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 4.60
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 4.4 KNOWN: Rectangular plate subjected to prescribed boundary conditions. FIND: Steady-state temperature distribution. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state, 2-D conduction, (2) Constant properties. ANALYSIS: The solution follows the method of
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 4.5
KNOWN: Boundary conditions on four sides of a rectangular plate. FIND: Temperature distribution. SCHEMATIC:
y
q s
W
T1
T1
0 0 T1 L
x
ASSUMPTIONS: (1) Two-dimensional, steady-state conduction, (2) Constant properties. ANALYSIS: This problem dif
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 4.14
KNOWN: Tube embedded in the center plane of a concrete slab. FIND: The shape factor and heat transfer rate per unit length using the appropriate tabulated relation, SCHEMATIC:
ASSUMPTIONS: (1) Two-dimensional conduction, (2) Steady-state cond
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 4.15 KNOWN: Dimensions and boundary temperatures of a steam pipe embedded in a concrete casing. FIND: Heat loss per unit length. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Negligible steam side convection resistance, pipe wall resist
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 4.16
KNOWN: Thin-walled copper tube enclosed by an eccentric cylindrical shell; intervening space filled with insulation. FIND: Heat loss per unit length of tube; compare result with that of a concentric tube-shell arrangement. SCHEMATIC:
ASSUMPTI
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 4.3
KNOWN: Temperature distribution in the two-dimensional rectangular plate of Problem 4.2. FIND: Expression for the heat rate per unit thickness from the lower surface (0 x 2, 0) and result based on first five non-zero terms of the infinite seri
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 4.48
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 4.50
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 4.52
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 4.54 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 4.1
KNOWN: Method of separation of variables for two-dimensional, steady-state conduction. FIND: Show that negative or zero values of 2, the separation constant, result in solutions which cannot satisfy the boundary conditions. SCHEMATIC:
ASSUMPTI
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 4.2
KNOWN: Two-dimensional rectangular plate subjected to prescribed uniform temperature boundary conditions. FIND: Temperature at the mid-point using the exact solution considering the first five non-zero terms; assess error resulting from using
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 4.51
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 4.67
KNOWN: Symmetrical section of a flow channel with prescribed values of q and k, as well as the surface convection conditions. See Problem 4.46. . FIND: Using the finite-element method of FEHT, (a) Determine the temperature distribution and pl
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 4.81
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 4.82
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