PROBLEM 4.40
KNOWN: Nodal point on boundary between two materials. FIND: Finite-difference equation for steady-state conditions. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant properties, (4) No internal

PROBLEM 4.53
KNOWN: Volumetric heat generation in a rectangular rod of uniform surface temperature.
FIND: (a) Temperature distribution in the rod, and (b) With boundary conditions unchanged, heat
generation rate causing the midpoint temperature to reach 6

PROBLEM 4.54 KNOWN: Flue of square cross section with prescribed geometry, thermal conductivity and inner and outer surface temperatures. FIND: Heat loss per unit length from the flue, q. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state, two-dimensional conductio

PROBLEM 4.55
KNOWN: Flue of square cross section with prescribed geometry, thermal conductivity and inner and outer surface convective conditions. FIND: (a) Heat loss per unit length, q , by convection to the air, (b) Effect of grid spacing and convection

PROBLEM 4.56
KNOWN: Rectangular air ducts having surfaces at 80C in a concrete slab with an insulated bottom and upper surface maintained at 30C. FIND: Heat rate from each duct per unit length of duct, q. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state condition

PROBLEM 4.57
KNOWN: Dimensions and operating conditions for a gas turbine blade with embedded channels. FIND: Effect of applying a zirconia, thermal barrier coating. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant proper

PROBLEM 4.58 KNOWN: Bar of rectangular cross-section subjected to prescribed boundary conditions. FIND: Using a numerical technique with a grid spacing of 0.1m, determine the temperature distribution and the heat transfer rate from the bar to the fluid. S

PROBLEM 4.60
KNOWN: Rectangular plate subjected to uniform temperature boundaries. FIND: Temperature at the midpoint using a finite-difference method with space increment of 0.25m SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional co

PROBLEM 4.59
KNOWN: Upper surface and grooves of a plate are maintained at a uniform temperature T1, while the lower surface is maintained at T2 or is exposed to a fluid at T. FIND: (a) Heat rate per width of groove spacing (w) for isothermal top and bott

PROBLEM 4.62
KNOWN: Edge of adjoining walls (k = 1 W/mK) represented by symmetrical element bounded by the diagonal symmetry adiabat and a section of the wall thickness over which the temperature distribution is assumed to be linear. FIND: (a) Temperature

PROBLEM 4.64
KNOWN: Straight fin of uniform cross section with prescribed thermal conditions and geometry; tip condition allows for convection. FIND: (a) Calculate the fin heat rate, q , and tip temperature, TL , assuming one-dimensional heat f transfer i

PROBLEM 4.52
KNOWN: Long bar of square cross section, three sides of which are maintained at a constant temperature while the fourth side is subjected to a convection process. FIND: (a) The mid-point temperature and heat transfer rate between the bar and

PROBLEM 4.51
KNOWN: Square shape subjected to uniform surface temperature conditions.
FIND: (a) Temperature at the four specified nodes; estimate the midpoint temperature To, (b) Reducing
the mesh size by a factor of 2, determine the corresponding nodal t

PROBLEM 4.50
KNOWN: Long rectangular bar having one boundary exposed to a convection process (T, h) while the other boundaries are maintained at a constant temperature (Ts). FIND: (a) Using a grid spacing of 30 mm and the Gauss-Seidel method, determine th

PROBLEM 4.39
KNOWN: Nodal point configurations corresponding to a diagonal surface boundary subjected to a convection process and to the tip of a machine tool subjected to constant heat flux and convection cooling. FIND: Finite-difference equations for th

PROBLEM 4.41 KNOWN: Two-dimensional grid for a system with no internal volumetric generation. FIND: Expression for heat rate per unit length normal to page crossing the isothermal boundary. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dime

PROBLEM 4.43
KNOWN: Two-dimensional network with prescribed nodal temperatures and thermal conductivity of the material. FIND: Heat rate per unit length normal to page, q. SCHEMATIC: Node 1 2 3 4 5 6 7 Ti(C) 120.55 120.64 121.29 123.89 134.57 150.49 147.1

PROBLEM 4.42
KNOWN: One-dimensional fin of uniform cross section insulated at one end with prescribed base temperature, convection process on surface, and thermal conductivity. FIND: Finite-difference equation for these nodes: (a) Interior node, m and (b)

PROBLEM 4.44
KNOWN: Nodal temperatures from a steady-state, finite-difference analysis for a one-eighth symmetrical section of a square channel. FIND: (a) Beginning with properly defined control volumes, derive the finite-difference equations for nodes 2,

PROBLEM 4.45
KNOWN: Steady-state temperatures (K) at three nodes of a long rectangular bar. FIND: (a) Temperatures at remaining nodes and (b) heat transfer per unit length from the bar using nodal temperatures; compare with result calculated using knowled

PROBLEM 4.47
KNOWN: Outer surface temperature, inner convection conditions, dimensions and thermal conductivity of a heat sink. FIND: Nodal temperatures and heat rate per unit length. SCHEMATIC:
20
ASSUMPTIONS: (1) Steady-state, (2) Two-dimensional conduc

PROBLEM 4.48
KNOWN: Steady-state temperatures (C) associated with selected nodal points in a two-dimensional system. FIND: (a) Temperatures at nodes 1, 2 and 3, (b) Heat transfer rate per unit thickness from the system surface to the fluid. SCHEMATIC:
ASS

PROBLEM 4.49
KNOWN: Nodal temperatures from a steady-state finite-difference analysis for a cylindrical fin of prescribed diameter, thermal conductivity and convection conditions ( T , h). FIND: (a) The fin heat rate, qf, and (b) Temperature at node 3, T3

PROBLEM 4.46
KNOWN: Steady-state temperatures at selected nodal points of the symmetrical section of a flow channel with uniform internal volumetric generation of heat. Inner and outer surfaces of channel experience convection. FIND: (a) Temperatures at n

PROBLEM 4.65
KNOWN: Long rectangular bar having one boundary exposed to a convection process (T, h) while the other boundaries are maintained at constant temperature Ts. FIND: Using the finite-element method of FEHT, (a) Determine the temperature distribu

PROBLEM 4.61
KNOWN: Long bar with trapezoidal shape, uniform temperatures on two surfaces, and two insulated surfaces. FIND: Heat transfer rate per unit length using finite-difference method with space increment of 10mm. SCHEMATIC:
ASSUMPTIONS: (1) Steady

PROBLEM 4.66
KNOWN: Log rod of rectangular cross-section of Problem 4.53 that experiences uniform heat generation while its surfaces are maintained at a fixed temperature. Use the finite-element software FEHT as your analysis tool. FIND: (a) Represent the

PROBLEM 4.81
KNOWN: Upper surface of a platen heated by hot fluid through the flow channels is used to heat a process fluid. FIND: (a) The maximum allowable spacing, W, between channel centerlines that will provide a uniform temperature requirement of 5C

PROBLEM 4.80
KNOWN: Plane composite wall with exposed surfaces maintained at fixed temperatures. Material A has temperature-dependent thermal conductivity. FIND: Heat flux through the wall (a) assuming a uniform thermal conductivity in material A evaluate

PROBLEM 4.82
KNOWN: Silicon chip mounted in a dielectric substrate. One surface of system is convectively cooled, while the remaining surfaces are well insulated. See Problem 4.75. Use the finite-element software FEHT as your analysis tool. FIND: (a) The