1. Consider a square plate of side a and assume that the plate is so thin that the temperature gradient in the thickness direction is negligible compared to the lateral temperature gradients. The temperature on the lateral surfaces is T, and convective heat transfer boundary condition applies on the front and the back surfaces. Thickness of the plate is t. Assume that the material properties are constant. (a) Starting from the basic principles obtain the governing differential equation for the time- dependent temperature field in the plate assuming that there is internal energy generation at a uniform rate ġ per unit volume. (b) Determine the steady-state temperature distribution in the plate. (c) Find the steady-state temperature distribution T(x, z) in the plate by applying a finite- difference method. Assume T, = 400 K, T. = 200 K, h= 100 W/m²K, k = 200 W/mK, t = 0.01 m, a = 1 m and ġ = 1 W/m³. (d) Compare the numerical results with the analytical solution of the problem. Find the error of the numerical approach. Lateral surfaces a a y `Lateral surfaces

1. Consider a square plate of side a and assume that the plate is so thin that the temperature gradient in the thickness direction is negligible compared to the lateral temperature gradients. The temperature on the lateral surfaces is T, and convective heat transfer boundary condition applies on the front and the back surfaces. Thickness of the plate is t. Assume that the material properties are constant. (a) Starting from the basic principles obtain the governing differential equation for the time- dependent temperature field in the plate assuming that there is internal energy generation at a uniform rate ġ per unit volume. (b) Determine the steady-state temperature distribution in the plate. (c) Find the steady-state temperature distribution T(x, z) in the plate by applying a finite- difference method. Assume T, = 400 K, T. = 200 K, h= 100 W/m²K, k = 200 W/mK, t = 0.01 m, a = 1 m and ġ = 1 W/m³. (d) Compare the numerical results with the analytical solution of the problem. Find the error of the numerical approach. Lateral surfaces a a y `Lateral surfaces

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.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.54P

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