EXAMPLE 10.4 Discretize the equation boundary as shown in Fig. 10.6. =0 at node (i, j) of a con vection ax ay ij+ 1 dq dq4 dq2 i-1,j i.j Ay bp Convection boundary Ar Fig. 10.6 Convection boundary condition.
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- A heat treat steel plate measures 3 m *1 m and is initially at 30 degree Celsius. It is cooled by blowing air parallel to 1 m edge at 9 km/hr. If the air is at 10 degree Celsius. Estimate the convective heat transfer from both sides of the plate.1-The wind blows with velocity 0.4 m/s parallel to the both sides of a flat plate with rectangular area 10m×10 m. The plate temperature is T0=60◦C, and the temperature of the air free stream is 20◦C. Assume laminar flow and calculate: (a) maximum boundary layer thickness, (b) the total force experienced by the plate, (c) estimate the total heat transfer rate by laminar forced convection (d) Make a qualitative sketch of how the local heat flux qx and τx varies along the length L.Consider two cases involving the parallel flow of dry air at V= 1.5 m/s, T∞=45°C, and atmospheric pressure over an isothermal plate at Ts=20°C. In the first case, Rex,c=R5 × 105, while in the second case the flow is tripped to a turbulent state at x=0 m. At what x‐location, in m, are the thermal boundary layer thicknesses of the two cases equal? What are the local heat fluxes, in W/m2, at this location for the two cases?
- A 0.407m long vertical steel plate at a surface temperature of 700K is in contact with hot air at 237K, latm absolute pressure. If E=0.81 for steel pipe:a. Calculate the total 1S1 transfer coefficient for the convection increase 1 convectionb. What is the heat loss per unit area of the surface?Problem: Convection related Air at atmospheric pressure and a temperature of 25°C is in parallel flow at a velocity of 5 m/s over a 1‐m‐long flat plate that is heated from below with a uniform heat flux of 1,250 W/m^2. Assume the flow is fully turbulent over the length of the plate. (a) Calculate the plate surface temperature, Ts(L), and the local convection coefficient, hx(L), at the trailing edge, x = L. (b) Calculate the average temperature of the plate surface, T¯s. (c) Plot the variation of the surface temperature, Ts(x), and the convection coefficient, hx(x), with distance on the same graph. Explain the key features of these distributions.FUNDAMENTALS OF CONVECTION Consider a flat plate positioned inside a wind tunnel, and air at 1 atm and 20°C is flowing with a free stream velocity of 60 m/s. What is the minimum length of the plate necessary for the Reynolds number to reach 2x107? If the critical Reynolds number is 5x105, what type of flow regime would the airflow experience at 0.2 m from the leading edge? Please, I need the solution from fundamental concepts of how the heat flow behaves in the system. That it be answered with theory of the subject
- A horizontal oil sump with a surface temperature of 40°C, 0.5 m long and 0.4 m wide containing oil at 75°C, (Pr = 546, β = 0.7 × 10–3 K–1 and ν = 4.168 × 10–5 m2/s). Calculate the grashof number.Air at atmospheric pressure and a temperature of 25 degrees C is in parallel flow at a velocity of 5 m/s over a 1-m-long flat plate that is heated from below with a uniform heat flux of 1250 W/m2 . Assume the flow is fully turbulent over the length of the plate. Take ν = 18.76 × 10−6 m2/s, k = 0.0284 W/m·K and Pr =0.703. (a) Calculate the plate surface temperature, Ts(L), and the local convection coefficient, hx(L), at the trailing edge, x = L. (b) Calculate the average temperature of the plate surface.Q2/ cylindrical electrical heating element (dissipated 1000 W/m) of diameter D=10 mm, thermal conductivity k=240 W/m K, density 2700 kg/m3, and specific heat cp = 900 J/kg K is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 27°C and 10 m/s, respectively. calculate the surface temperature per unit length of the heater.
- Air at standard pressure flows across a flat plate at 3m/s. The temperature surface is 50oC and the surrounding temperature is 20o Consider a point 1m away from the leading edge of the plate. See Table A-15 in Appendix 1 for properties of air. Determine the Reynold’s number and Prandtl number for this flow at the location described above. Determine the local flow boundary layer thickness. Determine the local thermal boundary layer thickness for this flow. Find the local Nusselt number. Based on this Nusselt number, what is the local convective heat flux from the plate to the air?Consider two cases involving parallel flow of dry air at V=V= 2.5 m/s, T∞=45°C, and atmospheric pressure over an isothermal plate at Ts=20°C. In the first case, Rex,c=Rex,c=5 × 105, while in the second case the flow is tripped to a turbulent state at x=0 m. a. At what x‐location, in m, are the thermal boundary layer thicknesses of the two cases equal? in m b. what is the q'' lam at W / m^2 c. what is the q'' turb at W / m^25.43 A refrigeration truck is traveling at 130 km/h on a desert highway where the air temperature is . The body of the truck is idealized as a rectangular box 3 m wide, 2.1 m high, and 6 m long, at a surface temperature . Assume that (1) the heat transfer from the front and back of the truck is neglected, (2) the stream does not separate from the surface, and (3) the boundary layer is turbulent over the whole surface. Calculate the required cooling rate of the refrigeration unit.