Unsteady free convection of second‐grade nanofluid with a new time‐space fractional heat conduction

Heat Transfer ◽  
2019 ◽  
Vol 49 (2) ◽  
pp. 709-725 ◽  
Author(s):  
Ming Shen ◽  
Yuhang Wu ◽  
Hui Chen
Keyword(s):  
Heat Conduction ◽  
Free Convection ◽  
Second Grade ◽  
Time Space ◽  
Fractional Heat Conduction ◽  
New Time

scholarly journals An analytical solution to the problem of time-fractional heat conduction in a composite sphere

2017 ◽  
Vol 65 (2) ◽  
pp. 179-186 ◽  
Author(s):  
S. Kukla ◽  
U. Siedlecka
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Thermal Contact ◽  
Time Derivative ◽  
Solid Sphere ◽  
Composite Sphere ◽  
Problem Of Time ◽  
Time Space ◽  
Fractional Heat Conduction

Abstract An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.

MINERAL DEPOSITS OF THE MIDCONTINENT RIFT SYSTEM - A NEW TIME/SPACE CLASSIFICATION

2018 ◽  
Author(s):  
Laurel G. Woodruff ◽  
◽  
Suzanne W. Nicholson ◽  
Connie L. Dicken ◽  
Klaus J. Schulz
Keyword(s):  
Mineral Deposits ◽  
Rift System ◽  
Midcontinent Rift ◽  
System A ◽  
Time Space ◽  
Midcontinent Rift System ◽  
New Time

scholarly journals An analysis of heat conduction in polar bear hairs using one-dimensional fractional model

2016 ◽  
Vol 20 (3) ◽  
pp. 785-788 ◽  
Author(s):  
Wei-Hong Zhu ◽  
Shao-Tang Zhang ◽  
Zheng-Biao Li
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Polar Bear ◽  
Thermal Protection ◽  
Polar Bears ◽  
Cold Environment ◽  
Membrane Pore ◽  
One Dimensional ◽  
Fractional Heat Conduction ◽  
Maintain Body Temperature

Hairs of a polar bear are of superior properties such as the excellent thermal protection. The polar bears can perennially live in an extremely cold environment and can maintain body temperature at around 37 ?C. Why do polar bears can resist such cold environment? Its membrane-pore structure plays an important role. In the previous work, we established a 1-D fractional heat conduction equation to reveal the hidden mechanism for the hairs. In this paper, we further discuss solutions and parameters of the equation established and analyze heat conduction in polar bear hairs.

Second Grade Fluid for Rotating MHD of an Unsteady Free Convection Flow in a Porous Medium

2015 ◽  
Vol 362 ◽  
pp. 100-107 ◽  
Author(s):  
Z. Ismail ◽  
I. Khan ◽  
A.Q. Mohamad ◽  
S. Shafie
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Initial Conditions ◽  
Boussinesq Approximation ◽  
Second Grade ◽  
Convection Flow ◽  
Inclined Plate ◽  
Free Convection Flow ◽  
Transform Method ◽  
The Laplace Transform

Rotating effects and magnetohydrodynamic (MHD) free convection flow of second grade fluids in a porous medium is considered in this paper. It is assumed that the bounding infinite inclined plate has ramped wall temperature with the presence of heat and mass diffusion. Based on Boussinesq approximation, the analytical expressions for dimensionless velocity, temperature and concentration are obtained by using the Laplace transform method. All the derived solutions satisfying the involved differential equations with imposed boundary and initial conditions. The influence of various parameters on the velocity has been analyzed in graphs and discussed.

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