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.

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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter6: Forced Convection Over Exterior Surfaces

Section: Chapter Questions

Problem 6.32P

See similar textbooks

Similar questions

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 <1
1. 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.
You have a 1-D steady-state conduction problem, constant thermal properties, with energy generation q_dot. The material is 4.0 cm thick and has a constant thermal conductivity of k = 65.0 (W/m-k). The temperature distribution within the object is: T(x) = a + bx^2 a = 100 Celcius b = -1000 Celcius/m^2 Starting with the Heat Diffusion Equation and using the data given above, determine the following: • Determine the heat generation rate q_dot within the wall. • Determine the heat flux q" at x=0 and at x=L.
The Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 00 0 -2.80 0 0 Is the system?: a. unstable b. C. not unstable x+ 6.15 0 0 0 0 3.04 0 0.052 not asymptotically stable d. asymptotically stable -1 u y = 0 0 0 0 -7.3 0 0 -25.0 X
i need help with all parts in this question
Q2 Consider a conical receiver shown in Figure 2. The inlet and outlet liquid volumetric flow rates are Fl and F2, respectiveily. ccorresponding radius in r) Figure 2 Conicul tank Develop the model equation with necessary assumption(s) with respect to the liquid height h. ii. What type of mathematical model is this? 1 R %3D Hint: Model: = F, – Fz, where the volume V=r h=nh, since = substitute V and Fz expressions and get the final form. %3D %3D %3D dt H.
hey can i get help with these two questions please. thank you.
I need answer within 20 minutes please please with my best wishes
34 Need A, B, C
Please don't provide handwritten solution ....
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…