Use scale analysis to find an expression for 8/x and Nu for flow over a flat plate with a thin thermal boundary Layer. Find the expression 8/x = 4.92 Re**
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- Introduction to heat convection Solved problems HW-10- 1- Determine the velocity distribution in the velocity boundary layer assuming second degree polynomial: u =C, +C,y+C,y? Answer: The boundary conditions are: du .. u = 0 at y = 0; u = u, ; at y = 6; = 0 at y = 8 dy 2 y This gives: يجب حفظ الشروط الحدية اذا كان الامتحان حضوري 2- Determine the velocity distribution in the velocity boundary layer assuming third degree polynomial: u = C, +C,y+C,y' +C,y' Answer: The boundary conditions are: .. u = 0 at y = 0 = 0 dy? at y = 0 du = 0 u = u, at y = 8 at y = 8 dy 3 y 1y This gives: 28 28 يجب حفظ الشروط الحدية اذا كان الامتحان حضوري 3- Determine the velocity distribution in the velocity boundary layer assuming fourth degree polynomial: 2 u = a, +a, y+a,y +a,y' +a,y Answer: The boundary conditions are: . u = 0 = 0 dy? at y = 0 at y = 0 du = 0 dy d'u at y = 6 ; dy? u = u, at y = 6 at y = 6 4. This gives: = 2 يجب حفظ الشروط الحدية اذا كان الامتحان حضوري 4- For flow over a slightly curved…Using dimensional analysis obtain an expression for nusselt number in terms of Reynolds number and prandtl numberConduct thorough a research on Boundary layer and viscous sub layer, Shear stress in circular pipe as it relates to mechanics of fluids
- A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Assuming kinetic viscosity, v = 30 x 10-6 m²/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is (up to three decimal)?An isothermal long cylinder with square (side of 0.4 m and diagonal of 0.5657 m) cross-section is placed in a flow with a velocity of 1 m/s as shown. The properties of the fluid are: kinematic viscosity is 1.38 x 10-5 m²/s, thermal conductivity is 0.024 W/m.°C, and Prandtl number is 0.73. What is the average Nusselt number for the flow? 1253 a Figure 1: Flow configuration for Problem 6. The dimensions are: a=0.4 m, b=0.5657 mIn a particular engineering application involving airflow (u) over a surface (length in the direction of the flow is L), the temperature distribution of the airflow T(x, y) is measured and can be approximated by the following expression: Tf(x,y)-Ts 1- exp(-º 0.0332 Re2Pr¹/3 = y), where x is the coordinate from the leading edge of x Too-Ts the surface and parallel to the flow direction, while y is the coordinate perpendicular to the surface. Ts is the temperature of the surface and Too is the temperature of the moving fluid, and both are constants. Rex is the Reynolds number with the characteristic length of.x, and Pr is the Prandtl number. Assume uniform properties in the fluid field (thermal conductivity ks, kinemati viscosity vs, etc.). (a) Based on the expression given above, derive the derivative of the fluid temperature (the slope) with respective to y, then find the derivative at the surface (x, y=0), i.e., ду TI at y=0 (b) Based on the derivation of (a), write the expression of…
- Under what conditions may one describe atmospheric processes using the incompressible form of the continuity equation?Forced air at T0 = 25°C and V = 17 m/s is used to cool electronic elements on a circuit board. One such element is a chip, 4 mm x 4 mm, located 129 mm from the leading edge of the board. Experiments have revealed that flow over the board is disturbed by the elements and that convection heat transfer is correlated by an expression of the form Nuz = 0.04RE0.85 Pr3 V, T. Chip Board L mm Estimate the surface temperature of the chip if it is dissipating 38 mW.Air is flowing naturally over a cylinder of D=(1) cm. Air has thermal conductivity 0.027W/mK, kinematic viscosity 1.9*10-5 m2/s, Rayleigh number 108, and Prandtl number0.72. Find the Nusselt number uses charts/table also if needed
- Fluid from a large reservoir at temperature T 0 fl ows into acircular pipe of radius R . The pipe walls are wound with anelectric resistance coil that delivers heat to the fl uid at a rateq w (energy per unit wall area). If we wish to analyze thisproblem by using the full continuity, Navier-Stokes, andenergy equations, what are the proper boundary conditionsfor the analysis?* ZAIN IQ liı. SuspendEA IN A ROom, Ana TS Subjected To Air Flow Parallel To I... A 2m by 3m flat plate is suspended in a room, and is subjected to air flow parallel to its surfaces along its 3m long side as shown in the figure. The free stream air temperature, T, is 20°C and the velocity is 7 m/s. The total drag force acting on the plate is measured to be 0.86 N. Determine the average convection heat transfer coefficient for the plate. Air 20°C, 7 m/s L= 3 m. This problem has been solved! See the answerA plate is cooled by a fluid with Prandtl number Pr >> 1. Surface temperature varies with distance form the leading edge according to where C is constant. For such a fluid it is reasonable to assume that axial velocity within the thermal boundary layer is linear given by u=V% y Determine the local Nusselt number and show that surface heat flux is uniform. Use a third degree polynomial temperature profile and assume laminar boundary layer flow y YA To Vo T₁(x,0)=T +C√√x U -8 &₁ X T₁(x) = T₁ +C√x