# I need help on number3 lelmperaturein the luid as a function of r, the distance from...

###### Question: i need help on number3

lelmperaturein the luid as a function of r, the distance from the descne t re? What are the boundary conditions? The thermal conductivity k of the fluid is considered center of the sphe constant. The temperature of the sphere constant at Ta boundary is constant at Tr. and the temperature far from the fluid is (b) Determine the temperature profile in the fluid. (c) From the temperature profile, obtain an expression for the heat flux at the surface. From this flux, deter mine the Nusselt number. (30 points) in a counter-current flow heat exchanger, the hot stream is cooled from 120 to 40°C while the cold strean temperature cha be the percent increase or decrease in heat transfer rate? nges from 30 to 60°C. If the same heat exchanger were operated with co-current flow, what would 3. (30 points) Let us consider an unsteady state heat conduction in a sphere of radius R. Initially the temperature distri bution within the sphere is uniform at To (T-T ). After time t = 0, the sphere surface temperature is changed t 0 (7-0). The thermal diffusivity of the sphere material is α. (a) What is the equation to find out the temperature distribution T(r,l) within the sphere? (b) What are the initial and boundary conditions? (c) The equation obtained in (a) is not easy to solve directly. So, put T(r,t)-Y(r,t)/r and derive a new equation on Y together with the boundary and initial conditions of (d) Solve the new equation to obtain T(r,t) 4. (40 points) Let us consider three parallel planes. The distance between two adjacent surfaces is 0.1m. Between t adjacent surfaces, air is filled. The bottom surface (S1) is maintained at 350K while the top surface (S3) is maintained at 300K. What is the temperature of the middle surface (S2)? Here all the surfaces are gray bodies of emissivity 0.5. Also assume that S2 is very thin and the conductivity of the material is very large so that the temperatures of the both sides of S2 are the same

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