1. Find T(x,t) for a case of transient one dimensional heat transfer with T=0 at both ends for all time and an initial temperature distribution given by f(x) = -4x²+8x³-5x²+x. Assume a dimensionless length scale with ends at 0 and 1 and α = 2 1/sec. Plot the initial temperature distribution and the temperature distribution at 5 seconds.
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- Q.5/ Find the temperature distribution for the following heat problem in dimensionless variables; Uxx - 2ut = 0 0 0 ux (0, t) = 0, u(1, t) = 0 and u(x,0) = x when 0 < x <11. Consider heat transfer from a circular cylinder whose axis is normal to a forced flow and which is rotating at an angular velocity, w. If the surface of the cylinder is maintained at a uniform temperature, find the dimensionless parameters on which the Nusselt number depends on.The Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…
- The Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…The Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…One model of the glomerular membrane is a microporous membrane in which right cylindrical porespenetrate all the way through the membrane. Assume that the pores have a length of 50 nm and aradius of 3.5 nm. The viscosity of plasma is 0.002 Pa s. The average hydrostatic pressure in theglomerulus is 60 mm Hg, hydrostatic pressure in Bowman’s space is 20 mm Hg and the averageoncotic pressure of glomerular capillary blood is 28 mm Hg.A. Calculate the flow through a single pore assuming laminar flow (use the Poiseuille flowequation).B. How many pores would there have to be to produce a normal GFR?C. If the total aggregate area of the kidneys for filtration is 1.5 m2, what is the density of thepores (number of pores per unit area)D. What fraction of the area is present as pores?
- For the following water liquid level system, 9mi(t) is the mass flow rate input deviation to the system and the restrictions can be considered linear resistances about the equilibrium: 9mi h2 Ro R1 a) Using basic fluids principles, develop the Dynamic Equations for the deviation of the two liquid level heights from their equilibrium height as a function of the input mass flow rate, Imi-Submit correct and complete solutions. give propriate Explanation. Provide step-by-step detailed explanations.Solve this whole problem and include the interpolation of the same table.
- 3.1 Two-dimensional incompressible flow can also be simulated using the vorticity w and streamfunction , instead of using the velocity and pressure variables. The vorticity field can be related to the velocity variables through the curl operation Əv ди Əx ду and the velocity field (u, v) can be related to the streamfunction with მს ду 11== v== Using the continuity equation, show that 2² 2² + əx² Əy² მს əx =-w. (3.252) (3.253)Hab. Tiruneh, [4/2/2023 1:23 AM]A solar flux q ^ * falls on a unit length of a very thin tube of diameter d. Inside the tube is a stationary water with initial temperature T_{i} (same as ambient and no gradient inside at any time) and absorbs some of the heat while the rest leaves by convection from the surface to the ambient at T_{m} Develop an equation that can help to determine the temperature of the water at any time. Plot the temperature of the water against time. For a long elapsed time what will be the temperature? To simplify the analysis use theta = T*T_{e} * d*theta = dT theta_{i} = T_{i}*T_{o} (initial condition. Hab. Tiruneh, [4/2/2023 11:53 AM]A flat wall is exposed to an environmental temperature of 38°C. The wall is covered with a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4W / (m ^2 *` C and the temperature of the wall on the inside of the insulation is 315°C. The wall loses heat to the environment by convection. Compute the value of the convection…4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of time. Assume that air resistance is proportional to the instantaneous velocity, with a constant of proportionality k > 0 (this is called the drag coefficient). Take the downward direction to be positive. (b) Solve the differential equation subject to the initial condition v(t = 0) = vo. (c) Determine the terminal velocity of the mass.

