Abstract
Nonlinear transient thermal analysis of a convective-radiative fin with functionally graded materials (FGMs) under the influence of magnetic field is presented in this study. The developed nonlinear thermal models of linear, quadratic, and exponential variation of thermal conductivity are solved approximately and analytically using the differential transformation method (DTM). In order to verify the accuracies of the nonlinear solutions, exact analytical solutions are also developed with the aids of Bessel, Legendre, and modified Bessel functions. Good agreements are established between the exact and the approximate analytical solutions. In the parametric studies, effects of heat enhancement capacity of fin with functionally graded material as compared to fin with homogeneous material are investigated. Also, influence of the Lorentz force and radiative heat transfer on the thermal performance of the fin are analyzed. From the results, it is shown that increase in radiative and magnetic field parameters as well as the in-homogeneity index improve the thermal performance of the fin. Also, the transient responses reveal that the FGM fin with quadratic-law and exponential-law function shows the slowest and fasted thermal responses, respectively. This study will provide a very good platform for the design and optimization of an improved heat transfer enhancement in thermal systems, where the surrounding fluid is influenced by a magnetic field.
Highlights
Nonlinear transient thermal analysis of a convective-radiative fin with functionally graded materials (FGMs) under the influence of magnetic field is presented in this study. e developed nonlinear thermal models of linear, quadratic, and exponential variation of thermal conductivity are solved approximately and analytically using the differential transformation method (DTM)
The transient responses reveal that the FGM fin with quadratic-law and exponential-law function shows the slowest and fasted thermal responses, respectively. is study will provide a very good platform for the design and optimization of an improved heat transfer enhancement in thermal systems, where the surrounding fluid is influenced by a magnetic field
Heat sinks are heat exchangers used in dissipating heat from functional thermal systems to the environment to ensure whether the device operates within safe temperature limits. e wide range of applications of heat sinks in cooling different electronic and micro electronics components such as the central processing unit (CPU), high-power semiconductor devices, highpower lasers, light-emitting diodes (LEDs), and sensitive devices affirm its effectiveness as a passive mode of cooling of thermal systems. e improvement of the thermal performance of heat sink and energy saving in the thermal system is timely owing to miniaturization in size of thermal systems, acoustic control due to its destructive effects, and energy saving using smaller fan size
Summary
Consider a heat sink made of FGM having length b and thickness t exposed on both faces to a convective-radiative environment at temperature T∞ as shown in Figure 1, assuming the fin medium is homogeneous, isotropic, and saturated with a single-phase fluid. Consider a heat sink made of FGM having length b and thickness t exposed on both faces to a convective-radiative environment at temperature T∞ as shown, assuming the fin medium is homogeneous, isotropic, and saturated with a single-phase fluid. Cases of linear, quadratic, and exponential variation of thermal conductivity with the fin length will be considered. Linear variation of thermal conductivity with the fin length: k(x) k0 1 + clx. Quadratic variation of thermal conductivity with the fin length: k(x) k01 + cqx2. Exponential variation of thermal conductivity with the fin length: k(x) k0ecix. For an intermediate and moderate heat transfer or enhancement process, linear thermal conductivity variation will be useful. Exponential variation of thermal conductivity with the fin length: ecixz2T zx. In order to nondimensionalize the developed governing equations, the following dimensionless parameters are used in equations (9)–(11): x.
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