Heat Transfer: Concepts & Engineering Applications

Explore convection as a heat transfer mode driven by bulk fluid motion, including natural or free convection and forced convection, due to density differences, with conduction when motion is absent.

Explore local and average convective heat transfer coefficients on a flowing flat plate, deriving the relation between Hx and Hbar under Newton's law of cooling.

Explore key dimensionless numbers for convective heat flow, including the Nusselt, Grashof, Prandtl, Rayleigh, Reynolds, and Stanton numbers. See how they relate convection to conduction and buoyancy to viscous forces.

Explore how the characteristic length governs buoyancy-driven convection in heat transfer, guiding choices in vertical and horizontal flat plates, cylinders, and spheres, with diameter or height depending on geometry.

Apply empirical correlations for free convection using Nusselt, Grashof, and Prandtl numbers to estimate heat transfer for plates, cylinders, wires, and spheres in laminar and turbulent regimes.

Explore forced convection correlations for flat plates and tubes, using Reynolds and Prandtl numbers to compute local and average Nusselt numbers and the convective coefficient at mean film temperature.

Compute TMF as the average of TS and T infinity, TMF = (TS + T infinity)/2, and TB as the bulk temperature of the mixed flowing fluid.

determine the convective coefficient for free convection around a 20 cm sphere in water, using Grashof and Prandtl correlations to yield Nu ≈ 198.6 and h ≈ 612 W/m²K.

Compute free-convection heat loss from a horizontal steam pipe by evaluating Grashof and Prandtl to get Rayleigh, then determine Nusselt and h to find the heat transfer rate.

Calculate maximum heat transfer by forced convection from the freezer top, with air at 30 °C flowing 0.7 m/s over a 0.6 by 1.8 m surface at 10 °C.

Compute heat transfer in forced convection through a 10 cm tube by applying Reynolds and Prandtl correlations to find Nusselt and convection coefficient, then determine heat flow rate.

Develop the boundary layer in pipe flow, noting confinement-limited thickness as wall layers meet at the center. Show laminar and turbulent regimes, fully developed flow, and 50–80 D development length.

Examine the development of the thermal boundary layer over a flat plate, driven by T s and T infinity, and analyze heat flow directions and boundary-layer thickness.

Derive the two-dimensional continuity equation for steady, incompressible flow in a boundary layer over a surface, using a dx by dy control volume to yield ∂u/∂x + ∂v/∂y = 0.

Derive the energy equation for a thermal boundary layer over a flat plate, including convection, y-direction conduction, and viscous heating, with 2d boundary layer assumptions and mean film temperature.

Explore the electromagnetic spectrum from gamma rays to radio waves, highlighting thermal radiation in the 0.1 to 100 micrometers range, including visible and infrared heating and solar energy applications.

Explain how absorptivity, reflectivity, and transmissivity describe the split of incident heat flux into absorbed, reflected, and transmitted portions, with alpha plus rho plus tau equals 1.

Apply energy balance to a radiant problem by linking absorptivity, reflectivity, and transmissivity; compute absorption, transmission, and reflection rates using alpha, rho, and tau with Q0 = 1000.

Explore radiation heat exchange by examining black bodies, gray bodies, specular and diffuse reflections, and transparent or opaque diathermous bodies, with absorptivity, reflectivity, and transmissivity relations.

Explore Planck's law for black body emissive power, its spectral distribution, and the short and long wavelength limits via Bain's law and Rayleigh-Jeans law, with Wien's relation.

Explore how the Stefan Boltzmann law yields the total emissive power of a black body from Planck's law by integrating over all wavelengths, giving EB = Sigma B t^4.

Apply Planck's law to derive Wien's displacement law, showing lambda max times temperature equals 0.0029 m K. Determine that emissive power scales as T^5 with E_lambda_max = 1.285e-5 T^5 W/m^2/m.

Compute the emissive power at 5 micrometers for a 3000 K blackbody using Planck's law. Then apply Wien's displacement law to locate peak wavelength and estimate emissive power with Stefan-Boltzmann.

Learn how heat exchange by radiation between two black bodies uses the configuration factor (shape factor) and derive the reciprocity theorem A1 F12 = A2 F21 for TA and TB.

Explains how to compute shape and configuration factors using the conservation principle and reciprocity theorem for arbitrary, cylindrical, and hemispherical cavities, with FAA, FAB, FBB, and FBA.

Kirchhoff's law links emissivity and absorptivity by showing that at the same temperature and wavelength, E/alpha equals Eb and emissivity equals absorptivity.

Define plane angle as arc length over radius, and solid angle as the projection over radius squared, linking radiative heat exchange to theta and steradian.

Explore Lambert's cosine law, where intensity in direction theta from the normal is proportional to cos theta, and examine heat exchange between black surfaces via solid angles and emissive power.

Analyze heat exchange between two non-black plane surfaces A and B, deriving the net transfer using absorptivities and emissivities, the interchange factor F_AB, Kirchhoff’s law, and the Stefan Boltzmann relation.

Explore radiative heat exchange between two infinite long concentric cylinders, applying reciprocity, shape factors, Kirchhoff's law, and emissivity-based terms to derive inter-cylinder heat transfer.

Relate the net radiative heat exchange between two small gray bodies, defined by their emissivities and absorptivities. Express Q_AB = epsilon_A epsilon_B A FAB (T_A^4 - T_B^4) under Kirchhoff's law.

Explain radiative heat exchange for a small body in a large enclosure, using interchange and shape factors (FAB and FBA), emissivity, areas, and the Stefan–Boltzmann law across geometries.

Use an electrical analogy to model irradiation and radiosity between two surfaces, deriving surface and space resistances and black surface heat expression Q = A1 F12 sigma (T1^4 - T2^4).

Compute heat flux between two infinite parallel planes at 520 kelvin and 460 kelvin using gray body factor and the Stefan–Boltzmann law, with emissivities 0.95 and 0.82.

Explore how radiation shields reduce heat transfer between parallel surfaces by adding surface and space resistances. The lecture shows calculating shield temperatures and the half reduction when emissivities are equal.

Explore radiation exchange between two parallel planes (emissivity 0.6) with and without two shields (emissivity 0.06), showing a 96.52% reduction in heat transfer.

Explore radiative heat transfer coefficient HR derived from f_AB and F_AB with TA and TB, and combine radiation with convection into heat transfer via Q = (HC+HR)(TG - TW).

Calculate radiative and convective heat transfer coefficients for a pipe at 520 K inside a 420 K enclosure, yielding HR 23.81 and HC 16.09 W/m2-K and total 39.9 W/m2-K.

Explore how heat exchangers transfer heat between hot and cold media, including tubular designs, and review applications from hvac and refrigeration to power, chemical processing, and waste heat recovery.

Classify heat exchangers by heat-exchange type (direct contact, regenerative, recuperative), flow arrangement (parallel, counter, cross), and mechanical design (concentric tubes, shell and tube with baffles) with industrial applications.

Determine the overall heat transfer coefficient by combining conduction and convection resistances, and apply Q = UA delta T; compute Ui and Uo for cylindrical walls.

This lecture introduces fouling and falling factors in heat exchangers, defining scale heat transfer coefficients hsi and hso and their resistances RSI and RSO to update ui and uo.

Learn how to compute the overall heat transfer coefficient between oil and water in a concentric pipe with an annular gap, given inner/outer diameters, material conductivity, and convection coefficients.

Explain how fluid heat capacity equals mass flow rate times specific heat, and apply Q = M C ΔT for hot and cold fluids in heat exchangers.

Explore the logarithmic mean temperature difference (LMTD) and its heat transfer equations for parallel and counter-flow heat exchangers, detailing theta differences, Q, and the LMTD formula.

Calculate heat transfer rate Q for hot water in a parallel-flow exchanger using m cp delta T, then apply LMTD with U to find the required area.

This counter flow heat exchanger uses lmtd to determine area; u = 800 w/m2k, hot water 40–20 c, brine -20 to -8 c, area 0.397 m2.

Counter flow heat exchangers achieve higher theta LMTD and reduced surface area than parallel flow, boosting heat transfer; an example shows calculating theta LMTD and Q = UA theta LMTD.

define capacity ratio CR as ratio of minimum to maximum heat capacity in heat exchanger design, with CH and CC setting C minimum and C max by smaller fluid capacity.

Effectiveness, epsilon, is the ratio of actual heat transfer to the maximum possible transfer, where Q_actual = Ch(ThA−ThB) or Cc(TcB−TcA) and Q_max = C_min(ThA−TcA) with C_min the smaller heat capacity.

understand the number of transfer units (ntu) as the ratio of ua to c minimum, with u as the overall heat transfer coefficient and a as the surface area.

Apply the ntu-effectiveness approach to parallel-flow heat exchangers, deriving the effectiveness-ntu relationship and guiding design with capacity ratio, c minimum, and lmt d insights.

Derive the counterflow ntu–effectiveness relation, arriving at the standard epsilon formula for counterflow heat exchangers. Note cr = cmin/cmax and link to lmt d and heat-transfer sizing.

Apply the ntu-effectiveness method to a counter-flow heat exchanger cooling air from 55 to 25 C with water at 10 C, and determine area using mass flow rates and U.

Explore how the correction factor CF adjusts heat transfer rate Q in multi-pass tube-and-shell and cross-flow heat exchangers, refining LMTD for counter-flow conditions using M and S.

Calculate surface area for a multi-shell and tube heat exchanger cooling hot fuel with water. Use correction factor charts and logarithmic temperature difference for counterflow and cross flow configurations.

Derive correction factors for heat exchangers using charts for single shell two-pass, two-shell four-pass, and cross-flow mixed types, based on parameters m and s, with manual data noting potential inaccuracies.