Fundamentals of Heat Transfer Part 2

Apply the empirical method to determine convection coefficients by relating average Nusselt numbers to Reynolds and Prandtl numbers through geometry-specific correlations and heated surface experiments.

Derive convection coefficients and boundary layer thickness for external flow over a flat plate using laminar and turbulent correlations. Determine regimes via Reynolds numbers and estimate heat transfer.

Analyze heat transfer from a flat plate to air in two orientations, using Reynolds numbers to assess laminar and turbulent boundary layers and applying flat-plate correlations for heat transfer coefficients.

Example 2 analyzes a refrigerated truck roof with aluminum panels and 50 mm insulation under 105 km/h wind and solar radiation to compute the outer surface temperature and heat load.

Explore the cylinder in cross flow, including stagnation pressure, pressure gradients, boundary-layer development, separation, and how Reynolds and Prandtl numbers determine average convection coefficients with correlations.

Compute the heat transfer rate per unit length from a steam pipe to air using the Chirchir correlation for the average convection coefficient, based on Reynolds and Prandtl numbers.

Study external flow over a sphere, including boundary layer transition and separation with wake mixing. Apply the Whiteaker correlation to estimate the average convection coefficient.

Compute the cooling time from 75°C to 35°C for a copper sphere in air at 10 m/s and 23°C using the capacitance method, checking Biot number and convection heat transfer.

examine how a circular pipe develops a velocity boundary layer, transitioning from laminar to fully developed flow; compare laminar and turbulent profiles, Reynolds number criteria, and hydrodynamic entry lengths.

Derive the fully developed laminar velocity profile in a circular pipe, showing a parabolic u(r) and the relation to mean velocity via u(r)/u_mean = 2(1 - r^2/a^2).

Explore how pressure gradient and friction factor determine pressure drop in fully developed laminar flow, linking Reynolds number, relative roughness, and pumping power.

Analyze how a thermal boundary layer develops in a pipe with uniform inlet temperature, under laminar and turbulent flows, and compare constant surface temperature with constant heat flux.

Examine thermally fully developed flow, detailing axial temperature profile evolution, dimensionless temperature independence from x, and a constant, x-independent local convection coefficient in the fully developed region.

Explain the constant surface heat flux condition using a differential control volume and area energy balance, showing mean temperature rises linearly with x in the thermally fully developed region.

Investigate how a constant surface temperature drives a temperature difference that decays exponentially along a pipe, using log mean temperature difference and average convection coefficient.

Compute the length needed to heat water from 20 to 60 C in a tube using energy balance with volumetric generation, and assess fully developed flow and outlet convection.

Calculate the water convection coefficient in a 50 mm, 6 m condensing steam tube, with water from 15 to 57 C, LMTD 61.63 C, h ≈ 755 W/m^2K.

Analyze surface thermal condition with external fluid and moving fluid to infinity, using an overall heat transfer coefficient to combine outer convection, conduction, inner convection, and log mean temperature difference.

Explore internal forced convection correlations for laminar and turbulent flow in circular and noncircular ducts, applying laminar Nu values and boulter, Sieder–Tate, and New Leonski models across Reynolds ranges.

Compute the resistance heater power to heat water from 15 to 65 C in a 3 cm, 5 m tube with uniform surface heat flux; estimate the end-surface temperature.

Analyze heat transfer in a 10 m insulated pipe carrying water vapor, calculate the overall heat transfer coefficient, and verify the insulation keeps the outer surface below 45 C.

Compute exit temperature and heat loss for air entering a 0.2 m square duct at 80 °C with 60 °C walls, yielding exit ≈71.3 °C and heat loss ≈1.31 kilowatts.

Explore natural convection around a heated vertical plate, driven by buoyancy from temperature-induced density differences, with boundary-layer development and velocity profiles, and how buoyancy affects the convection coefficient.

Explore the Grashof number and other key dimensionless numbers in natural convection, linking buoyancy, viscous forces, and characteristic length to convection coefficients for a heated vertical flat plate.

Learn to compute average natural convection coefficients for vertical and horizontal plates, cylinders, and spheres using Churchill correlations and geometry-specific characteristic lengths.

Analyze natural convection from a vertical glass panel between a fireplace and a room, yielding Nu ≈ 147 and a heat transfer rate of about 1.06 kW.

In example 2, an aluminum plate with electrical components dissipates power; energy balance shows convection and radiation losses, giving a maximum of about 583 W to stay below 77 C.

Compute the heat transfer rate per unit length from a 165 C pipe by combining natural convection at 23 C and radiation, using the given geometry.