Consider the flow of a liquid metal past a flat plate (Pr << 1). We have...

Consider the flow of a liquid metal past a flat plate (Pr << 1). We have shown that for a constant wall teemperature, T_o, the Nusselt number is given by Nu = 0.564*(Re^1/2)*(Pr^1/2). Show that if the surface is not a constant temperature, but is instead providing a constant heat flux, that the Nusselt number becomes Nu = 0.886*(Re^1/2)*(Pr^1/2). Start with the following expression for the temperature profile within a semi-infinite body with a constant heat flux boundary condition T - T_o = (q_s / k)[ ((4*alpha*t) / pi)^1/2 * exp(-x^2 / (4*alpha*t)) - x*erfc( x / (4*alpha*t)^1/2 ) ].

Expert Solution

samet mamat answered 2 years ago

A liquid flows tangentially past a flat plate of dimensions total length of 4 m (parallel...

A liquid flows tangentially past a flat plate of dimensions total length of 4 m (parallel to the flow direction) and width of 1.5 m. fluid velocity is 1 m/s (length wise). What is the skin friction drag (shear force) on both sides of the plate? liquid density = 1000 kg/m3, dynamic viscosity = 2 x 10-2 N*s/m2.

Heat & Mass Transfer Consider the flow of water over a flat plate at a film...

Heat & Mass Transfer Consider the flow of water over a flat plate at a film temperature of 25 °C. The plate is 10m long, and the Reynolds number at the end of the plate is 106. Determine: The free stream velocity Is the flow laminar or turbulent at the end of the plate? Is the flow laminar or turbulent at the mid-length? What is the average Nusselt number? What is the average heat transfer coefficient? What is the Nusselt...

When liquid water is poured onto a flat plate of glass, it spreads out, while liquid...

When liquid water is poured onto a flat plate of glass, it spreads out, while liquid mercury forms spherical beads under similar circumstances. Explain the difference in behavior of the two liquids by filling in the blanks in the following statements: The attractions between the water molecules and the glass are _____ than the attractions among the water molecules themselves, so the water spreads out. The attractions among the mercury atoms are _______ than the attractions between the mercury atoms...

how to find surface temperature of the flat plate which is subjected to air flow from...

how to find surface temperature of the flat plate which is subjected to air flow from one side and constant temperature on the other side using Ansys fluent ?

Re-derive an expression for average NuL (= hLL/k) for flow over a flat plate by integrating...

Re-derive an expression for average NuL (= hLL/k) for flow over a flat plate by integrating the expression for average hL for a mixed BL. For Rex,cr, use 123456 (keeping the same sequence), and find the constant B (in Eq. 7.38). Also show that for Rex,cr = 500,000, B is indeed equal to 871. eq. 7.38=> NuL=(0.037 ReL^(4/5)-B)Pr^(1/3) 0.6<=Pr<=60 Rex,c <= ReL <=108

Consider laminar steady boundary layer at a flat plate. Assume the velocity profile in the boundary...

Consider laminar steady boundary layer at a flat plate. Assume the velocity profile in the boundary layer as parabolic, u(y)=U(2 (y/δ)-(y/δ)^2). 1. Calculate the thickness of the boundary layer, δ(x), as a function of Reynold's number. 2. Calculate the shear stress at the surface, τ, as a function of Reynold's number. Re=ρUx/μ

Analytical Solution steps For a flat plate solar collector, with water as the working fluid, consider...

Analytical Solution steps For a flat plate solar collector, with water as the working fluid, consider a design for heating water from 22°C to 60°C. The temperature of the air and the surroundings is 310 K. The system is designed for a flow rate of 0.03 gpm. The water exhibits fully developed, laminar flow in a 0.05 diameter pipe, with a constant surface flux. The collector plate experiences losses due to convection and radiation, which can be accounted for using...

Question 1: Consider a metal rod of uniform temperature. Is it possible that heat spontaneously flow...

Question 1: Consider a metal rod of uniform temperature. Is it possible that heat spontaneously flow from one end of the rod to the other end so that they end up in different temperatures? Why? Question 2: The ocean is full of heat energy. Explains what limits people from using this energy to make electricity? Question 3: The density of water is about 1,000 kg/m3, and 1 mole of water molecules has a mass of 18 grams. Calculate the hidden...

Consider a 1.5m long 30cm wide flat plate exposed to two laminar flows of air (6...

Consider a 1.5m long 30cm wide flat plate exposed to two laminar flows of air (6 m/s free stream top surface and 12m/s free stream bottom surface) at 25ºC and atmospheric pressure. The top and bottom surfaces of the plate are electrically heated (1.5 kW total power, heaters assumed infinitesimally thin). The plate consists of 3 layers: a top and bottom layer of 1.0 cm balsa wood (k = 0.055 W/(m·K)), and a middle layer of 2.0 cm plywood (k...

Consider a flat plate with parallel airflow (top and bottom) characterized by u∞ 5 m/s, T∞...

Consider a flat plate with parallel airflow (top and bottom) characterized by u∞ 5 m/s, T∞ 20°C. Determine the average convection heat transfer coefficient, convective heat transfer rate, and drag force associated with an 2.8-m-long, 2.8-m wide flat plate with a surface temperature of 50°C. Assume the critical Reynolds number is 5x105. Determine the average convection heat transfer coefficient, in W/m2·K. Determine the convective heat transfer rate, in W. Determine the drag force, in N.

Question