Determine the maximum allowable uniform heat flux, in W/m², that may be imposed at a wall heating panel 1 m high if the maximum temperature is not to exceed 39°C when the ambient air temperature is 25°C. Assume laminar flow and use the more accurate Churchill and Chu correlation for laminar flow Nusselt number. 4 = I ! W/m² Physical Properties Mathematical Functions
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- Topic: Heat transfer Completely solve and box the final answer. 1. A 20degC water flows to 50cmx60cm flat plate with velocity of 5.2m/s . The flat plate surface temperature is maintained at 40deg C. The air flows parallel to the 50cm side of the plate. If the kinematic viscosity of water is 78x10-8 m2/s, at what length the flow become turbulent?HEAT TRANSFER From the heat transfer property table of water, the properties at 20 0C are as follows: Density = 997.36 kg/m3 Kinematic viscosity = 1.026 × 10-6 m2/s Prandtl number = 7.17 (i) Thickness of hydrodynamic boundary layer = 9.24 mm (ii) Thickness of thermal boundary layer = 4.79 mm (iii)Local friction coefficient = 0.001228 Average friction coefficient = 0.002456 ANSWER QUESTION (iv) ,(vi) and BAir stream (k = 0.02439 W/m.K, v = * m2/s, Pr = 0.7336) flows over a flat surface [L= 4.5 m, w = 2.5 m] with velocity of 158 km/hr, flow is parallel to L, What is the average convective heat transfer Coefficient "W/m?.°C" ? 1.426 ×10 %3D
- Topic: Heat transfer Completely solve and box the final answer. A 20degC water flows to 50cmx60cm flat plate with velocity of 6m/s . The flat plate surface temperature is maintained at 40deg C. The air flows parallel to the 50cm side of the plate. If the kinematic viscosity of water is 78x10-8 m2/s, at what length the flow become turbulent? If the average laminar heat transfer coefficient of water is 7740W/m2 degC, what is the overall heat transfer at the laminar section?Air at 22˚C and at atmospheric pressure flows over a flat plate at a velocity of 1.65 m/s. If the length of the plate is 2.179 m and its temperature is 98 ˚C, Calculate Heat rate by using exact and approximate methods both. What is the %age difference of the heat transfer rate values by these methods? Take width of the plate as unity. Properties given at 60˚C are as follows: Density: 1.058 kg/m3 , cp = 1.005 kJ/kg˚C, k= 0.02897 w/m˚C, Kinematic viscosity is 18.97 × 10-6 m2 /sObtain by dimensional analysis a functional relationship for the wall heat transfer coefficient h (W/m2-K) for a fluid flowing through a straight pipe of circular cross section. Assume that the effects of natural convection may be neglected in comparison with those of forced convection. Taking the heat transfer coefficient, h, as a function of the fluid velocity, density, viscosity specific heat and thermal conductivity, v, p, H, Cp and k, respectively, and of the inside diameter of the pipe, d. For recurring set, the variables d, u, k, and p. It found by experiment that, when the flow is turbulent, increasing the flowrate by a factor of 2 always results in a 60 percent increase in the coefficient. How would a 50 percent increase in density of the fluid be expected to affect coefficient, all other variables remaining constant?
- 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+C3y? Answer: The boundary conditions are: du .. u = 0 at y = 0 ; u = u, ; at y = 6 ; = 0 at y = 8 dy и y y This gives: 2.Mass flow rate of hot fluid is 0.007 kg/s. Convection heat transfer coefficient of hot fluid stream is 1000 W/m?.°C. Thermophysical properties are given as follows. Hot fluid; c, = 5000 J/kg.°C Water; dynamic viscosity, µ = 0.001 Pa.s; Prandti number, Pr = 6.14; thermal conductivity, k = 0.607 W/m.°C; density, p = 1000 kg/m³; specific heat c, = 4200 J/kg.°C. Neglecting conduction resistance of the pipe, calculate heat exchanger effectiveness (ɛ), heat transfer rate (Q in J/s), outlet temperatures of the hot fluid (Thout) and water (Tw.out) for varying mass flow rate values of water provided below. Mass flow rate of water, m (kg/s) 0.0025 0.01 0.025 0.05 0.075 0.1 Plot heat exchanger effectiveness (ɛ), heat transfer rate (Q in J/s), outlet temperatures of the hot fluid (Thout) and water (Tw.out) as a function of water mass flow rate (m .). Comment on the results. Hot fluid in (65 °C) Water Water in (25 °C) out d = 0.5 cm Hot fluid out L= 5 mHot water (cp=4.18 kJ/kg.K, m = 2.8 kg/min) flows inside a tube (inner diameter = 9 mm, Length = 93 cm, thickness = 1.0 mm, k outer surface is 204 kW/m .What is the temperature drop of water ( C)? 40 W/m.K), if the heat flux on the tube %3D tube
- Mass flow rate of hot fluid is 0.007 kg/s. Convection heat transfer coefficient of hot fluid stream is 1000 W/m?.°C. Thermophysical properties are given as follows. Hot fluid; c, = 5000 J/kg.°C Water; dynamic viscosity, u = 0.001 Pa.s; Prandti number, Pr = 6.14; thermal conductivity, k = 0.607 W/m.°C; density, p = 1000 kg/m?; specific heat c, = 4200 J/kg.°C. Neglecting conduction resistance of the pipe, calculate heat exchanger effectiveness (ɛ), heat transfer rate (Q in J/s), outlet temperatures of the hot fluid (Th,out) and water (Tw,out) for varying mass flow rate values of water provided below. Mass flow rate of water, m„ (kg/s) 0.0025 0.01 0.025 0.05 0.075 0.1 Plot heat exchanger effectiveness (8), heat transfer rate (Q in Jis), outlet temperatures of the hot fluid (Th,out) and water (Tw,.cut) as a function of water mass flow rate (m„.). Comment on the results. Hot fluid in (65 °C) Water Water in (25 °C) out d = 0.5 cm Hot fluid out L= 5 mMass flow rate of hot fluid is 0.007 kg/s. Convection heat transfer coefficient of hot fluid stream is 1000 W/m? °C. Thermophysical properties are given as follows. Hot fluid; c, = 5000 J/kg.°C Water; dynamic viscosity, u = 0.001 Pa.s; Prandtl number, Pr = 6.14; thermal conductivity, k = 0.607 W/m.°C; density, p = 1000 kg/m2; specific heat c, = 4200 J/kg.°C. Neglecting conduction resistance of the pipe, calculate heat exchanger effectiveness (ɛ), heat transfer rate (Q in J/s), outlet temperatures of the hot fluid (Th,out) and water (Tw.out) for varying mass flow rate values of water provided below. Mass flow rate of water, m (kg/s) 0.0025 0.01 0.025 0.05 0.075 0.1 Plot heat exchanger effectiveness (:), heat transfer rate (Q in J/s), outlet temperatures of the hot fluid (Thout) and water (Tw.out) as a function of water mass flow rate (m). Comment on the results. Hot fluid in (65 °C) Water Water in (25 °C) out d = 0.5 cm Hot fluid out L = 5 mIntroduction 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…