Suppose that a finite-difference solution has been obtained for the temperature T, near but not at an adiabatic boundary. in most instances, it would be necessary or desirable to evaluate the temperature at the boundary point itself. for this case of an adiabatic boundary, develop an expression for the temperature at the boundary T1, in the terms of temperatures at neighbouring points T2, T3, etc, by assuming that the temperature distribution in the neighbourhood of the boundary isa straight linea second-degree polynomiala cubic polynomial (you only need to indicate how you would derive this one)indicate the order of T.E in each of the above approximations used to evaluate T1 Ay-CONSTANTT2ADIABATIC BOUNDARYFigure P3.13.17 Suppose that a finite-difference solution has been obtained for the temperature T, near but notat an adiabatic boundary (i.e., aT/ay = 0 at the boundary) (Fig. P3.1). In most instances, it wouldbe necessary or desirable to evaluate the temperature at the boundary point itself. For this case ofan adiabatic boundary, develop expressions for the temperature at the boundary Ti, in terms oftemperatures at neighboring points T2, T, etc., by assuming that the temperature distribution in theneighborhood of the boundary is(a) a straight line(b) a second-degree polynomial(c) a cubic polynomial (you only need to indicate how you would derive this one).Indicate the order of the T.E. in each of the above approximations used to evaluate T,.

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Suppose that a finite-difference solution has been obtained for the temperature T, near but not at an adiabatic boundary. in most instances, it would be necessary or desirable to evaluate the temperature at the boundary point itself. for this case of an adiabatic boundary, develop an expression for the temperature at the boundary T₁, in the terms of temperatures at neighbouring points T_2, T₃, etc, by assuming that the temperature distribution in the neighbourhood of the boundary is

a straight line
a second-degree polynomial
a cubic polynomial (you only need to indicate how you would derive this one)

indicate the order of T.E in each of the above approximations used to evaluate T₁

Ay-CONSTANT
T2
ADIABATIC BOUNDARY
Figure P3.1
3.17 Suppose that a finite-difference solution has been obtained for the temperature T, near but not
at an adiabatic boundary (i.e., aT/ay = 0 at the boundary) (Fig. P3.1). In most instances, it would
be necessary or desirable to evaluate the temperature at the boundary point itself. For this case of
an adiabatic boundary, develop expressions for the temperature at the boundary Ti, in terms of
temperatures at neighboring points T2, T, etc., by assuming that the temperature distribution in the
neighborhood of the boundary is
(a) a straight line
(b) a second-degree polynomial
(c) a cubic polynomial (you only need to indicate how you would derive this one).
Indicate the order of the T.E. in each of the above approximations used to evaluate T,.

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