When evaluating fluid properties for convection calculations, the film temperature (Tf) is often used. How is this temperature calculated?
Explanation
Fluid properties like viscosity and thermal conductivity vary with temperature. Since the temperature changes across the boundary layer, a single reference temperature must be chosen to evaluate these properties. The film temperature, Tf = (Ts + T∞)/2, provides a reasonable average temperature for this purpose.
Other questions
What is the typical definition of the velocity boundary layer thickness, δ, in convection?
How is the local friction coefficient, Cf, defined for external flows?
What physical process governs the transfer of energy at the very surface of an object (at y=0) within a thermal boundary layer?
What does the Prandtl number (Pr) physically represent?
For laminar flow over a flat plate, what is the expected relationship between the velocity boundary layer thickness (δ) and the thermal boundary layer thickness (δt) for a fluid like oil, which has a Prandtl number (Pr) much greater than 1?
A long circular cylinder with a diameter of 20 mm is fabricated from solid naphthalene and is exposed to an airstream that provides for an average convection mass transfer coefficient of 0.05 m/s. The molar concentration of naphthalene vapor at the cylinder surface is 5 x 10^-6 kmol/m^3, its molecular weight is 128 kg/kmol, and the concentration in the free stream air is negligible. What is the mass sublimation rate per unit length of the cylinder?
What is the critical Reynolds number (Rex,c) value that is typically assumed for the onset of transition from laminar to turbulent flow for calculations involving a flat plate?
In a fully turbulent boundary layer over an isothermal flat plate, how does the local heat transfer coefficient (h) generally vary with distance (x) from the leading edge?
The Lewis number (Le) is defined as the ratio of thermal diffusivity to mass diffusivity (α/DAB) and is a measure of the relative thicknesses of which two boundary layers?
The Reynolds analogy provides a direct relationship between momentum, heat, and mass transfer. Under what specific, idealized conditions does it state that Cf/2 = St = Stm?
The local heat transfer coefficient for flow over a flat plate with an extremely rough surface is found to fit the relation hx(x) = a * x^-0.1, where 'a' is a coefficient. What is the expression for the ratio of the average heat transfer coefficient over a plate of length x, h_bar(x), to the local coefficient at that same position x, hx(x)?
Water at approximately 300 K flows at a velocity of 1 m/s over a 0.6 m long flat plate. Transition from laminar to turbulent flow is assumed to occur at a critical Reynolds number of 5 x 10^5. Given the properties of water at 300 K are ρ = 997 kg/m^3 and μ = 855 x 10^-6 N·s/m^2, what is the location (xc) from the leading edge where transition occurs?
What is a primary motivation for nondimensionalizing the boundary layer equations in the study of convection?
In the context of convection, what is an 'empirical correlation'?
The average convection coefficient (h_bar) for a surface of area As is related to the local coefficient (h) by which integral expression?
In the full energy equation for a viscous fluid, what physical process is represented by the term (μ/cp)(∂u/∂y)^2?
The Chilton-Colburn analogy, which states Cf/2 = St Pr^(2/3), is a modification of the Reynolds analogy that extends its applicability over a wide range of which dimensionless number?
During steady-state evaporative cooling from a liquid surface into a gas, if there is no external heat addition (q_add = 0), what is the energy balance at the surface?
Which dimensionless number is interpreted as the ratio of inertia forces to viscous forces within a fluid flow?
Experimental tests on a turbine blade with a chord length of 40 mm in an airflow at 1150 degrees Celsius and velocity 160 m/s show a heat flux of 95,000 W/m^2 when the blade surface temperature is 800 degrees Celsius. If the blade temperature is reduced to 700 degrees Celsius by increasing the coolant flow, while all other conditions and properties remain constant, what is the new heat flux?
What are the two main characteristics of the viscous sublayer within a turbulent boundary layer?
The Nusselt number (Nu) is a dimensionless parameter that represents the ratio of convection to pure conduction heat transfer. What physical quantity is it equal to at the surface?
In mass transfer, the Sherwood number (Sh) is the analog to the Nusselt number. What physical quantity does the Sherwood number provide a measure of?
What is the fundamental difference in the definition between the Biot number (Bi) and the Nusselt number (Nu)?
A container is wrapped in a fabric moistened with a volatile liquid and placed in dry ambient air at 40 degrees Celsius (313.15 K). The liquid has a molecular weight of 200 kg/kmol and a latent heat of vaporization of 100 kJ/kg. Its saturated vapor pressure is 5000 N/m^2, and its diffusion coefficient in air is 0.2 x 10^-4 m^2/s. Assuming an average boundary layer temperature of 300 K, the air properties are ρ = 1.16 kg/m^3, cp = 1.007 kJ/kg·K, and α = 22.5 x 10^-6 m^2/s. What is the steady-state temperature of the beverage?
The friction coefficient (Cf) and the convection coefficients (h and hm) are the key parameters in convection analysis. What physical phenomena are they the principal manifestations of?
In the analysis of convection mass transfer involving a dilute, binary gas mixture, when is it acceptable to assume that the properties of the mixture are approximately those of the bulk gas (species B)?
In the derivation of the boundary layer equations, what is the key approximation made regarding the diffusion of momentum, heat, and species?
The average Nusselt number for convection over a surface of a given geometry is generally a function of which two dimensionless parameters, assuming no mass transfer?
A solid object is suspended in air at 20°C flowing at 100 m/s. The solid has a length of 1 m and surface temperature of 80°C. The temperature at a point (x*, y*) in the boundary layer is 60°C. A second, geometrically similar solid of length 2 m has a film of water on its surface and is placed in dry air at 50°C flowing at 50 m/s. The surface is also at 50°C. What is the molar concentration of water vapor, CA(x*, y*), at the corresponding point in the boundary layer? Assume the properties of air and water vapor result in Pr = 0.70 and Sc = 0.70.
In the context of deriving convection transfer equations, what does the term 'advection' refer to?
The continuity equation, ∂u/∂x + ∂v/∂y = 0, is a simplified form of the general mass conservation equation. This form is valid under what key condition?
In Couette flow, where fluid is sheared between a stationary plate and a moving plate, what physical process does the term μ(∂u/∂y)^2 in the energy equation represent?
In the Couette flow problem described in Example 6S.1, with engine oil between two plates 3 mm apart, a moving plate at 10 m/s and 30°C, and a stationary plate at 10°C, where is the maximum temperature located?
In pure Couette flow, where the fluid motion is driven solely by the relative movement of two parallel plates, what is the value of the pressure gradient in the direction of flow (dp/dx)?
What is meant by the term 'similarity solution' in the context of the laminar boundary layer over a flat plate?
For laminar flow over an isothermal flat plate, the local friction coefficient, Cf,x, is proportional to what power of the local Reynolds number, Rex?
For laminar flow over an isothermal flat plate, the local Nusselt number (Nux) is proportional to what power of the local Reynolds number (Rex), for fluids with a Prandtl number greater than or equal to 0.6?
For laminar flow over a flat plate, what is the relationship between the average convection coefficient from the leading edge to a point x, h_bar(x), and the local convection coefficient at that same point, hx(x)?
For turbulent flow over a flat plate with Reynolds numbers up to 10^8, the local friction coefficient, Cf,x, is empirically correlated with what power of the local Reynolds number, Rex?
In turbulent flow, how do the thicknesses of the velocity (δ), thermal (δt), and concentration (δc) boundary layers generally compare?
For laminar flow over a flat plate with an unheated starting length ξ, followed by a heated section, how does the local Nusselt number (Nux) at a position x > ξ relate to the Nusselt number for a plate that is heated from the leading edge (Nux|ξ=0)?
For flow over a flat plate under a constant surface heat flux condition, how does the local Nusselt number in the laminar region compare to the case of a constant surface temperature?
Air at a pressure of 6 kN/m^2 and 300°C flows at 10 m/s over a 0.5 m long flat plate maintained at 27°C. The film temperature is 437 K. The kinematic viscosity of air at 437 K and standard atmospheric pressure (1 atm = 101.33 kN/m^2) is 30.84 x 10^-6 m^2/s. What is the kinematic viscosity at the operating pressure of 6 kN/m^2?
Air at 437 K flows at a velocity of 10 m/s over a 0.5 m long flat plate. The kinematic viscosity of the air at the operating conditions is 5.21 x 10^-4 m^2/s. What is the Reynolds number at the trailing edge of the plate?
For laminar flow of air (Prandtl number = 0.687) over a flat plate, if the Reynolds number at the end of the plate is 9597, what is the average Nusselt number for the plate?
A flat plate is heated by five 50-mm-long strip heaters. Air at 400 K (k = 0.0338 W/m·K, Pr = 0.690) flows over the plate at 60 m/s. Transition occurs at xc = 0.22 m. What is the average convection coefficient over the first four heaters (total length 0.2 m), which are entirely within the laminar region? The Reynolds number at the end of the fourth heater (x=0.2 m) is 4.56 x 10^5.
How is the Stanton number (St) defined in terms of the Nusselt number (Nu), Reynolds number (Re), and Prandtl number (Pr)?
The Whitaker correlation for heat transfer from a sphere, NuD = 2 + (0.4ReD^1/2 + 0.06ReD^2/3)Pr^0.4 (μ/μs)^1/4, includes a specific term to account for what physical effect?