Nusselt numbers of 4.36 (constant heat flux) and 3.66 (constant temperature), and understand thermal versus combined entry length.

Explore fully developed turbulent flow in circular tubes, applying the Dittus-Boelter equation (and Cedar–Tait) to compute heat transfer for heating or cooling, with properties evaluated at TM or TS.

Learn how convective correlations apply to noncircular tubes, select Nusselt numbers for constant heat flux or constant surface temperature, and use hydraulic diameter as an equivalent diameter.

solve numerical problems in heat transfer for internal flow, including tube and rectangular duct cases, to determine outlet and wall temperatures using Reynolds, Prandtl, and Nusselt analyses.

Explore free convection, contrast it with forced convection, and relate natural convection currents and conduction to heat transfer, noting the Nusselt number as a convective–conductive ratio.

Explore free convection and buoyant currents arising from temperature gradients and density differences. Understand buoyancy as the upward force on immersed bodies from density differences.

Explains the coefficient of expansion, beta, and how it relates to density differences caused by temperature changes; for a perfect gas, beta equals 1 over the absolute temperature, Kelvin.

Explore natural convection over vertical and inclined surfaces, revealing boundary layer development, no-slip behavior, and plume formation, governed by Grashof and Rayleigh numbers.

Compute heat loss from a 15 m rectangular heating duct carrying still air by applying mean film temperature, Grashof and Prandtl numbers, and Rayleigh-Nusselt correlations for vertical and horizontal surfaces.

Explore mass transfer and diffusion, drawing analogies to heat transfer, and explain how concentration gradients drive diffusion with the diffusion coefficient.

Explain diffusion as molecules move from high to low concentration, illustrated by nitrogen-oxygen exchange and salt diffusion in water. Introduce Fick's law, diffusion coefficient, and convective mass transfer.

Explain how mass convection blends diffusion with bulk flow to form a concentration boundary layer, analogous to velocity and thermal boundary layers, illustrated by air over water.

Explore the concentration boundary layer in internal flow, defining the concentration entry length and developed region, and compare with hydrodynamic, thermal, and velocity boundary layers in laminar and turbulent regimes.

Explore how heat transfer and mass transfer analogies relate dimensionless numbers like Prandtl, Schmidt, Lewis, Nusselt, Sherwood, and Stanton, and apply Reynolds and Chiltern Coleman analogies to convective transfer expressions.

Estimate the evaporation rate from a 500 m by 500 m lake by applying Reynolds and Sherwood numbers to compute mass transfer, humidity-driven concentration differences, yielding 34 kg/s.